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Training Guide

Version 7

RGA 7 Training Guide Part Identification: RG7-TG-01 ReliaSoft Corporation Worldwide Headquarters 1450 South Eastside Loop Tucson, Arizona 85710-6703, USA Telephone: 1.520.886.0410 Fax: +1.520.886.0399 Sales and Information: 1.888.886.0410 (Toll-free in the U.S. and Canada) [email protected] http://www.ReliaSoft.com © 2004-2010 ReliaSoft Corporation, ALL RIGHTS RESERVED. Notice of Rights No part of this document may be reproduced or transmitted, in any form or by any means, for any purpose, without the express written permission of ReliaSoft Corporation, Tucson, AZ, USA. Disclaimer Information in this document is subject to change without notice and does not represent a commitment on the part of ReliaSoft Corporation. Companies, names and data used herein are fictitious unless otherwise noted. Use of the software and this document are subject to the terms and conditions set forth in the accompanying License Agreement. This software and documentation were developed at private expense; no portion was developed with government funds. Trademarks ReliaSoft, RGA, Weibull, ALTA, BlockSim and XFRACAS are trademarks of ReliaSoft Corporation. Product names and services identified in this document are trademarks of their respective trademark holders, and are used for illustration purposes. Their use in no way conveys endorsement or other affiliation with ReliaSoft Corporation. 10 9 8 7 6 5 4 3

RGA 7 Training Guide

1.1 About this Training Guide

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This training guide is intended to provide you with many examples of how to use ReliaSoft's RGA software. It begins with step-by-step examples and then proceeds into more advanced examples and questions.

1.2 Other Example Files

In addition to the examples described in this training guide, ReliaSoft provides a large array of example files to demonstrate various types of analyses and product features. These files are located in the "Examples" folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Examples). The Examples folder is also accessible by clicking the Open Examples Folder link in the initial startup window or by choosing Help > Open Examples Folder.

1.3 RGA Documentation

Like all of ReliaSoft's standard software products, RGA is shipped with detailed printed documentation. For RGA 7, this includes documentation on the product interface (RGA 7 User's Guide) and documentation on the underlying principles and theory (ReliaSoft's Reliability Growth and Repairable System Data Analysis Reference). This training guide is intended to be a supplement to those references.

1.4 Minimum System Requirements

RGA 7 is compiled and designed for Microsoft Windows XP and Vista and takes advantage of the features available in these platforms. Minimum system requirements:

Windows XP or Vista. Intel Celeron or Pentium class or AMD processor with 256 MB of RAM (512 MB or more is recommended), SVGA display and at least 125 MB of hard disk space.

Please note that if you have set your computer to use large fonts, you will need to set your screen display to 1024x768 in order for all windows to display correctly.

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1.5 Contacting ReliaSoft

ReliaSoft can be reached at: ReliaSoft Corporation Worldwide Headquarters 1450 S. Eastside Loop Tucson, AZ 85710-6703 USA Phone: +1.520.886.0410 Toll-free in the U.S. and Canada: +1.888.886.0410 Fax: +1.520.886.0399 E-mail: [email protected] For up-to-date product information, visit our Web site at: http://RGA.ReliaSoft.com For assistance, you may contact out Worldwide Headquarters in Tucson, Arizona, or go to http://Directory.ReliaSoft.com to locate the office nearest you.

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Features Summary

This chapter is intended to give you a general overview of the software package.

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2.1 New Features and Enhancements

The new features and enhancements in RGA 7 offer more realistic and powerful reliability growth and fielded system data analysis capabilities than ever before.

Multi-Phase Data: Using a new methodology developed by Dr. Larry Crow, RGA 7's multi-phase data types accommodate data sets from practical testing situations where failures can be corrected at the time of failure, delayed until a later time during the current phase, fixed during another phase or fixed at the end of a phase. These data types allow for data to be recorded across multiple test phases and analyzed using the Crow Extended - Continuous Evaluation model. Growth Planning: Growth Planning Folios help you to determine necessary test time by providing projected growth curves across multiple test phases, based on initial and/or goal MTBFs, discovery rate, effectiveness factors, etc. MultiPhase Plots allow you to plot data from multiple test phases together, along with data from a Growth Planning Folio, if desired. Mission Profiles: Mission Profiles can help you to ensure that your testing is representative of the expected conditions of actual use by checking, at defined points, whether expected testing usage and actual testing usage are acceptably close. Design of Reliability Tests for Repairable Systems: Based on a non-homogeneous Poisson process, RGA's new Design of Reliability Tests utility allows you to design reliability demonstration tests for repairable systems. Monte Carlo Data Simulation and SimuMatic: The Monte Carlo Data simulation utility allows you to randomly generate times-to-failure data based on a selected data type. The SimuMatic utility expands on this capability by allowing you to automatically perform specified analyses on a large number of simulated data sets. This can help you to a) better understand reliability growth and repairable system analysis concepts, b) experiment with the influences of sample sizes and data types on analysis methods, c) construct simulation-based confidence bounds, d) better understand the concepts behind confidence bounds and e) design reliability tests. Template-Based Report Generation allows you to create and format reports with ease, using the same powerful tools and functions available in General Spreadsheets. Save your reports as templates for reuse, or use one of the templates included with the software.

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2 Features Summary

2.2 A Complete Set of Tools for Reliability Growth Analysis

There are many different ways that reliability growth data might be collected so the RGA software provides a comprehensive set of options for data entry and analysis.

2.2.1 Support for Traditional Reliability Growth Analysis Methods

RGA is designed for use with time-to-failure (continuous), discrete (success/failure) and reliability data, entered individually or in groups. Traditional reliability growth analysis is generally performed on developmental data, which come from in-house testing done during the stages of development for a particular product. Depending on the data/analysis type, Maximum Likelihood Estimation (MLE) or Least Squares are used for parameter estimation. 2.2.1.1 Times-to-Failure Data The most commonly observed type of reliability growth data, times-to-failure data come from developmental testing where the units are operated continuously until failure. For these data types, you can use the Crow-AMSAA (NHPP), Duane or Crow Extended models for data analysis. You will be able to estimate the MTBF, failure intensity or expected number of failures for a given time/stage. You also can determine the amount of testing that will be required to demonstrate a specified MTBF or failure intensity. Data types include:

Failure Times Grouped Failure Times Multiple Systems

Known Operating Times Concurrent Operating Times Multiple Systems with Dates Multiple Systems with Event Codes

2.2.1.2 Discrete Data When you have data from one-shot (pass/fail) reliability growth tests, you can use the Standard Gompertz, Modified Gompertz, Lloyd-Lipow. Logistic, Crow-AMSAA (NHPP) or Duane models for data analysis. The available models will depend on the data type. These include:

Sequential Sequential with Modes Grouped per Configuration Mixed

2.2.1.3 Reliability Data The Reliability data type is used when the reliability of the system is recorded at different times or stages. The reliability can be calculated by dividing the number of units still operating by the total number of units on test or can be computed using life data analysis methods. For these data sets, you can use the Standard Gompertz, Modified Gompertz, Lloyd-Lipow or Logistic models for data analysis. You will be able to estimate the reliability at a specified time/stage or determine the amount of testing that will be required to demonstrate a specified reliability.

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2.2 A Complete Set of Tools for Reliability Growth Analysis

2.2.2 Exclusive Support for the Latest Methods for Reliability Growth Projections, Planning and Management

Traditional reliability growth analysis models allow you to analyze data from tests where the corrective actions are incorporated during the test (test-fix-test). However, in actual practice, fixes may be delayed until after the completion of the test (test-find-test) or you may implement some fixes during the test while delaying others (test-fix-find-test). To better represent these practices, RGA 7 provides full support for the reliability growth test planning/management strategy and data analysis methodology developed by Dr. Larry Crow. These techniques provide useful metrics to support decision-making, including the MTBF demonstrated through testing, the growth in MTBF that will be achieved through implementation of corrective actions and the maximum potential MTBF that can likely be achieved for the product design given the current reliability growth management strategy. The software also provides estimates regarding latent failure modes that have not yet been uncovered through testing. Reliability growth projections analysis can be performed using the Crow Extended model and, new in Version 7, the Crow Extended - Continuous Analysis model for multi-phase data. This new model accommodates the fact that reliability growth testing is often conducted across multiple test phases, allowing you to analyze these phases in a single Folio rather than having to analyze each test phase separately. This also allows you to model more realistically the fixes that are implemented in later test phases instead of directly at the end of the phase when the failure mode occurred. Available multi-phase data types include:

Multi-Phase Failure Times Multi-Phase Grouped Failure Times Multi-Phase Mixed

2.2.3 Fielded Systems Analysis

In addition to its widespread use for reliability growth analysis, the non-homogeneous Poisson process (NHPP) model also can be applied for analyzing the reliability of repairable systems operating in the field. Analysis of fielded system data allows you to get an overview of the system without having the detailed data requirements that would normally be required for system reliability analysis. The available fielded data types are:

Repairable Systems Fleet

You can use the practical methods and models in RGA 7 for reducing the costs to maintain a fleet of repairable systems or major subsystems. The application gives the optimum overhaul schedule in order to have the lowest life cycle cost while maintaining a specified level of reliability. If you have planned improvements to the systems, you can use the Crow Extended model to project how the changes will affect the reliability of the population.

2.2.4 Multiple Systems Analysis

You can use RGA 7 to combine data from multiple individual systems into a single system for analysis purposes. This option is available for developmental testing analysis in cases where you have multiple systems data in which equivalent operating times are not known and for fielded systems analysis using repairable systems or fleet data.

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2 Features Summary

2.2.5 Theory Help

Theory Help is available for each model and data type to help you understand how the models apply to your data. Simply click the Theory Help button next to your selection and a window will appear with information on the principles and theory behind your selection.

2.2.6 Growth Planning

The Growth Planning Folio helps you to understand how reliability growth will proceed, given initial and/or goal MTBFs, your management strategy (the percentage of failures that will be addressed by corrective actions), the effectiveness of corrective actions, the rate of discovery for new failure modes, etc. Analyze test plans with one or more phases, with or without delayed fixes, to determine results such as the appropriate start time for testing so that reliability growth estimates will be most accurate and the amount of time necessary to reach your goals. You can then generate plots of your results, including detailed representations of the overall growth rate as well as the required reliability values for each testing phase, and how these relate to your overall reliability goals.

2.2.7 Mission Profiles

Mission Profiles provide a way to plan and evaluate developmental and/or operational testing to ensure that it is reflective of the expected field operating conditions. Whether your testing deals with a single task or many, all together or in multiple operating conditions, RGA allows you to specify points in the testing process where expected usage and actual usage must converge for all elements of the test. This helps you to ensure that testing proceeds appropriately, within tolerance bounds that you have set, and creates a balanced test that will generate data suitable for valid analysis with reliability growth models.

2.3 Results and Plots 2.3.1 Quick Calculation Pad

RGA's Quick Calculation Pad (QCP) provides you with a quick and accurate way of gaining access to some of the most frequently requested results from repairable system data analysis. The QCP extracts the parameters and other information from the Folio that you specify. The results provided are based on the type of data and the model used for your analysis. The QCP also provides confidence bounds on results and parameters for applicable analyses.

2.3.2 Unparalleled Plots and Graphs

RGA offers unparalleled plotting and graphics capabilities. With the click of a button, you can create a variety of plots that are specific to the type of analysis you are currently performing. All RGA plots can be saved as Windows metafile (*.wmf) graphics that can be used in other applications. The MultiPlot makes it easy to compare analyses by automatically plotting the results for multiple data sets together in the same plot. The Side-by-Side Plots utility allows you to view (and print) multiple plots for a given data set side-by-side. For example, you may want to show the average failure modes strategy, the discovery rate and the cumulative number of failures for a given analysis together in the same window. Alternatively, you may wish to compare the MTBF vs. Time plots for a given data set when analyzed with different models. Simply select the combination that meets your analysis/ reporting needs. New in Version 7, the MultiPhase Plot allows you to plot data from multiple test phases in a single plot. All phases can be contained in a multi-phase Data Sheet analyzed with the Crow Extended - Continuous Evaluation model, or phases can be contained in separate Data Sheets analyzed with the Crow Extended model. In addition, you can specify intra-phase analysis points, and can also include a Growth Planning Folio in the MultiPhase plot if desired.

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2.4 Additional Tools

You can use RS Draw, ReliaSoft's integrated metafile graphics editor, to edit and annotate the plots generated by RGA. This utility allows you to insert text, highlight a point or line, mark the coordinates of a point, and much more.

2.4 Additional Tools 2.4.1 Statistical Tests

RGA 7 provides Chi-Squared and Cramér-von Mises (CVM) methods for goodness-of-fit testing (depending on the data type), as well as the Common Beta Hypothesis (CBH) to indicate whether multiple systems should be combined into an "equivalent" or "superposition" system for analysis. Also available is the Laplace Trend Test, which provides an indication of whether the system's reliability is improving, deteriorating or staying the same. Version 7 also offers the Statistical Test for the Effectiveness of Corrective Actions utility, which allows you to assess whether or not corrective actions have been effective across phases in multi-phase data sets.

2.4.2 General Spreadsheets, Function Wizard and Chart Wizard

A General Spreadsheet, which can be incorporated into any RGA Standard Folio, is used just like an Excel® worksheet to perform your own customized analyses. These spreadsheets provide complete in-cell formula support, cell references, over 200 built-in functions and integration with the Function Wizard and the Chart Wizard. You can use the Function Wizard to insert a wide array of calculated results based on your inputs and, when applicable, a referenced Data Sheet. Available results range from basic math/statistical functions to reliability growth analysis results, and much more. In Version 7, this now works more like Excel functions, with the ability to type functions directly into cells and results that are updated automatically when the inputs change. The Chart Wizard leads you through a step-by-step process to create and configure your own custom charts/plots based on a selected data set.

2.4.3 Template-Based Report Generator

The Report Wizard utility allows you to design print-ready reports to showcase your analyses. The template feature makes it easy to apply the same report format to different analyses. Revised and enhanced in Version 7, this utility now provides an intuitive spreadsheet-based interface for creating and formatting reports.

2.4.4 Monte Carlo Data Simulation and SimuMatic

With the release of Version 7, RGA now provides a Monte Carlo simulation utility that allows you to randomly generate data sets based on the data type and other settings that you specify. The SimuMatic utility expands on this capability by performing specified analyses on a large number of simulated data sets. You may wish to use this tool to experiment with the influences of sample sizes and data types on analysis methods or to help you design reliability tests.

2.5 Simple, Powerful Data Import and Integration with Other Software

Of course, RGA makes it easy to import information from other RGA files. The software also provides a flexible wizard that allows you to "map" the data from an Excel® or delimited text file (*.txt, *.csv, *.prn, *.smc) for import into one of RGA's Folios. In addition, you can save these mappings for later re-use. RGA provides direct integration with ReliaSoft's Weibull++ and XFRACAS software tools.

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2.6 Intuitive, Flexible and Customizable Work Environment

The powerful and flexible interface allows you to keep all related analyses and information together in a single database file. Using the "Project Explorer" approach that is employed in many of ReliaSoft's other applications (e.g. Weibull++, ALTA and BlockSim, among others), RGA provides an intuitive, hierarchical (tree) structure that allows you to view and manage maintain multiple analyses, plots and attachments within a project. RGA's User Setup, Plot Setup and other customization tools allow you to configure the work environment and analysis settings to meet your particular needs. This includes calculation preferences such as displayed math precision, default plot styles, menu options, etc.

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First Steps

3.1 Starting RGA

To start RGA, choose Start > All Programs > ReliaSoft Office > RGA 7.

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3.2 Multiple Document Interface

The Multiple Document Interface (MDI) is the main window and "manager" for RGA. It contains the windows that you will use to enter and analyze your data. The menu and toolbar options available within RGA's MDI will vary depending on the windows that are currently open. In addition, RGA's flexible MDI allows the user to configure the workspace to meet individual needs by hiding or moving the menu bar and toolbars. The next figure displays the MDI and its components so that you can familiarize yourself with the options available within the MDI. Your screen may look slightly different from the one shown next, depending on the windows and tools currently open and on the configuration settings that you have established.

3.3 Getting Help in the RGA Environment

ReliaSoft's RGA includes complete on-line help documentation. This help can be obtained at any time by pressing F1 or by choosing Help > RGA Help.

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3.4 A Quick Overview Example

This example has been designed to familiarize you with RGA's interface and tools. You will:

Create a project. Create a Standard Folio with a Data Sheet for the Failure Times data type. Enter the failure times data into the Data Sheet. Select a model and calculate the parameters. Plot the data. Use the Quick Calculation Pad to calculate the instantaneous MTBF for the product at a given time. Save the project.

At this time, we assume that you have started the application and that you are looking at the Multiple Document Interface (MDI) without any open projects.1 The file for this example is located in the Training Guide folder within the Examples folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Quick Start.rga7."

3.5 Create a New Project with a Standard Folio

The first step is to create a project file (*.rga7) with a Standard Folio. The project contains all the Standard Folios, Additional Plots, Growth Planning Folios, Mission Profiles, Other Tools, Reports and Attachments related to a particular analysis in RGA. For this example, a product is under developmental testing and the failure times are recorded, as shown in the following table. Time to Event 15 25.3 47.5 54 56.4 72.2 99.6 100.3 102.5 112 Time to Event 120.9 125.5 133.4 164.7 177.4 213 244.8 249 250.8 260.1 Time to Event 274.7 285 304 324.5 342 364.6 373 389

Therefore, you will create a Standard Folio with a Data Sheet that will accommodate failure times data.

1. Please note that this example uses the default settings that are shipped with the application. If you have changed any of your settings, click the Reset Application Settings button on the Reset Settings page of the User Setup.

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3.5 Create a New Project with a Standard Folio

Create a new project by clicking Create New in the initial window that may appear at startup, by choosing File > New or by clicking the New icon.

The New Data Sheet Setup window will appear when you create a new project in RGA, allowing you to add a Standard Folio to the project. By default, the Expert view will be displayed, as shown next. You can also click the Wizard View button and answer a series of questions to set the data type.

For this example, the data set contains failure times obtained from developmental testing, so click the Developmental category and Times-to-Failure Data sub-category. Note that the right side of the window displays the available developmental data types. Click the Failure Times option, and then click OK to generate the new Standard Folio with the Data Sheet that you have defined.

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3.6 Enter Data and Calculate the Parameters

The next step is to enter the data, choose a model and calculate the results.

Type the failure times data in the Time to Event column of the Data Sheet, as shown next.

An additional column, Comments, appears in the Data Sheet by default. This column can be used for additional information about your data. The information in this column is not taken into consideration when calculating the parameters.

The next step is to select a model to perform the analysis. On the Main page of the Standard Folio Control Panel, notice that the Crow-AMSAA (NHPP) model is selected by default.

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3.6 Enter Data and Calculate the Parameters

Go to the Analysis page of the Control Panel by clicking the Analysis tab at the bottom of the panel.

Analysis Type indicates the method used for estimating the parameters. For t his example, use the default setting of Maximum Likelihood. Confidence Interval Method displays the method used for calculating the confidence bounds. For t his example, use the default setting of Crow. Note that by default, the Use Defined Gap option is not selected. This option allows you to specify whether or not a gap interval has been specified in the data set. When a gap is defined in the data, the application assumes that the data for that time period is unknown and ignores any entries that have been made for that time period. Under Other Options, note that Input is Cumulative is selected by default. This indicates that the data set is cumulative. For cumulative data, you will enter the time of each failure and for non-cumulative data, you will enter the time between each failure. This determines how the test time is calculated. For example, for the cumulative failure times 10, 20, 30 and 50, the test time would be 50 because the test time accumulates with each failure time. For the non-cumulative failure times 10, 20, 30 and 50, the test time would be 110 because the test time starts over at 0 for each failure time.

Return to the Main page of the Control Panel. The Termination Setting field indicates whether the test was time terminated. Click the [...] button in this field to open the Termination Time window. This window allows you to specify whether the test was time terminated or ended at the time of the last failure. For this example, the test was time terminated at 400 hours.

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Select the Time Terminated option and enter 400 into the input box, as shown next.

Click OK. Notice that the button on the Standard Folio Control Panel now displays the time at which the test was terminated. Now calculate the parameters by choosing Data > Calculate or by clicking the Calculate icon.

The Standard Folio with its parameters calculated is shown next.

The Information area is located above the Results area on the Main page. Notice that the Analysis Type in the upper left corner displays MLE for Maximum Likelihood Estimation. The Information area also displays the data category (Developmental), confidence interval method (Crow), specified gap (No Gap) and whether the data set is cumulative or non-cumulative (Cumulative). The appearance of the Information area will vary depending on the current data type and model. In addition, for some settings (the ones displayed in blue text), you can change the option from the Information area by clicking the box, which cycles through the available settings.

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3.7 Plot the Data

3.7 Plot the Data

The next step is to plot the data from the Data Sheet.

Choose Data > Plot or click the Plot icon.

By default, the Cumulative Number of Failures plot will appear in the Plot Sheet that is added to the Standard Folio, as shown next.

A variety of plot types are available in RGA's Plot Sheet, with the available plot types depending on the current data type and model. For this analysis, the MTBF vs. Time and Failure Intensity vs. Time plots are also available. The Cumulative Number of Failures plot shows the cumulative number of failures plotted against time. The points represent actual failures in the data set and the Expected Failures line represents the projected cumulative number of failures versus time based on the calculated parameters. This plot serves as an empirical goodness-of-fit test for the model used for analysis.

Choose MTBF vs. Time from the Plot Type drop-down list, as shown next, to display another plot.

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The MTBF vs. Time plot appears, as shown next.

The MTBF vs. Time plot shows the mean time between failures plotted against time. The points represent actual failures in the data set.

3.8 Calculate the Instantaneous MTBF

In addition to generating a variety of reliability growth plots, RGA is also capable of calculating standard reliability growth metrics based on the current calculated data set and model.

To calculate the instantaneous MTBF of the product at a specified time, choose Data > Quick Calculation Pad or click the QCP icon.

On the Basic Calculations page of the Quick Calculations Pad (QCP), make the following selections/ inputs:

Options for Calculations: Inst. MTBF Additional Required Information:

Time/Stage: 400 Type: Two-Sided Confidence Level: 0.9

Confidence Bounds:

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3.9 Save the Project

Click Calculate to obtain the results, as shown next.

You can see that the instantaneous MTBF at 400 hours is 14.5146 hours. The upper and lower 90% confidence intervals are also displayed. Click Close to close the Quick Calculation Pad and return to the Data Sheet. Close the Folio.

3.9 Save the Project

Next, you will save the project. To do this, choose File > Save or click the Save icon.

In the Save As window, browse to the desired location for the project, type the name QuickStart, accept the default file type (*.rga7) and click Save to continue.

By default, files will be saved in the "My Documents" directory on your computer. You can select a different directory, if desired, and RGA 7 will "remember" the directory for the next time you save the file.

3.10 Close the Project

Close the project by choosing File > Close or by clicking the Close icon.

You will now be looking at the MDI with no projects open.

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Step-by-Step Examples

4.1 List of Examples

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This chapter provides the following step-by-step examples, designed to help you explore the features of the RGA software:

Example 1 - Working with Grouped Failure Times - page 19 Example 2 - Working with Multiple Systems - Known Operating Times Data - page 25 Example 3 - Working with Sequential Success/Failure Data - page 31 Example 4 - Working with Grouped Configuration Success/Failure Data - page 35 Example 5 - Working with Mixed Discrete Data - page 40 Example 6 - Analyzing Reliability Data - page 45 Example 7 - Using the Crow Extended Model for Reliability Growth Test Planning - page 48 Example 8 - Working with Multiple Systems - Concurrent Times Data - page 59 Example 9 - Reliability Growth Analysis Based on Fleet Data from Fielded Systems - page 71 Example 10 - Analyzing Software Reliability Growth - page 79 Example 11 - Using Mission Profiles - page 87 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests - page 96 Example 13 - Fielded Repairable System Data Analysis - page 115

Please note that these examples use the default settings that are shipped with the application. If you have changed any of your settings, click the Reset Application Settings button on the Reset Settings page of the User Setup.

4.2 Example 1 - Working with Grouped Failure Times

A new helicopter system is under development. System failure data have been collected on five helicopters for the final test phase. The total number of flight hours is 500, accrued over a period of 12 weeks. The 500 flight hours are partitioned into six intervals, each covering a two-week period. Every two weeks, each helicopter undergoes a thorough inspection to uncover any failures that may have occurred since the last inspection. Therefore, although the actual failure times are unknown, the analysts have the cumulative total number of flight hours and the cumulative total number of failures for the five helicopters for each two-week period.

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4 Step-by-Step Examples

For each interval, the total number of flight hours and total number of assigned failures for the five helicopters are recorded, as shown in the following table. Interval 1 2 3 4 5 6 Failures in Interval 12 6 15 3 18 16 Interval Length 0-62 63-100 101-187 188-210 211-350 351-500

Do the following:

Create a Standard Folio with a Data Sheet for the Grouped Failure Times data type. Calculate the parameters using the Crow-AMSAA (NHPP) model. Plot the instantaneous MTBF vs. Time. Use the Quick Calculation Pad to obtain the instantaneous MTBF for the helicopter at 500 hours.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Grouped Failure Times Example.rga7."

Create a new project by choosing File > New or clicking the New icon.

By default, the Expert view will be displayed. You can also click the Wizard View icon and answer a series of questions to set the Folio type.

For this example, the data set was obtained from developmental testing, so click the Developmental category and Times-to-Failure Data sub-category. Note that the right side of the window displays the available developmental data types.

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4.2 Example 1 - Working with Grouped Failure Times

Click the Grouped Failure Times option, as shown next.

Click OK to generate the new Standard Folio with the Data Sheet that you have selected. Enter the data into the Data Sheet. The rows in the Data Sheet represent the intervals (e.g. row 1 is interval 1, row 2 is interval 2 and so on). Enter the failures for each interval in the Failures in the Interval column and enter the end point for each interval in the Interval End Time column. On the Main page of the Standard Folio Control Panel, use the Crow-AMSAA (NHPP) model, as shown next.

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Go to the Standard Folio Control Panel's Analysis page by clicking the Analysis tab.

Analysis Type indicates the method used for estimating the parameters. Use the default setting of Maximum Likelihood for this example. Note that for the current data type and model, this option cannot be changed. Confidence Interval Method displays the method used for calculating the confidence bounds. Use the default setting of Crow for this example.

Go back to the Standard Folio Control Panel's Main page by clicking the Main tab. Notice that the Information area displays MLE for Maximum Likelihood Estimation. The Information area also displays the data category (Developmental) and confidence interval method (Crow). Now calculate the parameters by choosing Data > Calculate or by clicking the Calculate icon.

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4.2 Example 1 - Working with Grouped Failure Times

The calculated parameters will appear in the Results area of the Standard Folio Control Panel, as shown next.

The next step is to plot the data from the Data Sheet. To do this, choose Data > Plot or click the Plot icon.

By default, the Cumulative Number of Failures plot will appear in the Plot Sheet that is added to the Standard Folio.

The plots available in RGA plot sheets vary depending on the current data type and model. For this analysis, the MTBF vs. Time and Failure Intensity vs. Time plots are also available.

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Choose MTBF vs. Time from the Plot Type drop-down menu to display another plot, as shown next.

By default, both the instantaneous MTBF vs. Time and cumulative MTBF vs. Time will be plotted. However, you can specify to plot the individual lines only. These options are available in the Show/Hide Items window, which you can access by right-clicking the plot and choosing Show/Hide Items.

To display only the cumulative MTBF line on the plot, clear the Instantaneous MTBF check box, then click OK. To calculate the instantaneous MTBF of the helicopter at a specified time, choose Data > Quick Calculation Pad or click the QCP icon.

On the Basic Calculations page, make the following selections/inputs:

Options for Calculations: Inst. MTBF Additional Required Information:

Time/Stage: 500 Type: Two-Sided Confidence Level: 0.9

Confidence Bounds:

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4.3 Example 2 - Working with Multiple Systems - Known Operating Times Data

Click Calculate to obtain the results, as shown next.

You can see that the instantaneous MTBF of the helicopter at 500 hours is 8.7792 hours. The 90% two-sided confidence bounds are also displayed.

Click Close to close the Quick Calculation Pad and return to the Data Sheet. Close the Folio. Choose File > Save or click the Save icon.

In the Save As window, browse to the desired location for the project. Type Grouped Failure Times as the file name and accept the default file type, RGA 7 file (*.rga7). Click Save to save the project. Close the project by choosing File > Close. You will now be looking at the MDI with no projects open.

4.3 Example 2 - Working with Multiple Systems - Known Operating Times Data

Two identical prototypes were tested. Any design changes made to improve the reliability of these systems were incorporated into both systems when either of the two systems failed. At the beginning of the test, only one prototype was available. For the purpose of not delaying the testing program, the testing commenced with just one unit until the second unit was available. At each observed failure, the operating time of each unit was recorded.

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Tables of the data obtained from the test are given next. Failed Unit ID 1 1 1 1 2 2 2 1 1 2 2 1 1 2 Do the following:

Time Unit 1 2.6 16.5 16.5 17 20.5 25.3 28.7 41.8 45.5 48.6 49.6 51.4 58.2 59

Time Unit 2 0 0 0 0 0.9 3.8 4.6 14.7 17.6 22 23.4 26.3 35.7 36.5

Failed Unit ID 2 1 1 2 1 1 1 2 2 1 2 2 2 END

Time Unit 1 60.6 61.9 76.6 81.1 84.1 84.7 94.6 104.8 105.9 108.8 132.4 132.4 132.4 132.4

Time Unit 2 37.6 39.1 55.4 61.1 63.6 64.3 72.6 85.9 87.1 89.9 119.5 150.1 153.7 167.6

Create a Standard Folio with a Data Sheet for the Multiple Systems - Known Operating Times data type. Specify the test termination time. Calculate the parameters using the Crow-AMSAA (NHPP) model. Use the QCP to determine the demonstrated MTBF at the end of the test. Assuming both units are tested for an additional 100 hours each, use the QCP to determine how many failures are expected to occur in that period.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Multiple Systems - Known Times Example.rga7."

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4.3 Example 2 - Working with Multiple Systems - Known Operating Times Data

Create a new project with a Standard Folio and a Data Sheet for multiple systems with known operating times data, as shown next.

Enter the data into the Data Sheet.

Notice that Unit 2 was tested for an additional 13.9 hours before testing was halted and no failures occurred during this period. This means that this is a time terminated test and the total test time is 132.4 + 167.6 = 300 hours.

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Specify the test termination time by clicking the ... button in the Test Termination field on the Standard Folio Control Panel's Main page. The Termination Time window will appear. Select the Time Terminated option and then enter 300 into the Termination Time input box, as shown next.

Click OK. Notice that the termination time now appears on the Time Terminated button on the Standard Folio Control Panel.

Note that not selecting the Time Terminated option would have indicated that the test ended with the last failure in the data set. For this example, the termination time would have been 286.1hours if you had not specified the actual termination time.

On the Main page, make sure that Crow-AMSAA (NHPP) is the model. On the Analysis page, make sure that the Input is Cumulative option is selected. Calculate the parameters. The results are shown next.

The demonstrated mean time between failures value at the end of the test is 15.5110 hours. This is found in the Results area in the Standard Folio Control Panel, in the DMTBF field. The demonstrated MTBF can also be calculated using the QCP, as described next.

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4.3 Example 2 - Working with Multiple Systems - Known Operating Times Data

Choose Data > Quick Calculation Pad to open the Quick Calculation Pad. To determine the instantaneous MTBF at 300 hours, on the Basic Calculations page, make the following selections/inputs:

Options for Calculations: Inst. MTBF Additional Required Information:

Time/Stage: 300 Type: Two-Sided Confidence Level: 0.95

Confidence Bounds:

Click Calculate to obtain the results, as shown next.

Again, the demonstrated MTBF at the end of the test is found to be 15.5110 hours, as shown in the Control Panel. The 95%, two-sided confidence bounds are also displayed. To show the calculated number of failures at 300 hours, select Number of Failures under Options for Calculations and click Calculate again.

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The results will appear, as shown next.

Notice that this value exactly matches the entered data. If both units are tested for an additional 100 hours each, then the total cumulative time in the test would be 500 hours. You can use the QCP to determine the number of expected failures at 500 hours.

To do this, enter 500 for the Time/Stage. Click Calculate. The results will appear, as shown next.

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4.4 Example 3 - Working with Sequential Success/Failure Data

From this calculation, it can be seen that the cumulative number of failures by 500 hours is approximately 39. However, this number includes the number of failures already observed, which is 27 in this case. Therefore, if both units are tested for an additional 100 hours each, then the expected number of additional failures is 39 - 27 = 12.

Close the QCP. Close the Folio. Save the project as Multiple Systems - Known Times.rga7. Close the project.

4.4 Example 3 - Working with Sequential Success/Failure Data

A missile is being launch tested. If it successfully launches, then the test is considered a success. If it fails to launch, then the test is considered a failure. Whether or not the target was destroyed is not under consideration at this development stage. The test consists of 20 launches. After each launch, the item is inspected and redesigned or repaired before the next launch. The data set obtained from the test is given next. Trial 1 2 3 4 5 6 7 8 9 10 Do the following:

Success/ Failure F F S S F S S S F S

Trial 11 12 13 14 15 16 17 18 19 20

Success/ Failure F S S S S S S S S S

Create a Standard Folio with a Data Sheet for the Sequential data type. Calculate the parameters using the Logistic model. Plot the Reliability vs. Time. If design changes continue to be incorporated and the testing continues, use the QCP to determine:

When the reliability goal of 99% will be achieved. The attainable reliability at the end of the 35th launch.

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Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Sequential Success Failure Data Example.rga7."

Create a new project with a Standard Folio and a Data Sheet for sequential success/failure data, as shown next.

The Data Sheet will appear. The row numbers that appear on the left side of the Data Sheet represent the sequence/trial number. Therefore, enter the success/failure data into the Success/Failure column, as shown next.

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4.4 Example 3 - Working with Sequential Success/Failure Data

Calculate the parameters using the Logistic model. The results will appear in the Results area of the Standard Folio Control Panel, as shown next.

Next, plot the data by choosing Data > Plot or by clicking the Plot icon.

By default, the Reliability vs. Time will appear in the Plot Sheet. If the termination line is displayed on your plot, open the Show/Hide Items window by right-clicking the plot and choosing Show/Hide Items from the shortcut menu that displays. Clear the Termination Line check box, then click OK. The plot will look like the one shown next.

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Open the QCP. On the Basic Calculations page, make the following selections/inputs:

Options for Calculations: Time/Stage given Additional Required Information:

Reliability: 0.99 Type: None

Confidence Bounds:

Click Calculate to obtain the results, as shown next.

Therefore, if design changes continue to be incorporated and the testing continues, the reliability goal of 99% will be achieved at the end of the 62nd launch. Now determine the attainable reliability at the end of the 35th launch if design changes continue to be incorporated and the testing continues.

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4.5 Example 4 - Working with Grouped Configuration Success/Failure Data

To do this, select Reliability and enter 35 for the Time/Stage. Click Calculate.

The attainable reliability at the end of the 35th launch will be 91.50%.

Close the QCP. Close the Folio. Save the project as Sequential Success Failure Data.rga7. Close the project.

4.5 Example 4 - Working with Grouped Configuration Success/Failure Data

A one-shot system under development underwent reliability growth testing for a total of 68 trials. Corrective actions were incorporated after the 14th, 33rd and 48th trials. The configuration was not changed from trial 49 to trial 68.

Configuration 1 (trials 1 to 14) experienced 5 failures. (The cumulative number of failures at that point was 5 failures in 14 launches.) Configuration 2 (trials 15 to 33) experienced 3 failures. (The cumulative number of failures at that point was 8 failures in 33 launches.) Configuration 3 (trials 34 to 48) experienced 4 failures. (The cumulative number of failures at that point was 12 failures in 48 launches.) Configuration 4 (trials 49 to 68) experienced 4 failures. (The cumulative number of failures at that point was 16 failures in 68 launches.)

Do the following:

Create a Standard Folio with a Data Sheet for the Grouped per Configuration data type. Calculate the parameters using the Crow-AMSAA (NHPP) model. Plot the Reliability vs. Time.

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Use the QCP to obtain the reliability achieved by Configuration 4.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Grouped per Configuration Data Example.rga7."

Create a new project with a Standard Folio and a Data Sheet for grouped per configuration data, as shown next.

Double-click the Number of Units column header to open the Change Heading window. In the field, change the heading text to "Trials (Cumulative)", as shown next.

Click OK. Enter the data into the Data Sheet. Each row in the Data Sheet represents a different configuration. Enter the cumulative number of launches for each configuration in the Trials (Cumulative) column and enter

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4.5 Example 4 - Working with Grouped Configuration Success/Failure Data

the cumulative number of failures for each configuration in the Number of Failures column, as shown next.

Calculate the parameters using the Crow-AMSAA (NHPP) model. The results are shown next.

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Plot the Reliability vs. Time, as shown next.

The plot displays lines for each of the four configurations, identified as "Data Intervals" in the plot. You can see from the plot that the reliability for Configuration 4 is about 80%. However, an exact calculation can be obtained from the QCP.

Open the Quick Calculation Pad. On the Basic Calculations page, make the following selections/inputs:

Options for Calculations: Reliability Additional Required Information:

Time/Stage: 4

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4.5 Example 4 - Working with Grouped Configuration Success/Failure Data

Click Calculate to obtain the results, as shown next.

You can see that the reliability of Configuration 4 is 80.96%.

Click Close to close the Quick Calculation Pad and return to the Data Sheet. Close the Folio. Save the project as Grouped per Configuration Data. Close the project.

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4.6 Example 5 - Working with Mixed Discrete Data

A system under development undergoes a reliability growth program. At specified time intervals during the testing, the number of failed units and the number of tested units is recorded. Based on the test results, the projected future reliability can be calculated. Each interval represents a different configuration. A table of the test results is given next. Interval 1 2 3 4 5 6 7 8 9 10 11 Do the following:

Number of Failures in the Interval 6 5 3 0 1 0 1 0 1 0 0

Cumulative Number of Trials at the End of Each Interval 16 40 51 54 55 59 60 64 68 75 76

Create a Standard Folio with a Data Sheet for the Mixed Data data type. Calculate the parameters using the Crow-AMSAA (NHPP) model. Plot the Reliability vs. Time. Use the QCP to calculate the instantaneous Reliability expected after 110 trials. Use the QCP to calculate the system's average Reliability between trials 60 and 76. Use the QCP to calculate the system's average Reliability between trials 16 and 76.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Mixed Discrete Data Example.rga7."

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4.6 Example 5 - Working with Mixed Discrete Data

Because the data set contains grouped data and individual success/failure data in combination, the Mixed data type is used to analyze the data.

Create a new project with a Standard Folio and a Data Sheet for mixed discrete data, as shown next.

In the Data Sheet, each row represents an interval. Enter the number of failed units in each interval in the Failures in Interval column and enter the cumulative number of trials at the end of each interval in the Cumulative Trials column, as shown next.

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Calculate the parameters using the Crow-AMSAA (NHPP) model. The results are shown next.

Plot the Reliability vs. Time, as shown next.

The plot graphically shows the reliability growth over time.

Next, open the QCP. To calculate the instantaneous reliability value expected after 110 trials, do the following:

Options for Calculations: Inst. Reliability Additional Required Information:

Time/Stage: 110 Type: Lower One-Sided Confidence Level: 0.95

Confidence Bounds:

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4.6 Example 5 - Working with Mixed Discrete Data

Click Calculate to obtain the results, as shown next.

The instantaneous reliability estimated for 110 trials is 87.20% with a 95% lower confidence bound of 64.22%. (The confidence bound value shows the most conservative estimate of the limit.)

Next, calculate the average reliability between stages 60 and 76. Select Average Reliability, enter 60 for Time/Stage 1 and enter 76 for Time/Stage 2. Click Calculate. The results are shown next.

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Notice that the average reliability between Stages 60 and 76 is 84.84%. By way of comparison, notice that the average reliability between Stages 16 and 76 is 81.94%, as shown next.

Close the QCP. Close the Folio. Save the project as Mixed Discrete Data.rga7. Close the project.

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4.7 Example 6 - Analyzing Reliability Data

4.7 Example 6 - Analyzing Reliability Data

A device is required to have a reliability of 92% at the end of a 12 month design and development period. At each development/growth phase, a sample of units from the latest prototypes are tested and the data are analyzed in order to calculate the reliability. A table of the calculated reliability values at the end of each test phase is given next. Group Number Test Time in Months 0 1 1 Reliability 0.58 0.66

2 2 3

0.72 0.78

4 3 Do the following:

0.82 0.85

5

Create a Standard Folio with a Data Sheet for the Reliability data type. Calculate the parameters using the Standard Gompertz model. Use the QCP to determine the reliability at the end of the 12 month period based on the information obtained from the first five months of testing. From the calculated results, determine the maximum achievable reliability if the reliability program plan pursued during the first 5 months is continued.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Reliability Data Example.rga7."

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Create a new project with a Standard Folio and a Data Sheet for reliability data, as shown next.

Enter the data into the Data Sheet, as shown next.

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4.7 Example 6 - Analyzing Reliability Data

Calculate the parameters using the Standard Gompertz model. The results are shown next.

Next, open the QCP. On the Basic Calculations page, make the following selections/inputs:

Options for Calculations: Reliability Additional Required Information:

Time/Stage: 12 Type: None

Confidence Bounds:

Click Calculate to obtain the results, as shown next.

The reliability after a 12 month period is found to be 93.14%, which exceeds the reliability goal of 92%.

Close the QCP.

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The theoretically maximum achievable reliability is parameter a of the Gompertz model. For this example, this is 94.22%, as shown in the Results area of the Control Panel.

Close the Folio. Save the project as Reliability Data.rga7. Close the project.

4.8 Example 7 - Using the Crow Extended Model for Reliability Growth Test Planning

This example is based on the paper "An Extended Reliability Growth Model For Managing and Accessing Corrective Actions" by Dr. Larry Crow, presented at the 2004 RAMS. RGA provides full support for the reliability growth test planning/management strategy and data analysis methodology developed by Dr. Larry Crow. These techniques provide useful metrics to support decisionmaking, including the MTBF demonstrated through testing, the growth in MTBF that will be achieved through implementation of corrective actions, the maximum potential MTBF that can likely be achieved for the product design and estimates regarding latent failure modes that have not yet been uncovered through testing. Reliability growth projection data analysis can be performed using the Crow Extended reliability growth analysis model. This model utilizes A, BC and BD failure mode classifications to analyze reliability growth data. Using this terminology, you can specify which failure modes you are not going to fix (A), which failure modes will be fixed while the test is in progress (BC) and which failure modes will be corrected at the end of the test (BD). In addition, you can assign a factor to each BD mode that estimates the effectiveness of the correction that will be implemented after the test. (There is no reliability growth for A modes and the effectiveness of the corrective actions for BC modes is assumed to be demonstrated during the test.) Analysis with the Crow Extended model then allows you to consider different management strategies to see if you will reach your goal for reliability growth. For this example, a product underwent developmental testing. The observed failure modes were identified during testing. Some modes were corrected during the test (BC modes), some modes were corrected after the end of the test phase (delayed fixes, BD modes) and some modes were left in the system (A modes). The final testing time is 400 hours.

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4.8 Example 7 - Using the Crow Extended Model for Reliability Growth Test Planning

The following tables give the data from the test. Failure Time 0.7 3.7 13.2 15 17.6 25.3 47.5 54 54.5 56.4 63.6 72.2 99.2 99.6 100.3 102.5 112 112.2 120.9 Mode BC17 BC17 BC17 BD1 BC18 BD2 BD3 BD4 BC19 BD5 A BD5 BC20 BD6 BD7 A BD8 BC21 BD2 Failure Time 121.9 125.5 133.4 151 163 164.7 174.5 177.4 191.6 192.7 213 244.8 249 250.8 260.1 263.5 273.1 274.7 282.8 Mode BC22 BD9 BD10 BC23 BC24 BD9 BC25 BD10 BC26 BD11 A A BD12 A BD1 BD8 A BD6 BC17 Failure Time 285 304 315.4 317.1 320.6 324.5 324.9 342 350.2 355.2 364.6 364.9 366.3 373 379.4 389 394.9 395.2 Mode BD13 BD9 BD4 A A BD12 BD10 BD5 BD3 BC26 BD10 A BD2 BD8 BD14 BD15 A BD16

Note: The Mode column typically contains text that describes the actual failure mode. For purposes of the

examples shown in this Training Guide, numbers are used to identify unique modes.

An effectiveness factor has been assigned for each of the BD failure modes (delayed fixes). The effectiveness factor is based on engineering assessment and represents the fractional decrease in failure intensity of a failure mode after the implementation of a corrective action. The effectiveness factors for the BD modes are given in the following table. BD Mode 1 2 3 Effectiveness Factor 0.7 0.7 0.8

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BD Mode 4 5 6 7 8 9 10 11 12 13 14 15 16 Do the following:

Effectiveness Factor 0.8 0.9 0.9 0.5 0.9 0.9 0.7 0.7 0.6 0.6 0.7 0.7 0.5

Configure the software to calculate the unbiased beta. Create a Standard Folio with a Data Sheet for the Failure Times data type. Assign effectiveness factors to the BD modes. Define the test termination time. Calculate the parameters using the Crow Extended model. Plot the Growth Potential MTBF. From this plot, determine the demonstrated MTBF for the system and the growth potential MTBF. Plot the Failure Mode Strategy to view the break-down of the unique failure modes and what percentage each contributes to the total number of failure modes in the system. Plot the Individual Mode MTBF and determine the failure mode with the lowest MTBF.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Growth Planning Management Example.rga7." When using the Crow Extended model, it is common practice to calculate the unbiased beta. You can specify to calculate the unbiased beta via the User Setup. (Note that for the projections, the unbiased beta is always used, regardless of the setting in the User Setup.)

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4.8 Example 7 - Using the Crow Extended Model for Reliability Growth Test Planning

Choose File > User Setup. On the Calculations page, select Calculate Unbiased Beta, as shown next.

Click OK to exit the User Setup. Create a new project with a Standard Folio and a Data Sheet for failure times data as shown next.

Choose Crow Extended as the model. This adds the Project columns (Classification and Mode) to the Data Sheet.

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Enter the data into the Data Sheet.1 Enter the failure times in the Time to Event column. Enter the mode classification information into the Classification column. Classification information must be entered as follows:

A indicates that no corrective action was or will be performed (management chooses not to address for technical, financial or other reasons). BD indicates delayed corrective action (aka "B" modes). You will be required to define the effectiveness factor for each BD mode to estimate the fractional decrease in failure intensity. BC indicates that corrective action was taken during the test (aka "C" modes). The analysis assumes that the effect of the corrective action was experienced during the test (as with other test-fix-test reliability growth analyses).

You can then enter the corresponding failure mode identification (e.g. 1) into the Mode column. Note that there is no failure mode identification for the A classifications since corrective action is not performed on A modes.

Tip: If you enter "C" into the Classification column, the application will automatically convert it to "BC" and if you

enter "D" into the Classification column, the application will automatically convert it to "BD."

Your Data Sheet will look like the one shown next. (Please note that the following Data Sheet displays only 27 rows of data. Be sure to enter all of the data for this example as given in the table on page 49. Your Data Sheet will contain 56 rows of data.)

Before calculating the parameters for the data set, you will be required to define the effectiveness factor for each BD mode to estimate the fractional decrease in failure intensity.

1. Instead of typing the data by hand, you can open the Growth Planning Management Example.rga7 file, copy the data from it and then paste the data into your file.

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4.8 Example 7 - Using the Crow Extended Model for Reliability Growth Test Planning

To define the effectiveness factors, choose Data > Effectiveness Factors or click the Effectiveness Factor icon.2

The Effectiveness Factor window will appear. Enter the effectiveness factor for each BD mode, as shown next.

The BD Mode column displays each unique mode name in the current Data Sheet that has been assigned a BD classification. The Effectiveness Factor column allows you to define the effectiveness factor. This can be a value between 0 and 1 where 0 indicates that the corrective action will remove 0% of the failure intensity for the mode from the system and 1 indicates that the corrective action will remove 100% of the failure intensity for the mode from the system. The Comments column allows you to type any additional information about the effectiveness factors. The information in the Comments column is not taken into consideration when the parameters are calculated. The average effectiveness factor will appear in the status bar in the bottom right corner of the window.3

Click OK to save the information and return to the Data Sheet. Specify the test termination time by clicking the ... button in the Test Termination field on the Standard Folio Control Panel's Main page. The Termination Time window will appear. Select the Time Terminated option and enter a termination time of 400 into the Termination Time input box, as shown next.

If you click Calculate before assigning the effectiveness factors, a window will appear notifying you that all unique BD modes have not been given a valid effectiveness factor. Click Yes to assign the effectiveness factors. 3. You can also define a fixed effectiveness factor by clicking the Use Fixed Effectiveness Factor button on the toolbar and entering the fixed value into the input box that appears. This can be a value greater than 0 and less than or equal to 1. This will be used instead of any values that may appear in the Spreadsheet area.

2.

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Click OK to return to the Data Sheet. Notice that the termination time appears on the Time Terminated button on the Standard Folio Control Panel. Calculate the parameters. The results will appear, as shown next.

When using the Crow Extended model for reliability growth projections, a Results drop-down menu will appear in the Results area. This drop-down menu allows you to select the modes in the data set that you want to view the results for in the Results area. For example, if you select All Modes, the results for all modes in the data set will appear in the Results area. If you select BC Modes, only the results for all BC modes in the data set will appear in the Results area. The available classifications in the drop-down menu will correspond with the modes that exist in the data set. If other words, if your data set has only A and BC modes, you could view the results for A modes and BC modes, but the BD modes option will not appear in the menu.

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4.8 Example 7 - Using the Crow Extended Model for Reliability Growth Test Planning

Now create the Growth Potential MTBF plot, as shown next.

The Growth Potential MTBF plot displays three lines: the demonstrated MTBF, the projected MTBF and the growth potential MTBF. The demonstrated MTBF line represents the MTBF at the end of the test without any delayed corrective actions. The projected MTBF line displays the estimated MTBF after the delayed corrective actions have been implemented. The growth potential MTBF line represents the maximum achievable MTBF based on the current management strategy. From this plot, it can be determined that the demonstrated MTBF, which is the result of the corrective action taken during the test (BC modes) for this system, is about 7.85 hours. If the 16 delayed corrective actions are implemented (the fixes for the BD modes), the MTBF is projected to be about 11.32 hours. If testing continues with the current management strategy in place (i.e. modes corrected vs. modes not corrected) and with the current effectiveness of each corrective action, then the maximum attainable MTBF is estimated to be about 15 hours. This is called the growth potential MTBF.

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Now plot the Average Failure Mode Strategy, as shown next.

The Failure Mode Strategy plot type is a pie chart that breaks down the average failure intensity of the entire system into the following categories:

Type A modes will not be addressed - 9.48% of the total. Type BC modes are addressed during the test.

Type BC - Seen represents the percent of average system failure intensity due to BC modes observed during the test - 14.167% of the total. Type BC - Unseen represents the percent of average system failure intensity due to BC modes which have not yet been seen - 31.042% of the total. Type BD - Unseen represents the percent of system failure intensity due to BD modes which have not yet been seen - 33.226% of the total. Type BD - Remain modes represent the BD mode average failure intensity portion that remains in the system because the corrective actions were not 100% effective - 3.323% of the total. Type BD - Removed modes represent the average failure intensity portion that will be removed through the implementation of the delayed corrective actions - 8.761% of the total.

Type BD modes are addressed after the test.

Now plot the Individual Mode MTBF. This bar chart shows the MTBF of each individual failure mode, which allows you to identify the failure modes with the lowest MTBF. These are the failure modes that cause the majority of the system failures.

Before represents the mode's MTBF at the end of the test. This is available for A, BC and BD modes. For BD modes, this is the MTBF before corrective actions are implemented at the end of the test.

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4.8 Example 7 - Using the Crow Extended Model for Reliability Growth Test Planning

After is available only for BD modes and represents the mode's MTBF after the corrective actions have been implemented at the end of the test.

Specify to plot only the BD modes on the chart. To do this, choose Plot > Plot Modes. The Select Modes to Plot window will appear, as shown next.

By default, all of the modes are selected to be plotted. Choose BD Modes from the Select by Mode field in the bottom left corner of the window. Only the BD modes are selected in the window. Click OK. The plot will automatically be refreshed and only BD modes will appear on the plot. By default, the X-axis numbers will appear horizontally on the plot. You can change the orientation of the number to vertical by selecting Plot > Plot Setup or by clicking the Plot Setup icon.

In the Plot Setup window, click the Plot Labels page, as shown next.

Click the Set Font button next to the Show X-Axis Labels check box to open the Font Dialog.

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In the Orientation field, enter 90, then click OK to return to the Plot Setup window.

Click OK to close the Plot Setup window and refresh the plot.

As you can see from the plot, the BD10 mode has the lowest "After" MTBF, about 333 hours. Note that you can pause on a mode to read the value on the chart. This plot also show you which failure mode makes the biggest contribution to your failures and which failure mode had the greatest improvement.

Close the Folio. Save the project as Growth Planning Management.rga7. Close the project. Choose File > User Setup. On the Calculations page, clear the Calculate Unbiased Beta check box, then click OK.

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4.9 Example 8 - Working with Multiple Systems - Concurrent Times Data

4.9 Example 8 - Working with Multiple Systems - Concurrent Times Data

A system under development undergoes a reliability growth program. Six systems are field tested at different geographical locations. The systems are identical and testing commences at approximately the same time in all locations. When a failure occurs in any system, the failure time is recorded and the engineers decide if a corrective action will be taken. If they decide to take corrective action, the design change is implemented in all systems within a reasonable amount of time. The only information that is available is the failure time of each system. Tables of the data obtained from the test are given next.

System 1 Time to Event Start Time Failure Times 0 21 29 43 43 43 66 115 159 199 202 222 248 248 255 286 286 304 320 348 364 404 410 429 End Time 504 End Time End Time System 2 Time to Event Start Time Failure Times 0 83 83 83 169 213 299 375 431 541 System 3 Time to Event Start Time Failure Times 0 26 26 57 64 169 213 231 231 231 231 304 383 454

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System 4 Time to Event Start Time Failure Times 0 36 306 306 334 354 395 403 448 456 461 End Time 474

System 5 Time to Event Start Time Failure Times 0 23 46 127 166 169 213 213 255 369 374 380 415 End Time 436

System 6 Time to Event Start Time Failure Times 0 7 13 13 31 31 82 109 137 166 200 210 220 301 422 437 469 469 End Time 500

Do the following:

Create the appropriate Data Sheet. Create a Standard Folio with a Data Sheet for the Multiple Systems - Concurrent Operating Times data type. Calculate the parameters using the Crow-AMSAA (NHPP) model. Determine whether all systems have the same failure intensity behavior. Use the Common Beta Hypothesis, Cramér-von Mises and Laplace Trend statistical tests and identify the system(s) that do not follow the same trend as the rest of the systems. If one or more systems do not follow the same trend, repeat the analysis without including these system(s). Use the QCP to determine the demonstrated MTBF.

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4.9 Example 8 - Working with Multiple Systems - Concurrent Times Data

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Multiple Systems - Concurrent Times Example.rga7."

Create a new project with a Standard Folio and a Data Sheet for multiple systems-concurrent operating times data, as shown next.

RGA offers two views for entering data from multiple systems. For this example, you will use the Advanced Systems View. The Advanced Systems View displays the data for each system in a separate Data Sheet. By default, your Data Sheet should be in this view. If it is not, choose Systems > Systems View > Advanced Systems View or click the Switch Systems View icon on the Standard Folio's Control Panel.

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Your Data Sheet will look like the one shown next.

When you select to use the Advanced System View, the Advanced Systems View Explorer will be displayed on the left side of the Standard Folio. This Explorer displays all of the systems that have been defined in the Standard Folio and the corresponding data. In addition, the Explorer allows you to select which systems will be included in the combined "superposition" or "equivalent" system analysis. By default, all systems are selected to be included in the analysis. However, you can select or clear the box to the left of the system name to include it in or remove it from the combined analysis. The Time to Event column allows you to define the start and end times of the observation period for the analysis in addition to the times of the failures that occurred during the observation period. The start time of the observation period is entered into the Start row and the end time of the observation period is entered into the End row. (These are the first two rows of the Data Sheet, which are reserved for this information.) The times of the failures are entered into the subsequent rows, starting with row 3.

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4.9 Example 8 - Working with Multiple Systems - Concurrent Times Data

Enter the data for System 1 into the System 1 Data Sheet, as shown next.

Now add another system to the Advanced Systems View Explorer by choosing Systems > Add System, or by right-clicking inside the Explorer and choosing Add System from the shortcut menu that displays. System 2 will appear in the Advanced Systems View Explorer. Click its name in the Explorer to access the System 2 Data Sheet and enter the data for System 2. Repeat these steps to continue adding systems and entering the remaining data. Your Standard Folio will look like the one shown next once you have entered all data.

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To view the data as entered in the Normal View, choose Systems > Systems View > Normal View or click the Switch Systems View icon. Your Standard Folio will look like the one shown next.

Notice that the system names are displayed in the System Name column and that the Event column displays the event types (S for System Start, F for Failure and E for System End).

Switch back to the Advanced Systems View. To expand the hierarchy in the Advanced Systems View Explorer to show the start and end time data below each system choose, Systems > Expand All or click the + (Expand) button next to each system. The first number is the start time (i.e. the beginning of the observation period), as defined in the Time to Event column and Start row in the Data Sheet. The second number is the end time (i.e. the end of the observation period), as defined in the Time to Event column and End row in the Data Sheet.

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4.9 Example 8 - Working with Multiple Systems - Concurrent Times Data

Next, calculate the parameters using the Crow-AMSAA (NHPP) model. The results will appear in the Results area of the Standard Folio Control Panel, as shown next.

In the Results area, the CBH (Common Beta Hypothesis) displays "Passed," which suggests that it can be assumed that all systems have the same failure intensity behavior. However, it is always recommended to further investigate this assumption. This can be achieved in RGA by looking at the statistical test results and at the System Operation plot.

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To view the statistical test results, choose Data > Statistical Tests. The Results Panel will appear, as shown next.

The statistical tests results indicate that System 4 has failed the Cramér-von Mises goodness-of-fit test. In addition, the Laplace Trend test suggests a deteriorating system.

Close the Results Panel by clicking Close.

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4.9 Example 8 - Working with Multiple Systems - Concurrent Times Data

Plot the System Operation, as shown next.

To get a better look at the individual systems on the plot, remove the Equivalent system time line from the plot by choosing Plot > Plot Systems. The Select Systems to Plot window will appear, as shown next.

To remove the Equivalent system time line from the plot, clear the Plot System Time Line option and click OK.

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The plot will be refreshed without the Equivalent system time line, as shown next.

As can be seen in the plot, System 4 appears to have a very different behavior than the rest of the systems. It appears that the failure intensity increases with time. An investigation into the reasons why the failure intensity increases with time for System 4 begins. Meanwhile, the engineers decide to proceed with the analysis and temporarily remove System 4 from the data set until the investigation is complete.

To remove System 4 from the analysis, return to the Data Sheet.

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4.9 Example 8 - Working with Multiple Systems - Concurrent Times Data

In the Advanced Systems View Explorer, clear the check box to the left of System 4 to remove it from the analysis. Recalculate the parameters, as shown next.

View the statistical test results again by choosing Data > Statistical Tests. The Results Panel will appear, as shown next.

Notice that System 4 is not included in the results since it was removed from the analysis.

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Close the Results Panel and open the QCP. To calculate the instantaneous demonstrated MTBF at the termination time (2435 hours, which is the sum of the end times of the five systems that remain in the analysis), open the QCP. On the Basic Calculations page, make the following selections/inputs:

Options for Calculations: Inst. MTBF Additional Required Information:

Time/Stage: 2435 Type: Two-Sided Confidence Level: 0.95

Confidence Bounds:

Click Calculate to obtain the results, as shown next.

The demonstrated MTBF is found to be 40.9830 hours. This is also shown in the Results area of the Standard Folio Control Panel as the DMTBF.

Close the QCP. Close the Folio.4 Save the project as Multiple Systems - Concurrent Times.rga7. Close the project.

4.

Note that upon further investigation, it turns out that several failures were not reported for System 4 and this is why the failure intensity for this system exhibited a different trend. If the missing failure times can be obtained, the analysis could be repeated with the updated data set.

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4.10 Example 9 - Reliability Growth Analysis Based on Fleet Data from Fielded Systems

4.10 Example 9 - Reliability Growth Analysis Based on Fleet Data from Fielded Systems

The failure history for the last completed cycle is recorded for a fleet of 27 repairable systems. A cycle is defined as a complete history from overhaul to overhaul. These systems are randomly selected and information is recorded in the order that the systems were selected. The data set includes the time of each failure along with the failure mode and whether it will be corrected in the revised design. The purpose of this analysis is to investigate the effect of possible reliability improvements after delayed fixes are implemented.

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Tables of the data recorded for the systems are given next. System Time to Event Mode System Start 0 1 Failure 1,396 BD1 15 End 1,396 Start 0 2 Failure 4,497 BD2 16 End 4,497 Start 0 3 Failure 525 A End 525 17 Start 0 4 Failure 1,232 BD3 End 1,232 Start 0 18 5 Failure 227 BD4 End 227 Start 0 19 6 Failure 135 BD2 End 135 Start 0 20 7 Failure 19 BD2 End 19 Start 0 8 Failure 812 BD1 End 812 21 Start 0 9 Failure 2,024 BD1 End 2,024 22 Start 0 316 BD5 10 Failure 943 A End 943 23 Start 0 11 Failure 60 BD1 End 60 24 Start 0 4,233 BD2 12 Failure 4,234 BD6 25 End 4,234 Start 0 1,877 BD7 13 Failure 2,527 BD2 26 End 2,527 Start 0 2,074 BD4 27 14 Failure 2,105 BD2 End 2,105 Do the following:

Time to Event Start 0 Failure 5,079 End 5,079 Start 0 546 Failure 577 End 577 Start 0 453 Failure 4,085 End 4,085 Start 0 Failure 1,023 End 1,023 Start 0 Failure 161 End 161 Start 0 36 Failure 4,767 End 4,767 Start 0 3,795 Failure 4,375 6,228 End 6,228 Start 0 Failure 68 End 68 Start 0 Failure 1,830 End 1,830 Start 0 Failure 1,241 End 1,241 Start 0 871 Failure 2,573 End 2,573 Start 0 Failure 3,556 End 3,556 Start 0 Failure 186 End 186

Mode BD1

BD1 A

BD8 BD1

A

BD3

BD2 BD1

BD1 BD9 BD1

BD10

BD1

BD11

BD12 BD1

BD13

BD2

Create a Standard Folio with a Data Sheet for the Fleet data type. Group the data into intervals of 10,000, 20,000, 30,000 and 40,000 hours. The final interval is defined by the termination time: 52,110 hours.

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4.10 Example 9 - Reliability Growth Analysis Based on Fleet Data from Fielded Systems

Define the effectiveness factors for the unique BD modes. Calculate the parameters using the Crow Extended model. Use the QCP to predict the improvement in the fleet MTBF after the delayed fixes are implemented. Show the improvement graphically.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Fleet Reliability Growth Example.rga7."

Create a new project with a Standard Folio and a Data Sheet for fielded fleet data, as shown next.

Select Crow Extended as the model. This will automatically add columns to the Data Sheet for entering the failure classification and mode.

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Enter the data into the Data Sheet5, using the Advanced System View, as shown next (with the sheet for System 1 visible and the data for the other systems on subsequent sheets).6

Click Calculate.

The Group Data window will appear, which allows you to group the data in the Data Sheet into specified intervals. The intervals help to smooth out the differences in the data points. As the data set is cumulative, the maximum value is 52,110 hours, so you will create intervals of 10,000 hours for each of the first four intervals. The last interval contains the remaining data.

Select the User Defined option at the top of the window.

5. Instead of typing the data by hand, you can switch to the Normal View, open the Fleet Reliability Growth Example.rga7 file, switch to the Normal View in it, and then copy and paste the data into your file. 6. If your Data Sheet is in the normal view, click the Switch Systems View icon or choose Systems > Systems View > Advanced Systems View.

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4.10 Example 9 - Reliability Growth Analysis Based on Fleet Data from Fielded Systems

Enter 10000, 20000, 30000 and 40000 into the Intervals area, as shown next.

Note: Using this method results Phase 4 lasting for 12,110 hours. If instead you had specified a Constant value of 10,000 hours, Phase 4 would only have lasted for 10,000 hours and a new Phase 5, lasting for 2110 hours, would be included. While this has no effect on the Calculated Results, it does have a slight effect on the Projected MTBF for the system.

The final interval is determined by the termination time, which is displayed at the bottom of the window. For this example, it is 52,110 hours.

Click OK. A window will appear notifying you that all unique BD modes have not been given a valid effectiveness factor, as shown next.

Click Yes and the Effectiveness Factor window will be displayed.

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At the top of the Effectiveness Factor window, click the Use Fixed Effectiveness Factor button and enter 0.5 into the input box to the right, as shown next. This indicates that the delayed fixes for all of the failure modes identified in the data are expected to have the same degree of improvement (0.5).

Click OK. The parameters will be calculated, as shown next.

Next, open the QCP. The calculations on the Extended Calculations page of the QCP are available for data sets that have been analyzed using the Crow Extended model, provided that there are BD failure modes in the data set On the Extended Calculations page, make the following selections/inputs:

Options for Calculations: Demonstrated Results Options: MTBF Confidence Bounds:

Type: None

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4.10 Example 9 - Reliability Growth Analysis Based on Fleet Data from Fielded Systems

Click Calculate to obtain the results, as shown next.

The demonstrated MTBF (i.e. without the improvements) is found to be about 1,408 hours. This can also be found in the Results area of the Standard Folio Control Panel as the "DMTBF".

The projected MTBF also can be calculated by selecting the Projected calculation option, as shown next.

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The improvement in the fleet MTBF after the delayed fixes are implemented (i.e. the Projected MTBF) is 638.823 hours, which is the Projected value of 2047.2014 hours minus the Demonstrated value of 1408.3784 hours.

Next, calculate the growth potential MTBF by selecting the Growth Potential calculation option, as shown next.

The growth potential MTBF (the maximum achievable MTBF value with the current management decisions about which modes to fix) is found to be about 2,542 hours.

Close the QCP.

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4.11 Example 10 - Analyzing Software Reliability Growth

Create a Growth Potential MTBF plot of all three results, as shown next.

Close the Folio. Save the project as Fleet Reliability Growth.rga7. Close the project.

4.11 Example 10 - Analyzing Software Reliability Growth

When considering reliability growth, some sort of hardware is typically being analyzed. But the same theory and analysis procedures can also be applied to the analysis of software under development. The faults (bugs) that are found during each day's testing of the software can be recorded and then analyzed, just as would be done for hardware. This example will explore how software reliability growth can be analyzed using RGA. Software for a particular application is under development. The reliability requirement is that no more than one fault may occur during every 8 hours of continuous operation. Testing begins when the software reaches the "Beta" phase. Three employees are assigned to perform continuous testing during business hours. This results in 24 hours of software testing per day. The software faults are reported and captured in a Failure Reporting, Analysis And Corrective Action System (FRACAS). Given that a new compile of the software is available for testing every week, design engineers implement fixes within a week with the exception of the last two weeks of testing, when fixes are implemented at a faster rate. The failure rate goal for this software is to have no more than one failure per 8 hours of operation or 1/8 = 0.125 failures per hour. In one day of testing (3 x 8 = 24 hours), the failure intensity goal is 0.125 x 24 = 3 faults per day.

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Assume that the following data set is extracted from the FRACAS system: Failures in Interval 45 34 25 17 21 14 10 Days of Testing 5 10 15 20 23 26 28

The data set is grouped by the number of days until a new compile of the software is available. Do the following:

Create a Standard Folio with a Data Sheet for the Grouped Failure Times data type. Calculate the parameters using the Crow-AMSAA (NHPP) model. Use the QCP to estimate the demonstrated failure intensity. Determine when the goal of no more than three faults per day will be achieved and how many days of developmental testing are required.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Software Reliability Growth Example.rga7."

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4.11 Example 10 - Analyzing Software Reliability Growth

Create a new project with a Standard Folio and a Standard Folio for grouped failure times, as shown next.

Enter the data into the Data Sheet. Calculate the parameters using the Crow-AMSAA (NHPP) model, as shown next.

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Use the QCP to estimate the instantaneous failure intensity demonstrated after 28 days of testing, as shown next.

Currently, the demonstrated failure intensity is 4.4947 faults per day. Therefore, the question is: "If we continue testing with the same growth rate, when will we achieve the goal of no more than three faults per day?"

Use the Time/Stage given Instantaneous Failure Intensity calculation option to answer this question, as shown next.

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4.11 Example 10 - Analyzing Software Reliability Growth

Therefore, 149 - 28 = 121 additional days of testing and development (test-analyze-and-fix) are required to achieve the failure intensity goal. This is much more time than the analysts anticipated so they decide to take a closer look.

Close the QCP, then plot the Failure Intensity vs. Time. On the Plot Sheet Control Panel, clear the Use Logarithmic Axes check box. If Auto Refresh is selected, the plot will automatically refresh itself; otherwise you will have to click the Refresh Plot icon on the Control Panel. Your plot will look like the one shown next.

From this plot, it can be seen that there is a jump in the failure intensity between 20 and 23 days. This is the reason why it is estimated that more development time is required. Therefore, the next step is to analyze the data set for the period up to 20 days of testing.

To do this, insert a new Data Sheet into the current Standard Folio by choosing Folio > Insert Data Sheet. The New Data Sheet Setup window will appear. Select Grouped Failure Times and click OK.7 Enter the data set for up to 20 days of testing into the new Data Sheet, Data 2. You can either copy the data from the Data 1 sheet and paste it into the Data 2 sheet or re-enter the data.

7.

Note that you can also create a copy of the Data 1 Data Sheet and delete the last three rows of data. If you do so, you can rename the new Data Sheet to "Data 2."

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Calculate the parameters using the Crow-AMSAA (NHPP) model, as shown next.

Plot the Failure Intensity vs. Time for Data 2. On the Plot Sheet Control Panel, clear the Use Logarithmic Axes check box. Your plot will look like the one shown next.

This plot shows the decrease in the failure intensity rate over the first 20 days of testing.

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4.11 Example 10 - Analyzing Software Reliability Growth

Re-open the QCP and calculate the additional days of testing and development that are required to achieve the failure intensity goal based on the first 20 days of test data, as shown next.

The calculation indicates that a total of 55 days of testing are required. Since we have already completed 28 days of testing, this indicates that only 27 more days would be required based on the analysis from the 20th day of testing. This is much different than the result obtained from the analysis of the full data set. So the question is: "What happened when the failure intensity jumped on the 23rd day of testing and development?" It turns out that new functionality was implemented at the request of a customer, which caused major redesign on some general modules of the software. This type of jump is typical in both software and hardware development when new features are introduced and observed. Due to these significant changes, it is decided that the clock should be reset and the analysts should track the reliability growth from the 20th day forward. In other words, the origin of the test is set at 20 days and the data thereafter are considered as follows: Failures in Interval 21 14 10

Days of Testing 3 6 8

Close the QCP and insert another Data Sheet for grouped failure times into the current Standard Folio by choosing Folio >Insert Data Sheet.

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Enter the data set from the previous table into the new Data Sheet, Data 3, and calculate the parameters using the Crow-AMSAA (NHPP) model, as shown next.

Plot the Failure Intensity vs. Time for Data 3 and clear the Use Logarithmic Axes check box. The plot will look like the one shown next.

This plot shows the decrease in the failure intensity rate over the last 8 days of testing.

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4.12 Example 11 - Using Mission Profiles

Re-open the QCP and calculate the additional days of testing and development that are required to achieve the failure intensity goal based on the analysis from days 20 through 28 of the testing, as shown next.

Therefore, when considering this data set, 51 - 8 = 43 more days of developmental testing are required. Of course, it is too early to make any predictions based on just 8 days of testing, but this result can be used to get a general idea of the remaining development time required and to come up with a new testing plan. In this case, it is decided that three more employees need to be added to testing and, if possible, that a new compile needs to be created every two days. This yields a much more aggressive testing and development program with the objective of completing the project within one month.

Close the QCP. Close the Folio. Save the project as Software Reliability Growth.rga7. Close the project.

4.12 Example 11 - Using Mission Profiles

It is common practice for systems to be subjected to operational testing during a development program. The objective of this testing is to evaluate performance of the system, including reliability, under conditions that represent actual use. Because of budget, resources, schedule and other considerations, these operational tests rarely match exactly the actual use conditions. Rather, stated mission profile conditions are usually used for operational testing. These mission profile conditions are typically general statements that guide testing on an average basis. Because of practical constraints, these full mission profile conditions are typically not repeated one after the other during testing. Instead, the elements that make up the mission profile conditions are tested under varying schedules with the intent that on average the mission profile conditions are met. In practice, reliability corrective actions are generally incorporated into the system as a result of this type of testing.

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RGA provides functionality that helps the analyst to ensure that testing is representative of the expected conditions of actual use. In this example, a Multi-Function Printer (MFP) under development was tested for 7200 hours. The MFP has three distinct functions that need to be tested:

Printing from a PC Copying using the scanner Faxing

To ensure that the test was balanced, the reliability team decided to use operational mission profiles for all three functions to be tested. They decided to require convergence points at times T=2500, 5000 and 7200 hours. (A convergence point is a time during the test when all the operational mission profile tasks meet their expected averages or fall within an acceptable range.) They have the test data in a Microsoft Excel® file. Do the following:

Import the Mission Profile data from another RGA file. Import the test data from Microsoft Excel®. Associate the test data with the mission profile data. Calculate the parameters using the Crow Extended model. View the results.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Mission Profile Example.rga7."

Create a new project and click Cancel in the New Data Sheet Setup window that displays. This will create a project with no Folios.

For this example, you will import the mission profile data from another project.

Choose Project > Import. In the window that appears, navigate to the Mission Profile Example Phase Data.rga7 file, which is located in the Training Guide folder within your application directory

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4.12 Example 11 - Using Mission Profiles

(e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and click Open to select the file. The Import window displays, as shown next.

Select the Mission Profile check box and then click OK. The Mission Profile1 Folio is added to your project. In the Project Explorer, double-click the Mission Profile1 Folio to open it. The first sheet in the Folio will look like the one shown next.

The Printing, Copying and Faxing Data Sheets show the expected usage and the actual usage for their respective functions.

Click the Plot icon in the Mission Profile Control Panel.

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The Mission Profile window looks like the one shown next.

The Expected Usage line shows what you expected the printer usage to be while the Actual Usage line shows the printer usage as given during the test.

In the Show area, select the Intervals check box and in the Available Profile Sheets area, select the Copying and Faxing check boxes.

The plot shows that at the three convergence points (intervals) the actual and expected results for each of the three profiles are equal.

Close the Mission Profile Folio.

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4.12 Example 11 - Using Mission Profiles

The failure times observed during the test were entered in a Microsoft Excel® file. The file contains the data that should be entered in a Failure Times Folio in RGA. Column A contains the Time to Event data; column B the Classification data; and column C contains the Mode data.

To import the data from Excel, choose Project > Import. In the Files of type field select Excel Files (*.xls). Browse for the Multi-Function Printer Data.xls file, which is located in the Training Guide folder within your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and click Open. The File Import Wizard window displays.

Select Import Sheet in the Control Panel. In the Data Type field select Failure Times. This sets the Folio type. The spreadsheet on the left side of the utility displays the data from the file. The buttons on the right side of the utility represent the columns available in the RGA Folio. To use the utility, match each column of data from the original file to a column available in the RGA Folio by selecting the column in the spreadsheet and then clicking a button.

Select Column A, then click Time to Event. This specifies the type of data in the column.

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Continue to set the other columns in this manner. Once you have set the columns, the File Import Wizard window will look like this:

Note: In many cases, the imported data includes additional comments in another column. While this example file does not include any comments, if the sheet you are importing data from does, you would mark the column(s) with the Comment button during the import.

Click the Save Import Mapping icon on the File Import Wizard Control Panel and save the import mapping template that you have created as Mission Profile. Use the default file type and save it in the default location. This allows you to use the same import mapping again if you ever need to import failure time data from an Excel file that follows the same format. Click the Import icon on the File Import Wizard's toolbar to import the data into a new Folio.

Associating the Multi-Function Printer Data Folio with the Mission Profile1 Folio groups the data based on the convergence points specified in the Mission Profile.

To associate the Multi-Function Printer Data Folio with the Mission Profile Folio, click the Mission Profile Analysis icon.

The Select Mission Profile window displays.

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4.12 Example 11 - Using Mission Profiles

In the Available Profiles field, choose Mission Profile1, then click OK. A new Data Sheet containing the grouped data, called "Mission Profile1 - Multi-Function Printer Data," is added to the Folio.

Click the Effectiveness Factors icon and enter the effectiveness factor for each BD mode, as shown next.

Set the Test Termination to Time Terminated and specify a termination time of 7200 hours.

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Calculate the parameters. The results will appear, as shown next.

The objective of this process is that we are able to apply the Crow Extended model directly in such a way that the projection and other key reliability growth parameters can be estimated in a valid fashion. To do this, grouped data is applied with intervals at the convergence points of the associated mission profiles. This way, it is assured that the respective mission profile usage for each of the profiles meets its expected value at the specified intervals and any variations in between intervals are smoothed out.

Next, plot the MTBF vs. Time, as shown next.

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4.12 Example 11 - Using Mission Profiles

Note that the plot shows both the Cumulative MTBF line and the Instantaneous MTBF line. To hide the Instantaneous MTBF line, choose Plot > Show/Hide Items. In the Show/Hide Items window that appears, clear the Instantaneous MTBF check box, then click OK. To plot the confidence bounds for the cumulative data, choose Plot > Confidence Bounds. In the Confidence Bounds Setup window that appears, do the following:

Select the Two-Sided option in the Sides area. Select the Function Type II (MTBF bounds on mode) option in the Type area. Clear the Instantaneous Line check box. Enter 90 in the Confidence Level field. The Confidence Bounds window will look like the one shown next.

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Click OK to close the window. The Plot window will look like the one shown next.

Close the Folio. Save the project as Mission Profile.rga7. Close the project.

4.13 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests

As shown in "Example 7 - Using the Crow Extended Model for Reliability Growth Test Planning" on page 48, the Crow Extended model is designed for analyzing the data from a single test phase. However, in many cases, testing for a system is conducted in multiple phases. The Crow Extended - Continuous Evaluation model is designed for analyzing data across multiple test phases. The 3-parameter Crow-Extended - Continuous Evaluation model is designed for the practical testing situation where you need the flexibility to apply corrective actions at the time of the failure or at any later time during the test, at the end of the test or at the next test phase. The model is free of the constraint that testing must be stopped and all BD modes must be corrected at time T, as in the Crow Extended model. The failure modes can be corrected during the test or when the testing is stopped to incorporate the fixes, or even not corrected at all at the end of the test phase. Based on this flexibility, the end of the testing time is also not predefined, and it can be continuously updated with new test data, and that is the reason behind the name "continuous evaluation." The model uses several event codes:

F indicates a failure time. I indicates the time at which a certain BD failure mode has been corrected. BD modes that have not received a corrective action by time T will not have an associated I event in the data set.

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4.13 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests

Q indicates a failure that was due to a quality issue, such as a bolt not being tightened down properly. You decide whether or not to include quality issues in the analysis by selecting or clearing the Include Q Events check box on the Analysis tab of the Folio's Control Panel. P indicates a failure that was due to a performance issue. You decide whether or not to include performance issues in the analysis by selecting or clearing the Include P Events check box on the Analysis tab of the Folio's Control Panel. AP indicates an analysis point. Analysis points can be shown in a multi-phase plot to track overall project progress and can be compared to an idealized growth curve. PH indicates the end of a test phase. Tests phases can be shown in a multi-phase plot to track overall project progress and can be compared to planned growth phases. X indicates that the data point should be excluded from the analysis. You can put an "X" in front of any other event code or it can be entered by itself.

The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Growth Planning Example.rga7."

4.13.1 Part 1: Using Growth Planning

For this example, which deals with a repairable system, you want to design a reliability growth program that contains three test phases. The first phase is planned to end at 3000 hours of cumulative test time, while the second phase will end at 6000 hours and the third phase will end at 11,000 hours.

Note: The cumulative test time may not be the same as calendar time. For example, if you test 30 units for 100

hours, then the calendar time will be 100 hours but the cumulative test time will be 3000 hours.

The average fix delay for the three phases are 1000, 1500 and 3700 hours, respectively. The average fix delay reflects how long it takes from the time when a failure mode is discovered in the test to the time when the corrective action is incorporated into the design and reliability growth is realized. These values are also entered in terms of test time rather than calendar time and they will be reflected in the idealized growth curve for the test plan. For this specific example, the average fix delay is shorter for early test phases, since, in this case, it is considered to be easier to implement changes in the test units in the early phases and longer in the later test phases when it is considered to be more difficult. The MTBF goal for the program is 350 hours. The Growth Potential (GP) design margin is considered to be 1.35. (The GP design margin is an amount by which the MTBF target exceeds the requirement or goal MTBF. This provides a "safety factor" to ensure that the requirement is met; the higher the GP design margin, the less risk there is in the program.) The average Effectiveness Factor is considered to be 0.6, based on experience with previous programs. The management strategy is to address at least 90% of all unique failure modes. The beta parameter for the rate of discovery of new failure modes (Discovery beta) is considered to be 0.7. (The discovery function represents the rate at which new, distinct failure modes are encountered during testing.) Based on these assumptions, you will create an overall growth planning model that shows the nominal and actual idealized growth curve and the planned growth MTBF for each phase. For this part, do the following:

Create a Growth Planning Folio. Define the growth planning goals.

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Solution

Create a new project and click Cancel in the New Data Sheet Setup window that displays. This will create a project with no folios. To create a Growth Planning Folio, choose Project > Add Growth Planning. The Growth Planning Folio displays.

Enter 3000, 6000 and 11000 for the Cumulative Phase Times and 1000, 1500 and 3700 for the Average Phase Delays, as shown next.

Click the Calculate icon.

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4.13 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests

The Planning Calculations window displays. Make the required inputs, as shown next, and then click Calculate.

As you can see, given the MTBF goal and design margin that you specified, along with the other required inputs to describe the planned reliability growth management strategy, the utility calculates the final MTBF that can be achieved along with other useful results.

Click OK to close the window. The planning information is now displayed in the Growth Planning Folio's Control Panel, as shown next.

Click the Plot icon in the Control Panel.

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The Growth Planning window looks like the one shown next.

The plot displays the MTBF vs. Time values for the three phases that you have planned for the test.

Close the Growth Planning Folio. Save the project as Growth Planning.rga7.

4.13.2 Part 2: Working with Failure Time Data from Multiple Test Phases

The following table gives the data from the three phases of testing. Note that due to the amount of information, the table extends to the following pages. Phase (Not in Event Time to Event Classification Mode the Interface) 1 F 1 A 1 1 F 302 BD 3000 1 F 450 BC 401 1 Q 534 A 5 1 F 599 BC 200 1 F 602 A 1 1 F 657 BD 5000 1 F 700 BC 400 1 F 800 BD 9000 1 AP 1000 1 F 1057 BC 600 1 F 1111 A 1 1 F 1151 BD 5000 1 F 1201 A 4 1 F 1237 BD 5000 1 F 1298 BC 400 1 AP 2000 1 F 2367 BD 8000 1 F 2401 A 1 1 F 2458 A 4 1 F 2667 BD 5000 1 F 2856 A 1

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Phase (Not in the Interface) 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Event PH F F X F F F F F AP F I F F F F AP F F F F PH P I AP F F F AP F F F F F F AP I F AP F F PH

Time to Event 3000 3121 3359 3400 3451 3501 3670 3703 3780 4000 4615 4689 4710 4750 4762 4915 5000 5075 5356 5658 5954 6000 6113 6959 7000 7352 7448 7847 8000 8169 8195 8200 8228 8306 8959 9000 9358 9916 10000 10083 10500 11000

Classification BD BC A A BC BD BC BD A BD BC A BC BD BC BC BD BD BD BD BD A A BC BD A BC BD BC BD BD A BD

Mode 5000 700 5 1 600 8000 100 5000 2 8000 700 4 400 1300 110 120 5000 1300 2000 1300 1400 2 3 160 1400 1 900 5000 400 5000 1500 2 9000

In this data set, you can see that I (implementation) events have been entered for some of the BD (delayed fix) failure modes. For example, the BD 8000 failure mode was first observed at 2367 cumulative test hours and then occurred again at 3670 hours. The I event at 4689 cumulative test hours indicates that the fix for this failure mode was implemented into all test units at that point. With this information, the Crow Extended - Continuous Evaluation model will be able to evaluate the impact of this fix without any additional input from the user. However, there are some BD failure modes in the data set that do not have associated I events in the data. For these modes, it is assumed that the fix either was not implemented or it was implemented between test phases. For those modes, the user must specify which phase the fix was implemented after (if any) and the effectiveness factor. The following table gives this information for the BD failure modes that

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did not have an associated I event during the three test phases. As you can see, the fixes for BD 3000 and BD 9000 still had not been implemented by the end of the test program but the fixes for BD 1400 and BD 1500 were implemented after the end of Phase 3. BD Mode 3000 9000 1400 1500 For this part, do the following:

Effectiveness Factor 0.75 0.6 0.67 0.71

Implemented at End of Phase Not Implemented Not Implemented Phase 3 Phase 3

Create a Standard Folio with a Data Sheet for the multi-phase Failure Times data type. Create the appropriate Data Sheet for multi-phase data. Calculate the parameters using the Crow Extended - Continuous Evaluation model. Plot the Growth Potential MTBF, Failure Mode Strategy, Rate of Discovery and Individual Mode MTBF plots. Generate the Event Report. Use the QCP to calculate the Discovery Rate and Parameter Bounds. Associate the Testing data and the Growth Planning data in a MultiPhase plot.

Solution

Choose File > User Setup. On the Calculations page, select Calculate Unbiased Beta, then click OK.

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4.13 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests

Create a new Standard Folio and a Data Sheet for multi-phase failure times data, as shown next.

Enter the data into the Data Sheet.

Note: Instead of typing the data by hand, you can open the Growth Planning Example.rga7 file, copy the data from it and then paste the data into your file.

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Your Data Sheet will look like the one shown next. (Please note that the following picture displays only 27 rows of data. Be sure to enter all of the data for this example as given in the table on page 100. Your Data Sheet will contain 64 rows of data.)

Go to the Standard Folio Control Panel's Analysis page by clicking the Analysis tab. Notice that the Include Q Events and Include P Events check boxes are selected by default. Clear the Include Q Events and Include P Events options. This excludes the Q (quality) and P (performance) events from the analysis. (If Include Q Events and Include P Events are selected those failures are treated as F-type failures for calculation purposes.)

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4.13 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests

By omitting, or "commenting out," these events from the analysis, you indicate that the problems are not reliability-related, but rather are quality and/or performance issues.

Return to the Standard Folio Control Panel's Main page. Enter the effectiveness factors for the BD modes that did not have associated I events in the data set and specify their implementation times, as shown next.

Now calculate the parameters using the Crow Extended - Continuous Evaluation model, as shown next.

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Next, plot the Growth Potential MTBF, as shown next.

The Growth Potential MTBF plot displays three lines: the demonstrated MTBF, the projected MTBF and the growth potential MTBF. The demonstrated MTBF line represents the MTBF at the end of the test without any corrective actions. The projected MTBF line displays the estimated MTBF after the delayed corrective actions have been implemented. The growth potential MTBF line represents the maximum achievable MTBF based on the current management strategy. If the MTBF goal is higher than the Growth Potential line, then this indicates that the current design cannot achieve the desired goal and a redesign or change of goals may be required. For this example, the goal MTBF of 350 hours is well within the growth potential and is expected to be achieved after the implementation of the delayed BD fixes.

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4.13 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests

Plot the Average Failure Mode Strategy, as shown next.

The "Unseen" modes percentages are based on the rate of discovery of the failure modes in the data. This gives an estimate of how many new failure modes you may find if you continue to test. While this is not a guarantee that you will see new modes, it is possible based on the rate at which you discovered the current ones.

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Plot the Individual Mode MTBF bar chart, as shown next.

This chart shows the MTBF for the individual modes seen before and after the test. Since the modes BD 1400, BD 1500, BD 3000 and BD 9000 received delayed fixes at the end of the test, as specified in the Effectiveness Factors window, they show an increase in their individual MTBF values. The BD modes that had an "I" event (an implemented fix) during the test are treated as BC modes (corrective action implemented during the test) for calculation purposes so they do not show a jump in the MTBF after the end of the test.

Return to the Data Sheet. Now create the Event Report. To do this, choose Data > Event Report or click the Event Report icon.

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4.13 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests

The Event Report window displays, as shown next.

The Event Report lists all of the unique failure modes that were reflected in the test data. The report includes the mode ID and classification along with the time of the first failure and the total number of failures due to each mode. The last three columns in this report are applicable only for BD failure modes that were not fixed at a specific time during one of the test phases (i.e. without an associated "I" event). The additional columns present the Effectiveness Factors defined for these modes and which phase the fix was implemented after (if any). The Effectiveness Factor is not considered in the analysis until the point at which the fix has been implemented and reliability growth occurs. Prior to the implementation of the fix, this is called the "Nominal EF" and the "Actual EF" for analysis purposes is 0. After the implementation of the fix, the "Nominal EF" and "Actual EF" are the same.

Close the Event Report window. Next, open the QCP. On the Multi-Phase Calculations page, make the following selections/inputs:

Options for Calculations: Discovery Rate Additional Required Information:

Time: 1000 Type: Two-Sided Confidence Level: 0.9

Confidence Bounds:

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Click Calculate to obtain the results, as shown next.

This shows the rate of discovery of new unseen BD modes at 1000 hours is 0.0011 per hour.

Next, to view the two-sided parameter bounds for Beta, click the Parameter Bounds icon.

The Parameter Bounds are displayed in the Results Panel.

This shows that both Beta bounds are less than 1, which indicates that there is growth in the system.

Close the Results window. Close the QCP.

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4.13 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests

Next, you will create a MultiPhase plot and compare the Standard Folio with the Growth Planning Folio to track the developmental test data and how closely it fits to the overall reliability growth program plan.

Choose Project > Add Additional Plot > Add MultiPhase Plot. The MultiPhase Plot Wizard window displays.

Select Multi-Phase on the first page of the wizard, then click Next. In the Multi-Phase Data Sheet area, click ... to open the Data Sheet Selection window. Click the Data 1 check box, as shown next.

Click OK to select the Data 1 Folio. In the Planning Folio, click ... and, in the Select Planning Folio window, select Planning Data Folio, then click OK.

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The Multi-Phase Plot Wizard will look like this:

Click Finish. The MultiPhase Plot window displays. In the Set Phases area, first clear all check boxes, then, in the Phases area, select the Phase Termination Line check box. In the Analysis Points area, select the Demonstrated, Projected and Growth Potential check boxes. In the Planning area, select the Nominal Idealized and Actual Idealized check boxes. In the Scaling area, clear the X­Axis check box. Next, enter 0 for the lower X-axis and 11000 for the upper X-axis, then press ENTER.

The plot show the Nominal and Actual Planning curves as well as the actual test data, in terms of analysis points of the demonstrated, projected and growth potential MTBF values. The phase termination lines are also shown. The plot also demonstrates that the MTBF goal is met at the end of the last phase.

Close the MultiPhase Plot window.

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4.13 Example 12 - Working with MultiPhase Tests, Growth Planning and Design of Reliability Tests

Close the Folio. Save the project.

4.13.3 Part 3: Using Design of Reliability Tests to Demonstrate the Reliability of a System

In Parts 1 and 2 you used the Crow Extended - Continuous Evaluation model to track the developmental test data and evaluate how closely it fit the overall reliability growth program plan. In this case, the multi-phase analysis shows that the target MTBF goal was within the target range and achieved after the implementation of delayed fixes. Now you will assume that the developmental testing phase is complete and that a demonstration phase will be performed to assure customers that the MTBF for the final product has been reached before shipping. As stated in Part 1, the MTBF goal was 350 hours. You need to design a reliability demonstration test to demonstrate this goal for the final product and provide your management with an estimate of the total number of units that should be tested. You can do this by using the new Repairable Systems - Design of Reliability Tests utility in RGA 7. Since the product is assumed to be stable, with no more developmental changes, the assumed value for Beta is 1. You will use a confidence level of 95%. You also know that because of scheduling constraints, you can afford to spend only about 1000 test hours per unit. You also decide to allow for a maximum of 3 total failures across all systems being observed during the test. Note that this example is for a repairable system and therefore it is not appropriate to use the parametric binomial, non-parametric binomial or exponential chi-squared methods that are typically used for designing reliability demonstration tests for non-repairable items. Instead, you can use a method based on the nonhomogeneous Poisson process that is suitable for tests involving repairable systems. For this part, do the following:

Open the DRT utility and make the required inputs. View the results. Consider a range of other test options and plot the results.

Solution

To open the utility, choose Tools > Repairable Systems DRT or click the Repairable Systems DRT icon.

The Repairable Systems - Design of Reliability Tests window displays.

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Set the required inputs as shown next:

Click Calculate. The results indicate that you will need to test 3 units for 1000 hours each in order to demonstrate a cumulative MTBF of 350 hours with 95% confidence. Click Plot to open the Repairable Systems DRT Results window, then click the Calculate icon. The table shows a range of other options for the number of units and allowable failures. For example, if you were to test more than 4 units, e.g. 6 units, then you can decrease your testing time to approximately 453 hours and still demonstrate the MTBF goal with no more than 3 failures.

Notice that the table is based on the values set in the Table/Plot Setup area. You define the range of results you want to generate there. While this example uses the default values, you can experiment with different values to see what other options are possible.

Click the Plot icon to display the plot.

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4.14 Example 13 - Fielded Repairable System Data Analysis

Click the Select Failures check box to display the plots for all defined numbers of failures.

Close the Repairable Systems DRT Results window and close the Repairable Systems - Design of Reliability Tests window. Save the project. Close the project. Choose File > User Setup. On the Calculations page, clear the Calculate Unbiased Beta check box, then click OK.

4.14 Example 13 - Fielded Repairable System Data Analysis

This example is based on the data given in the article "Graphical Analysis of Repair Data" by Dr. Wayne Nelson, published in the Reliability Edge 3, no. 3 (2002): 16-18. The reliability growth models available in the RGA software also can be applied for repairable systems analysis. This approach allows you to calculate metrics of interest without the detailed data sets that would normally be required for that type of analysis. The following data set represents repair data on an automatic transmission from a sample of 34 cars. Assume that the objective is to estimate the number of warranty claims for a 36,000 mile warranty policy for an estimated fleet of 35,000 vehicles. Car 24 26 27 Mileage (+ latest mileage observed) 7,068 28 48 26,744+ 13,809+ 1,440 29,834+

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Car 29 31 32 34 35 98 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 129 130 131 132 133

Mileage (+ latest mileage observed) 530 21,762+ 14,235+ 1,388 21,401+ 21,876+ 5,094 21,691+ 20,890+ 22,486+ 19,321+ 21,585+ 18,676+ 23,520+ 17,955+ 19,507+ 24,177+ 22,854+ 17,844+ 22,637+ 375 19,403+ 20,997+ 19,175+ 20,425+ 22,149+ 21,144+ 21,237+ 14,281+ 8250 19,250 21,974+ 21,888+ 19,607+ 18,228+ 21,133+ 25,660+

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4.14 Example 13 - Fielded Repairable System Data Analysis

Do the following:

Create a Standard Folio with a Data Sheet for the Repairable data type. Calculate the parameters using the Power Law model. Plot the instantaneous Failure Intensity vs. Time. Plot the cumulative Number of Failures vs. Time. Use the QCP to determine the number of warranty claims for a 36,000 mile warranty policy for an estimated fleet of 35,000 vehicles.

Solution The file for this example is located in the Training Guide folder in your application directory (e.g. C:\Program Files\ReliaSoft\RGA7\Training Guide) and is named "Repairable System Example.rga7."

Create a new project with a Standard Folio and a Data Sheet for fielded repairable systems, as shown next.

For this example, the start time for all cars is 0. The end time is the latest mileage observed for the car. The failure times are the car mileage at each transmission repair.

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Enter the data into the Data Sheet, using the Advanced System View, as shown next (with the sheet for Car 24 visible and the data for the other cars on subsequent sheets).

Now calculate the parameters using the Power Law model, as shown next.

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4.14 Example 13 - Fielded Repairable System Data Analysis

The beta parameter of the power law model is estimated to be 0.3420, which indicates a rapidly decreasing failure intensity (infant mortality).

This also can be shown by creating the Failure Intensity vs. Time plot, as shown next. Please note that you will have to change the scaling to get the plot to look like the one shown next. To do this, clear the Use Logarithmic Axes check box and the Y­Axis check box in the Scaling area on the Plot Sheet Control Panel. Next, enter 0 for the lower Y-axis and 0.00016 for the upper y-axis, then press ENTER.

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Next, enter 1 in the upper Y-Axis scaling box and then plot the Cumulative Number of Failures, as shown next.

Use the QCP to obtain the expected number of failures at 36,000 miles, as shown next.

The model predicts that 0.3552 failures per system will occur by 36,000 miles. This means that for a fleet of 35,000 vehicles, the expected warranty claims are 0.3552 x 35,000 = 12,432.

Close the QCP.

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4.14 Example 13 - Fielded Repairable System Data Analysis

Close the Folio. Save the project as Repairable System.rga7. Close the project.

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