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MANUAL ON STATISTICAL PLANNING AND ANALYSIS FOR FATIGUE EXPERIMENTS

Sponsored by Committee on Publications AMERICAN SOCIETY FOR TESTING AND MATERIALS

ASTM SPECIAL TECHNICAL PUBLICATION 588 R. E. Little University of Michigan, Dearborn Campus Assisted by E. H. Jebe Environmental Research Institute of Michigan

List price $15.00 04-588000-30

AMERICAN SOCIETY FOR TESTING AND MATERIALS 191 6 Race Street, Philadelphia, Pa. 191 03

(~) BY AMERICAN SOCIETY FOR TESTING AND MATERIALS 1975 Library of Congress Catalog Card N u m b e r : 75-13060.

NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication.

Printed in Lutherville-Tlmonium, Md November 1975

Foreword

In 1949 Committee E-9 on Fatigue published ASTM STP 91, Manual on Fatigue Testing. Seven years later E-9 published ASTM STP 91A, A Guide for Fatigue Testing and the Statistical Analysis of Fatigue Data. Both publications were modest efforts, presenting what was then considered the current practice and views of Committee E-9 members. Subsequently effort was expended intermittently in Committee E-9 for over a decade in various attempts to revise and expand these STP's to reflect advances in the state of the art and in statistical analyses. This activity ultimately led to ASTM STP 566, Handbook of Fatigue Testing, and to the present Manual on Statistical Planning and Analysis for Fatigue Experiments. The present manual is the last of several attempts to revise ASTM STP 91A to include more information on statistical planning of fatigue experiments. The reader will find in the first two chapters an effort to present and explain the basic terminology and fundamental concepts of planned experiments, and to indicate the necessary steps in a professional statistical analysis (using a simple randomized complete block fatigue test program for purposes of illustration). The last two chapters cover statistical planning of S-N and fatigue strength (response) tests, with specific recommendations regarding specimen replication; and nonparametric comparison of two censored life samples, with extensive computer tables. Overall, the intent is to provide sufficient information to permit fatigue investigators to conduct fatigue test programs with statistically planned organizational structures. In the acknowledgments at the end of this manual I have expressed my appreciation to those individuals who contributed to this manual. As Chairman of Subcommittee E09.06, I would also like to express my sincere appreciation to all those individuals who worked on various antecedents to the present manual.

R. E. Little, Chairman ASTM Committee E09.06 on Statistical Aspects of Fatigue

Related ASTM Publications

Handbook of Fatigue Testing, STP 566 (1974), $17.25, 04-566000-30 The Influence of State of Stress on Low-Cycle Fatigue of Structural Materials: A Literature Survey and Interpretive Report, STP 549 (1974), $5.25, 04-549000-30 Fatigue at Elevated Temperatures, STP 520 (1973), $45.50, 04-520000-30

A Note of Appreciation to Reviewers

This publication is made possible by the authors and, also, the unheralded efforts of the reviewers. This body of technical experts whose dedication, sacrifice of time and effort, and collective wisdom in reviewing the papers must be acknowledged. The quality level of ASTM publications is a direct function of their respected opinions. On behalf of ASTM we acknowledge with appreciation their contribution.

A S T M Committee on Publications

Editorial Staff

Jane B. Wheeler, Managing Editor Helen M. Hoersch, Associate Editor Charlotte E. Wilson, Senior Assistant Editor Ellen J. McGlinchey, Assistant Editor

Contents

Introduction Chapter 1--Fundamental Concepts in the Statistical Planning (Design) of Fatigue Experiments Introduction Organizational Structure of Planned Experiments Paired Comparison Test Program Elementary Uniformity Trial Test Program Completely Randomized Design (CRD) Test Program Ramdomized Complete Block (RCB) Test Program Elementary Split Plot Test Program Summary and Perspective Appendix Chapter 2--Necessary Steps in Statistical Analysis for Planned Experiments Introduction Necessary Steps in Analysis of Variance (ANOVA) for a Paired Comparison Program Step 1 : Write the Mathematical Model Step 2: Plot the Transformed Data Step 3: Explain the Data (by appropriate parameter estimation) Step 4: Statistical Analysis (generally analysis of variance (ANOVA)) Summary Chapter 3--Planning S - N and Response Tests Introduction Conventional S - N Tests Preliminary and Exploratory Tests Replicated S - N Tests Replication Guidelines for S - N Testing Discussion of Guidelines Fatigue Strength and Fatigue Limit Tests Probit Method Up-and-Down Method Two-Point Method vii 1

3 3 6 6 9 16 18 25 28 28 34 34 34 34 38 39 41 45 46 46 46 46 49 51 52 52 52 54 54

viii

CONTENTS

Chapter 4--Distribution-Free Statistical Tests for Comparing Two Censored Life Samples (in a CRD Test Program) Nomenclature Introduction Complete (uncensored) Data Censored Data Test of Hypothesis Alternative Hypotheses Complete (uncensored) Data Mann and Whitney's U Statistic Mann and Whitney's Tables Censored Data Run-Outs Halperin's Un Statistic Halperin's Tables Accelerated Comparisons Young's Ur Statistic Young's Tables Appendix I Appendix II References Acknowledgments

61 61 61 62 62 63 64 64 65 65 66 66 71 71 72 112 113 129 145 147 149

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