MANUAL ON STATISTICAL PLANNING AND ANALYSIS FOR FATIGUE EXPERIMENTS

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2 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 $ AMERICAN SOCIETY FOR TESTING AND Race Street, Philadelphia, Pa MATERIALS

3 (~) BY AMERICAN SOCIETY FOR TESTING AND MATERIALS 1975 Library of Congress Catalog Card Number: 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

4 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

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

6 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 STM Committee on Publications

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

8 Contents Introduction 1 Chapter 1--Fundamental Concepts in the Statistical Planning (Design) of Fatigue Experiments 3 Introduction 3 Organizational Structure of Planned Experiments 6 Paired Comparison Test Program 6 Elementary Uniformity Trial Test Program 9 Completely Randomized Design (CRD) Test Program 16 Ramdomized Complete Block (RCB) Test Program 18 Elementary Split Plot Test Program 25 Summary and Perspective 28 Appendix 28 Chapter 2--Necessary Steps in Statistical Analysis for Planned Experiments 34 Introduction 34 Necessary Steps in Analysis of Variance (ANOVA) for a Paired Comparison Program 34 Step 1 : Write the Mathematical Model 34 Step 2: Plot the Transformed Data 38 Step 3: Explain the Data (by appropriate parameter estimation) 39 Step 4: Statistical Analysis (generally analysis of variance (ANOVA)) 41 Summary 45 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

9 viii CONTENTS Chapter 4--Distribution-Free Statistical Tests for Comparing Two Censored Life Samples (in a CRD Test Program) 61 Nomenclature 61 Introduction 61 Complete (uncensored) Data 62 Censored Data 62 Test of Hypothesis 63 Alternative Hypotheses 64 Complete (uncensored) Data 64 Mann and Whitney's U Statistic 65 Mann and Whitney's Tables 65 Censored Data 66 Run-Outs 66 Halperin's Un Statistic 71 Halperin's Tables 71 Accelerated Comparisons 72 Young's Ur Statistic 112 Young's Tables 113 Appendix I 129 Appendix II 145 References 147 Acknowledgments 149