Statistical uncertainty in the fatigue threshold staircase test method

Kim Wallin (Corresponding Author)

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

Abstract

A popular method of estimating a materials fatigue threshold is the so called staircase test, where a relatively small number of test specimens are used to estimate the materials fatigue strength. Usually the test results are analysed using the maximum likelihood method (MML), either directly or by using the approximation by Dixon and Mood. There has been several studies looking at the bias and confidence of both the mean estimate as well as the standard deviation, but a comprehensive study of the reliability of the estimate has been missing. Here, the accuracy of the MML estimate is studied in detail. It is shown that the MML method is not suitable to estimate the scatter of the fatigue strength from a staircase test. An optional analysis method allowing for a better estimate of confidence bounds, based on binomial probability is presented. Even this new analysis method suffers from similar problems as the MML estimate. The conclusion is that the staircase test cannot be used to estimate the scatter in fatigue strength.
Original languageEnglish
Pages (from-to)354-362
Number of pages9
JournalInternational Journal of Fatigue
Volume33
Issue number3
DOIs
Publication statusPublished - 2011
MoE publication typeA1 Journal article-refereed

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Fatigue
Maximum likelihood
Fatigue of materials
Uncertainty
Maximum Likelihood Method
Fatigue Strength
Estimate
Scatter
Confidence Bounds
Mood
Standard deviation
Confidence
Fatigue strength
Approximation

Keywords

  • Staircase test
  • fatigue
  • threshold stress
  • maximum likelihood
  • binomial probability

Cite this

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Statistical uncertainty in the fatigue threshold staircase test method. / Wallin, Kim (Corresponding Author).

In: International Journal of Fatigue, Vol. 33, No. 3, 2011, p. 354-362.

Research output: Contribution to journalArticleScientificpeer-review

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AB - A popular method of estimating a materials fatigue threshold is the so called staircase test, where a relatively small number of test specimens are used to estimate the materials fatigue strength. Usually the test results are analysed using the maximum likelihood method (MML), either directly or by using the approximation by Dixon and Mood. There has been several studies looking at the bias and confidence of both the mean estimate as well as the standard deviation, but a comprehensive study of the reliability of the estimate has been missing. Here, the accuracy of the MML estimate is studied in detail. It is shown that the MML method is not suitable to estimate the scatter of the fatigue strength from a staircase test. An optional analysis method allowing for a better estimate of confidence bounds, based on binomial probability is presented. Even this new analysis method suffers from similar problems as the MML estimate. The conclusion is that the staircase test cannot be used to estimate the scatter in fatigue strength.

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