Estimating the Median Fatigue Limit for Very Small Up-and-Down Quantal Response Tests and for S-N Data with Runouts

Abstract

Much basic fatigue data may be categorized for analytical purposes as small sample quantal response data. For example, both small sample up-and-down test outcomes and most S-N data fall into this category. But reliable median fatigue-limit estimates for small samples are not directly available using large sample statistical formulas. Rather, small sample estimates must be examined carefully regarding both their variability under repeated sampling and their “sensitivity” relative to various analytical methods and assumptions. The variability of small sample response estimates has been studied by Dixon and others. This paper considers the sensitivity of these estimates to such key assumption alternatives as, for example, minimum chi square analysis versus maximum likelihood analysis, and an underlying extreme value (smallest) response distribution versus a normal response distribution. Engineering assessment of the “accuracy” of the estimated median fatigue limit requires careful consideration of both its statistical variability and its analytical sensitivity as established herein.