A note on a difficulty inherent in estimating reliability from stress–strength relationships

Abstract

This note calls attention to a difficulty which arises frequently in the application of stress‐strength methods in reliability theory. This difficulty has led to unanticipated catastrophic failures in a number of applications.

Statistical inference for P(X<Y)

“…Thus P(X <Y ), the so-called stress-strength model in engineering, measures the reliability of the component. The reliability is usually very close to 1, commented by Harris and Soms [1], because often the 'useful' life of a device is sufficiently long.…”

“…As in Newcombe [22], we express small data sets by strings of Xs and Ys. For example, XY Y XY in Table IX denotes a data set in which n 1 = 2, n 2 = 3 and X (1) <Y (1) <Y (2) <X (2) <Y (3) . The numerical results are presented in 273 characteristics.…”

Should Probabilistic Design Replace Safety Factors?

“…Although the central parts of the statistical distributions used in these models are fairly wellknown, their tails can only be inferred under assumptions about the mathematical structure of the distribution that lack direct empirical evidence. This is the so-called distribution arbitrariness (Ditlevsen 1994;Harris and Soms 1983). Extreme value analysis often involves extrapolation to values beyond the largest or smallest observed value in order to assign probabilities to extreme events.…”