3 Stress-strength models for reliability

Abstract

When ascertaining the reliability of equipment or the viability of a material, it is also necessary to take into account the stress conditions of the operating environment. That is, uncertainty about the actual environmental stress to be encountered should be modeled as random. The terminology stress-strength model makes explicit that both stress and strength are treated as random variables. In the simplest stress-strength model, X is the stress placed on the unit by the operating environment and Y is the strength of the unit. A unit is able to perform its intended function if its strength is greater than the stress imposed upon it. Reliability is defined as the probability that the unit is strong enough to overcome the stress. This model has found an increasing number of applications in civil, mechanical, and aerospace engineering. The chapter discusses the nonparametric inference about stress–strength reliability, nonparametric inference about stress–strength reliability, the normal and the Weibull stress–strength models, extensions of the basic stress–strength model, and Bayesian inference procedures.