Assessing how the dependence structure affects the reliability parameter of the strength-stress model

The stress-strength model is a basic modeling tool in reliability analysis. In simple terms, it considers a component (or a system) with an intrinsic strength Y , which is subjected to a stress X; the component works if and only if Y is greater than X. If stress and strength are regarded as random variables, then the probability that the component works is given by P(X<Y ) and is usually called “reliability parameter”. Statistical independence is usually assumed between the two random variables X and Y : for this case, the literature on this topic is particularly rich. This strong assumption, in fact, makes the calculation and estimation of the reliability parameter R more tractable. However, this hypothesis is not always verified in practice, and this translates into an over- or under-estimation of R. To avoid this drawback, statistical dependence can be introduced and modeled between X and Y , for example resorting to copulas. In some recent works, the problem of computing and estimating R is considered when the stress and strength variables, belonging to the same parametric family of distributions, are linked by a specific copula. In this work, we further consider the computational issues related to this copula approach applied to the stress-strength model, when other families of copulas are selected. A sort of sensitivity analysis is performed in order to assess how the value of the reliability parameter is affected by the choice of the copula binding X and Y together and of its parameters. As a limit case, we consider the situation where no information on the dependence structure of the stress and strength margins is available and try to provide lower and upper bounds for R.