A family of distributions to model load sharing systems

The main characteristic of a load sharing system is that after the failure of one component the surviving components have to shoulder extra load and hence are prone to failure at an earlier time than what is expected under the original model. In others, the failure of one component may release extra resources to the survivors, thus delaying the system failure. In this paper we consider such m component systems and some observation schemes and identifiability issues under them. Then we construct a general semiparametric multivariate family of distributions which explicitly models this phenomenon through proportional conditional hazards. We suggest estimates for the constant of proportionality. We propose a nonparametric test for the hypothesis that the failures take place independently according to the common distribution against the alternative hypothesis that the second failure takes place earlier than warranted, study its properties and illustrate its use.