A load share model for non-identical components of a k-out-of-m system

Abstract

We consider a k-out-of-m load sharing system when the lifetimes of the components are not necessarily identically distributed random variables. For such systems, a model for the load sharing phenomenon through the exponentiated conditional survival functions of ordered failure times is proposed. This model is more general than the load sharing model with identically distributed component lifetimes and leads to a different family of distributions for ordered random variables. A general expression for the reliability of the system is given. The computations of the reliability for a two component parallel load sharing system corresponding to the exponential and Weibull distributions are discussed. For illustrative purpose, we discuss the inference procedures for a two component parallel load sharing system corresponding to the exponential distributions. A simulation study is carried out to assess the proposed estimation and testing procedures. The applicability of the proposed load sharing model is shown through two data sets.