Comparisons of Mixed Systems Using Mean Vitality Function

Abstract

‎The concept of system signature is widely used for comparing of mixed (coherent) systems‎. ‎In practical situations‎, ‎it is usually impossible to compare mixed systems‎. ‎To do this‎, ‎some partial orders are considered in the literature‎. ‎In this paper‎, ‎we define a new concept of stochastic order for comparing mixed systems based on mean vitality function‎. ‎We assume that component lifetimes of competing systems are independent and identically distributed (iid) with a common distribution function‎. ‎The obtained results are extended for comparing systems in which the component lifetimes are iid while the common component lifetime distributions are not identical‎. ‎Some illustrative examples are also given‎.