Mean Past and Mean Residual Life Functions of a Parallel System with Nonidentical Components

Abstract

One of the most important types of system structures is the parallel system. Asadi (2006) and Asadi and Bayramoglu (2005), proposed new definitions for the mean past lifetime (MPL) and the mean residual life function (MRL) of a parallel system as follows, respectively: where T 1:n , T 2:n ,…, T n:n are the ordered statistics corresponding to T 1, T 2,…, T n the lifetimes of the components that are independent and identically distributed and r ≤ n. They obtained some of their properties. In this article, most of those properties are extended for the case where T i 's are independent but not identical. It is shown that and are increasing and decreasing functions of n and r, respectively. A comparison between two parallel systems are made based on their MPL's. A characterization of the uniform distribution is given based on . It is also shown that is a decreasing function of t when the lifetimes of components are increasing failure rate (IFR). Finally, an upper bound for and a lower bound for are given.