Diagonally Dependence and Its Applications in Series and Parallel Systems

Abstract

Abstract: In many practical applications in statistics and particularly in system reliability studies, the independence assumption is not valid and realistic. In this paper we consider the effect of dependence between lifetimes of system components on the reliability and the mean time to failure (MTTF) of the system. We want to know if the degree of dependency(correlation) between system component lifetimes in some sense is increased(decreased), whether the system reliability will be increased(decreased) or not. Obviously it depends on the structure of the system and we show at least in series and parallel systems that the reliability of these systems have quite different behaviors. For this we first define a new concept of dependency and call it diagonally dependence and then use it for stochastic ordering and redundancy allocation problems in series and parallel systems. Finally we show that how the diagonally dependence is helpful to prove some well known results in literatures under more weak conditions.