Reliability Properties of Series and Parallel Systems under Equilibrium Distribution

Equilibrium distribution finds various applications in reliability, stochastic processes, repairable systems and many areas of applied probability such as renewal risk model etc. This paper deals with some of the reliability properties of reliability structures under equilibrium random variable(s). The likelihood ratio ordering for the series and parallel systems has been established under equilibrium. Further, the log-concavity properties of series and parallel systems having independently and identically distributed (i.i.d.) components under the condition of equilibrium have been studied.