Stochastic Comparisons of Lifetimes of Used Standby Systems

Abstract

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold standby system with age t and the lifetime of a cold standby system consisting of used components with age t using the likelihood ratio order and the usual stochastic order. We use illustrative examples to explore the results presented.

Keywords

• likelihood ratio order
• usual stochastic order
• cold standby system
• log-concave
• log-convex
• lifetime