Effective procedure of verifying stochastic ordering of system lifetimes. (16th January 2019)

• Record Type: Journal Article
• Authors: Rychlik, Tomasz; Navarro, Jorge; Rubio, Rafael
• Is Part Of: Journal of applied probability. Volume 55:Number 4(2018)
• Page Start: 1261
• Page End: 1271
• Publication Date: 2019-01-16
• Subjects: Coherent system, -- mixed system, -- Samaniego signature, -- stochastic order; Primary 60E15, -- 62N05, -- Secondary 62G30; 519.2
• DOI: 10.1017/jpr.2018.84
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: The Samaniego signature is a relevant tool for studying the performance of a system whose component lifetimes are exchangeable. It is well known that the stochastic ordering of the signatures of two systems implies the same for the respective system lifetimes. We prove that the reverse claim is not true when the component lifetimes are independent and identically distributed. There exist small proportions of systems with stochastically ordered lifetimes whose signatures are not ordered. We present a simple procedure in order to check whether the system lifetimes are stochastically ordered even if their signatures are not comparable.