On the Survival Time of a Duplex System: A Sokhotski-Plemelj Problem

[摘要] We analyze the survival time of a renewable duplex system characterizedby warm standby and subjected to a priority rule. In orderto obtain the Laplace transform of the survival function, we employa stochastic process endowed with time-dependent transition measuressatisfying coupled partial differential equations. The solution procedureis based on the theory of sectionally holomorphic functions combinedwith the notion of dual transforms. Finally, we introduce a securityinterval related to a prescribed security level and a suitable risk criterionbased on the survival function of the system. As an example, weconsider the particular case of deterministic repair. A computer-plottedgraph displays the survival function together with the security intervalcorresponding to a security level of 90%.

[学科分类] 应用数学