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

Abstract EN

We analyze the survival time of a renewable duplex system characterized by warm standby and subjected to a priority rule.

In order to obtain the Laplace transform of the survival function, we employ a stochastic process endowed with time-dependent transition measures satisfying coupled partial differential equations.

The solution procedure is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms.

Finally, we introduce a security interval related to a prescribed security level and a suitable risk criterion based on the survival function of the system.

As an example, we consider the particular case of deterministic repair.

A computer-plotted graph displays the survival function together with the security interval corresponding to a security level of 90%.