Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 905721, 13 pages
Research Article

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

Edmond J. Vanderperre

Department of Decision Sciences, University of South Africa, P.O. Box 392, Pretoria 0003, South Africa

Received 9 June 2008; Accepted 1 September 2008

Academic Editor: Karl Sigman

Copyright © 2008 Edmond J. Vanderperre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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%.