Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 905721, 13 pages
doi:10.1155/2008/905721
Research Article
On the Survival Time of a Duplex System: A Sokhotski-Plemelj Problem
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.
Abstract
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%.