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Advances in Decision Sciences
Volume 2012, Article ID 289035, 14 pages
http://dx.doi.org/10.1155/2012/289035
Research Article

An Allocation Scheme for Estimating the Reliability of a Parallel-Series System

1Department of Physics, University of Science and Technology of Oran-Mohamed Boudiaf (USTOMB), BP 1505 El M'Naouer, Oran 31000, Algeria
2Department of Mathematics, University of Oran, BP 1524 El M'Naouer, Oran 31000, Algeria

Received 28 April 2012; Revised 28 July 2012; Accepted 8 October 2012

Academic Editor: Wai Ki Ching

Copyright © 2012 Zohra Benkamra et al. 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 give a hybrid two-stage design which can be useful to estimate the reliability of a parallel-series and/or by duality a series-parallel system. When the components' reliabilities are unknown, one can estimate them by sample means of Bernoulli observations. Let be the total number of observations allowed for the system. When is fixed, we show that the variance of the system reliability estimate can be lowered by allocation of the sample size at components' level. This leads to a discrete optimization problem which can be solved sequentially, assuming is large enough. First-order asymptotic optimality is proved systematically and validated Monte Carlo simulation.