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 component reliabilities are unknown as well as the total numbers of
units allowed to be tested in each subsystem. When a total sample size is fixed
large, asymptotic optimality is proved systematically and validated via Monte
Carlo simulation.Comment: 16 pages, 4 figure

Benkamra, Zohra

Terbeche, Mekki

Tlemcani, Mounir

Advances in Decision Sciences

English

arXiv

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 T be the total number of observations allowed for the system. When T is fixed, we show that the variance of the system reliability estimate can be lowered by allocation of the sample size T at components' level. This leads to a discrete optimization problem which can be solved sequentially, assuming T is large enough. First-order asymptotic optimality is proved systematically and validated T Monte Carlo simulation

Zohra Benkamra

Mekki Terbeche

Mounir Tlemcani

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

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 T be the total number of observations allowed for the system. When T is fixed, we show that the variance of the system reliability estimate can be lowered by allocation of the sample size T at components' level. This leads to a discrete optimization problem which can be solved sequentially, assuming T is large enough. First-order asymptotic optimality is proved systematically and validated T Monte Carlo simulation.</jats:p

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An allocation scheme for estimating the reliability of a parallel-series
  system

An allocation scheme for estimating the reliability of a parallel-series system

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