Construction of optimal reliability test plans for multi-state coherent systems of type 1

Abstract

This research article deals with construction of system based optimal reliability test plans for Multi-state Coherent Systems (MCSs) of Type 1 having $(M+1)$ states. The development of optimal reliability test plans for the MCS of Type 1 is based on the framework of multivariate counting process and a simple version of the multivariate central limit theorem. It may be noted that four reliability test plans using four combinations of two theoretical decision rules (TDR1, TDR2) and two data based decision rules (DDR1, DDR2), taken one from each category, have been proposed in this paper. Each of these test plans is demonstrated for $M=2$ and for a Farlie-Gumbel-Morgenstern (F-G-M) distribution using (i) a multi-state coherent series system, (ii) a multi-state coherent parallel system, each MCS consisting of two components, and (iii) a combination of series and parallel multi-state coherent system consisting of three components. The reliability test plan constructed using (TDR2, DDR2) combination turns out to be more economical than those constructed using (TDR1, DDR1), (TDR1, DDR2) and (TDR2, DDR1) decision rules.

Keywords:

• Multi-state coherent system of type 1
• multivariate central limit theorem
• multivariate counting processes
• reliability test plan

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