Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach

Delia Montoro-Cazorla and Rafael Pérez-Ocón
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Delia Montoro-Cazorla: Department of Statistics and Operational Research, University of Jaén, 23071 Jaén, Spain
Rafael Pérez-Ocón: Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain

Mathematics, 2022, vol. 10, issue 11, 1-13

Abstract: An N-system with different units submitted to shock and wear is studied. The shocks cause damage and, eventually, simultaneous failures of several units. The units can also fail due to internal failures. At random times, the system is inspected, and the down units are simultaneously replaced by identical ones. The arrival of shocks is governed by a Markovian arrival process. The operational times and the interarrival times between inspections follow phase-type distributions. The generator of the multidimensional Markov process modeling the system is constructed. This is performed introducing indicator functions for the different transition rates among the units using the algorithm of Kronecker. This is a general Markov process that can be applied for modeling different reliability systems depending on the structure of the units and how the systems operate. The general model is applied to the study of k-out-of-N systems, calculating the main performance measures. A practical example is presented showing the approximation of the model to a system with units following different Weibull distributions.

Keywords: Markovian arrival process; phase-type distribution; multiple failures; multiple replacements; k-out-of-N system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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