Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach
Metadatos
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MDPI
Materia
Markovian arrival process Phase-type distribution Multiple failures Multiple replacements K-out-of-N system
Fecha
2022-06-02Referencia bibliográfica
Montoro-Cazorla, D.; Pérez-Ocón, R. Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach. Mathematics 2022, 10, 1902. [https://doi.org/10.3390/math10111902]
Resumen
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.