Constructing a Markov process for modelling a reliability system under multiple failures and replacements. (May 2018)

• Record Type: Journal Article
• Authors: Montoro-Cazorla, Delia; Pérez-Ocón, Rafael
• Is Part Of: Reliability engineering & system safety. Volume 173(2018)
• Page Start: 34
• Page End: 47
• Publication Date: 2018-05
• Subjects: Markov process -- Reliability system -- Multiple failures -- Availability -- Multiple replacements; Reliability (Engineering) -- Periodicals; System safety -- Periodicals; Industrial safety -- Periodicals; Fiabilité -- Périodiques; Sécurité des systèmes -- Périodiques; Sécurité du travail -- Périodiques; 620.00452
• DOI: 10.1016/j.ress.2017.12.017
• Languages: English
• ISSNs: 0951-8320

Abstract

Highlights: A multicomponent system under simultaneous failures is studied. It is subject to inspections and multiple replacements of the failed components. A Markov process for modeling the system is constructed. The study is performed in transient regime. An application to three systems is performed considering operational cycles. Abstract: We present a reliability system subject to shocks, internal failures, and inspections. Shocks cause damage or failure to several units simultaneously. The units undergo internal failures. After an inspection, the units that have failed are replaced by new and identical ones. The shocks are governed by a Poisson process, the internal failures and the inspection times are exponentially distributed. Under these assumptions a Markov process governing the system is constructed. The states of the system are formed by state-vectors associated to the units of the system. The instantaneous transitions among the states are constructed by using intermediate functions and indicators. A system with three components illustrating the procedure is studied and a numerical application is performed, comparing the performance measures of the k-out-of-3 systems for k = 1, 2, 3.