A Time-Inhomogeneous Prendiville Model with Failures and Repairs

Virginia Giorno and Amelia G. Nobile
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Virginia Giorno: Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Salerno, Italy
Amelia G. Nobile: Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Salerno, Italy

Mathematics, 2022, vol. 10, issue 2, 1-20

Abstract: We consider a time-inhomogeneous Markov chain with a finite state-space which models a system in which failures and repairs can occur at random time instants. The system starts from any state j (operating, F , R ). Due to a failure, a transition from an operating state to F occurs after which a repair is required, so that a transition leads to the state R . Subsequently, there is a restore phase, after which the system restarts from one of the operating states. In particular, we assume that the intensity functions of failures, repairs and restores are proportional and that the birth-death process that models the system is a time-inhomogeneous Prendiville process.

Keywords: continuous-time ehrenfest model; first-passage time densities; proportional intensity functions; asymptotic behaviors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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