Dynamic reliability via computational solution of generalized state-transition equations for entry-time processes

Paul Nelson and Shuwen Wang

Reliability Engineering and System Safety, 2007, vol. 92, issue 9, 1281-1293

Abstract: Entry-time processes are finite-state continuous-time jump processes with transition rates depending only on the two states involved, the calendar time, and the most recent arrival time (entry time). Entry-time processes are transformed into Markov processes via the standard technique of incorporating entry time into the state variables. It is shown that the associated state-transition (Chapman–Kolmogorov) equations can be written as a coupled pair of integrodifferential equations. A finite-difference approximation to these equations is developed. This computational approach is verified, and some of its properties delineated, via two hypothetical examples. One of these examples admits a semi-analytic solution, while simulations provide the base of comparison for the other.

Keywords: Dynamic reliability; Semi-Markov processes; Chapman–Kolmogorov equations; Computational solution; State model; Entry-time process (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:92:y:2007:i:9:p:1281-1293

DOI: 10.1016/j.ress.2006.08.005

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