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

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  • Nelson, Paul
  • Wang, Shuwen

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.

Suggested Citation

  • Nelson, Paul & Wang, Shuwen, 2007. "Dynamic reliability via computational solution of generalized state-transition equations for entry-time processes," Reliability Engineering and System Safety, Elsevier, vol. 92(9), pages 1281-1293.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:9:p:1281-1293
    DOI: 10.1016/j.ress.2006.08.005
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    Cited by:

    1. Oduor, Peter G. & Kotchman, L. & Nakamura, A. & Jenkins, S. & Ale, G., 2012. "Spatially constrained forest cover dynamics using Markovian random processes," Forest Policy and Economics, Elsevier, vol. 20(C), pages 36-48.
    2. Moura, Márcio das Chagas & Droguett, Enrique López, 2009. "Mathematical formulation and numerical treatment based on transition frequency densities and quadrature methods for non-homogeneous semi-Markov processes," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 342-349.
    3. Moghaddass, Ramin & Zuo, Ming J., 2012. "A parameter estimation method for a condition-monitored device under multi-state deterioration," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 94-103.
    4. Brissaud, Florent & Smidts, Carol & Barros, Anne & Bérenguer, Christophe, 2011. "Dynamic reliability of digital-based transmitters," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 793-813.

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