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Discrete-time semi-Markov model for reliability and survival analysis. (English) Zbl 1089.60525

Summary: We define a discrete-time semi-Markov model and propose a computation procedure for solving the corresponding Markov renewal equation, necessary for all our reliability measurements. Then, we compute the reliability and its related measures, and we apply the results to a three-state system.

MSC:

60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
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[1] Anderson P. K., Statistical Models Based on Counting Processes (1993)
[2] DOI: 10.1215/S0012-7094-60-02703-4 · Zbl 0104.37001
[3] Çinlar E., Introduction to Stochastic Processes (1975)
[4] Csenki A., Stochastic Models in Reliability and Maintenance pp 219– (2002)
[5] DOI: 10.2307/1427818 · Zbl 0817.60088
[6] Howard R., Dynamic Probabilistic Systems (1971) · Zbl 0227.90031
[7] DOI: 10.1016/0167-6687(84)90057-X · Zbl 0546.60087
[8] DOI: 10.1023/A:1013719007075 · Zbl 0991.60082
[9] DOI: 10.1007/978-1-4612-0161-8
[10] Mode C. J., Stochastic Processes in Epidemiology (2000) · Zbl 0984.92028
[11] Neuts M., Matrix-Geometric Solutions in Stochastic Models (1981) · Zbl 0469.60002
[12] Port S. C., Theoretical Probability for Applications (1994) · Zbl 0860.60001
[13] Shiryaev A. N., 3rd ed., in: Probability (1996)
[14] DOI: 10.2307/3214890 · Zbl 0766.90051
[15] DOI: 10.1016/0024-3795(94)90470-7 · Zbl 0813.60084
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