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Availability of periodically inspected systems with Markovian wear and shocks

  • Jeffrey P. Kharoufeh (a1), Daniel E. Finkelstein (a1) and Dustin G. Mixon (a1)

Abstract

We analyze a periodically inspected system with hidden failures in which the rate of wear is modulated by a continuous-time Markov chain and additional damage is induced by a Poisson shock process. We explicitly derive the system's lifetime distribution and mean time to failure, as well as the limiting average availability. The main results are illustrated in two numerical examples.

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Copyright

© Applied Probability Trust 2006 

Corresponding author

∗ Postal address: Department of Operational Sciences, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433-7765, USA. Email address: jeffrey.kharoufeh@afit.edu
∗∗ Postal address: Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433-7765, USA.

References

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[1] Abate, J. and Whitt, W. (1995). Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. 7, 36–43.
[2] Çinlar, E. (1977). Shock and wear models and Markov additive processes. In Theory and Application of Reliability: with Emphasis on Bayesian and Nonparametric Methods, eds Shimi, I. N. and Tsokos, C. P., Academic Press, New York, pp. 193–214.
[3] Esary, J. D., Marshall, A. W. and Proschan, F. (1973). Shock models and wear processes. Ann. Prob. 1, 627–649.
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[5] Kharoufeh, J. P. (2003). Explicit results for wear processes in a Markovian environment. Operat. Res. Lett. 31, 237–244.
[6] Kiessler, P. C., Klutke, G.-A. and Yang, Y. (2002). Availability of periodically inspected systems subject to Markovian degradation. J. Appl. Prob. 39, 700–711.
[7] Klutke, G.-A. and Yang, Y. (2002). The availability of inspected systems subject to shocks and graceful degradation. IEEE Trans. Reliab. 51, 371–374.
[8] Klutke, G.-A., Wortman, M. and Ayhan, H. (1996). The availability of inspected systems subject to random deterioration. Prob. Eng. Inf. Sci. 10, 109–118.
[9] Nakagawa, T. (1979). Replacement problem of a parallel system in random environment. J. Appl. Prob. 16, 203–205.
[10] Råde, J. (1976). Reliability systems in random environment. J. Appl. Prob. 13, 407–410.
[11] Shanthikumar, J. G. and Sumita, U. (1983). General shock models associated with correlated renewal sequences. J. Appl. Prob. 20, 600–614.
[12] Skoulakis, G. (2000). A general shock model for a reliability system. J. Appl. Prob. 37, 925–935.

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Availability of periodically inspected systems with Markovian wear and shocks

  • Jeffrey P. Kharoufeh (a1), Daniel E. Finkelstein (a1) and Dustin G. Mixon (a1)

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