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Availability of periodically inspected systems with Markovian wear and shocks

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Jeffrey P. Kharoufeh ,
Daniel E. Finkelstein  and
Dustin G. Mixon
Jeffrey P. Kharoufeh*
Affiliation:
Air Force Institute of Technology
Daniel E. Finkelstein*
Affiliation:
Air Force Institute of Technology
Dustin G. Mixon*
Affiliation:
Air Force Institute of Technology
*
∗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.
∗∗Postal address: Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433-7765, USA.
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Abstract

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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.

Keywords

Shock modelwear processreliabilityaverage availability

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K37: Processes in random environments
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 303 - 317
Copyright
© Applied Probability Trust 2006 

References

Abate, J. and Whitt, W. (1995). Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. 7, 36–43.CrossRefGoogle Scholar
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.Google Scholar
Esary, J. D., Marshall, A. W. and Proschan, F. (1973). Shock models and wear processes. Ann. Prob. 1, 627–649.Google Scholar
Igaki, N., Sumita, U. and Kowada, M. (1995). Analysis of Markov renewal shock models. J. Appl. Prob. 32, 821–831.Google Scholar
Kharoufeh, J. P. (2003). Explicit results for wear processes in a Markovian environment. Operat. Res. Lett. 31, 237–244.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Klutke, G.-A. and Yang, Y. (2002). The availability of inspected systems subject to shocks and graceful degradation. IEEE Trans. Reliab. 51, 371–374.Google Scholar
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.Google Scholar
Nakagawa, T. (1979). Replacement problem of a parallel system in random environment. J. Appl. Prob. 16, 203–205.Google Scholar
Råde, J. (1976). Reliability systems in random environment. J. Appl. Prob. 13, 407–410.Google Scholar
Shanthikumar, J. G. and Sumita, U. (1983). General shock models associated with correlated renewal sequences. J. Appl. Prob. 20, 600–614.Google Scholar
Skoulakis, G. (2000). A general shock model for a reliability system. J. Appl. Prob. 37, 925–935.CrossRefGoogle Scholar