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Availability of periodically inspected systems subject to Markovian degradation

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Peter C. Kiessler ,
Georgia-Ann Klutke  and
Yoonjung Yang
Peter C. Kiessler*
Affiliation:
Clemson University
Georgia-Ann Klutke*
Affiliation:
Texas A&M University
Yoonjung Yang*
Affiliation:
Samsung Electronics Co. Ltd
*
∗ Postal address: Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA.
∗∗ Postal address: Department of Industrial Engineering, Texas A&M University, College Station, TX 77843-3131, USA. Email address: [email protected]
∗∗∗ Postal address: SCM Group, Memory Division, Samsung Electronics Co. Ltd, San #16 Banwol-Ri, Taean-Eup, Hwasung City, Kyunggi 445-701, Republic of Korea.
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Abstract

This paper studies inspected systems with non-self-announcing failures where the rate of deterioration is governed by a Markov chain. We compute the lifetime distribution and availability when the system is inspected according to a periodic inspection policy. In doing so, we expose the role of certain transient distributions of the environment.

Keywords

AvailabilityMarkovian degradationnon-self-announcing failurelifetime distributionperiodic inspectionsFourier expansion

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K15: Markov renewal processes, semi-Markov processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 700 - 711
Copyright
Copyright © Applied Probability Trust 2002 

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References

[1]. Çinlar, E. (1975). Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
[2]. Çinlar, E. (1984). Markov and semi-Markov models of deterioration. In Reliability Theory and Models, eds Abdel-Hamid, M., Çinlar, E. and Quinn, J., Academic Press, New York, pp. 3–41.CrossRefGoogle Scholar
[3]. Çinlar, E. and Özekici, S. (1987). Reliability of complex devices in random environments. Prob. Eng. Inf. Sci. 3, 97–115.Google Scholar
[4]. Çinlar, E., Shaked, M., and Shanthikumar, J. G. (1989). On lifetimes influenced by a common environment. Stoch. Process. Appl. 33, 347–359.Google Scholar
[5]. Horn, R. A., and Johnson, C. R. (1991). Topics in Matrix Analysis. Cambridge University Press.Google Scholar
[6]. 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.CrossRefGoogle Scholar
[7]. Lefèvre, C., and Milhaud, X. (1990). On the association of the lifelengths of components subjected to a stochastic environemt. Adv. Appl. Prob. 22, 961–964.Google Scholar
[8]. Özekici, S. (1995). Optimal maintenance policies in random environments. Europ. J. Operat. Res. 82, 283–294.CrossRefGoogle Scholar
[9]. Özekici, S. (1996). Complex systems in random environments. In Reliability and Maintenance of Complex Systems, ed Özekici, S., Springer, New York, pp. 137–157.CrossRefGoogle Scholar
[10]. Pitman, J. W., and Speed, T. P. (1973). A note on random times. Stoch. Process. Appl. 1, 369–374.CrossRefGoogle Scholar
[11]. Rogers, L. C. G., and Williams, D. (1987). Diffusions, Markov Processes and Martingales, Vol. 2, Itô Calculus. John Wiley, New York.Google Scholar
[12]. Ross, S. M. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.Google Scholar
[13]. Rudin, W. (1987). Real and Complex Analysis, 3rd edn. McGraw-Hill, Boston, MA.Google Scholar
[14]. Shaked, M., and Shanthikumar, J. G. (1989). Some replacement policies in a random environment. Prob. Eng. Inf. Sci. 3, 117–134.CrossRefGoogle Scholar
[15]. Stroock, D. W. (1999). A Concise Introduction to the Theory of Integration, 3rd edn. Birkhäuser, Boston, MA.Google Scholar
[16]. Wortman, M., and Klutke, G.-A. (1994). On maintained systems operating in a random environment. J. Appl. Prob. 31, 589–594.CrossRefGoogle Scholar
[17]. Yang, Y., and Klutke, G.-A. (2000). Improved inspection schemes for deteriorating equipment. Prob. Eng. Inf. Sci. 14, 445–460.Google Scholar
[18]. Yang, Y., and Klutke, G.-A. (2000). Lifetime characteristics and inspection schemes for Lévy degradation processes. IEEE Trans. Reliab. 49, 377–382.CrossRefGoogle Scholar