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Availability analysis of periodically inspected systems with random walk model

Part of: Operations research and management science Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Lirong Cui  and
M. Xie
Lirong Cui*
Affiliation:
National University of Singapore
M. Xie*
Affiliation:
National University of Singapore
*
∗ Postal address: Department of Industrial and Systems Engineering, National University of Singapore, Singapore 119260.
∗∗ Email address: lirongcui@excite.com
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Abstract

In this paper, the instantaneous availability of a system maintained under periodic inspection is investigated using random walk models. Two cases are considered. In the first model, the system is repaired or modified and it is assumed to be as good as new upon periodic inspection and maintenance. In the second model, the system is not modified after the inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. For both models the failures only can be found through the inspection. Perfect repair or replacement of a failed system is assumed to be carried out, but the time it takes can be constant or of a random length. The relationship between this problem and the random walk model in a two-dimensional plane is described. Several new results are also shown.

Keywords

Random walkperiodic inspectioninstantaneous availabilityrepair or replacementstochastic process

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60G35: Signal detection and filtering
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 860 - 871
Copyright
Copyright © by the Applied Probability Trust 2001 

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References

Aven, T., and Jensen, U. (1999). Stochastic Models in Reliability. Springer, New York.CrossRefGoogle Scholar
Barlow, R. E., and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Chang, G. J., Cui, L. R., and Hwang, F. K. (2000). Reliabilities of Consecutive-k Systems. Kluwer, Dordrecht.Google Scholar
Chelbi, A., and Ait-Kadi, D. (2000). Generalized inspection strategy for randomly failing systems subjected to random shocks. Internat. J. Production Econom. 64, 379–384.CrossRefGoogle Scholar
Cohen, J. W. (1992). Analysis of Random Walks. IOS Press, Amsterdam.Google Scholar
Cui, L. R., and Xie, M. (2001). Availability of a periodically inspected system with random repair or replacement time. Submitted.Google Scholar
Dieulle, L. (1999). Reliability of a system with Poisson inspection times. J. Appl. Prob. 36, 1140–1154.CrossRefGoogle Scholar
Doyle, P. G., and Snell, J. L. (1984). Random Walks and Electric Networks (Carus Math. Monogr. 22). Mathematical Association of America, Washington, DC.CrossRefGoogle Scholar
Gåasemyr, J., and Aven, T. (1999). Asymptotic distributions for downtimes of monotone systems. J. Appl. Prob. 36, 814–824.CrossRefGoogle Scholar
Höyland, A., and Ransand, M. (1994). System Reliability Theory. John Wiley, New York.Google Scholar
Ito, K., and Nakagawa, T. (2000). Optimal inspection policies for a storage system with degradation at periodic tests. Math. Comput. Modelling 31, 191–195.CrossRefGoogle Scholar
Mi, J. (1995). Limiting behavior of some measures of system availability. J. Appl. Prob. 32, 482–493.CrossRefGoogle Scholar
Sarkar, J., and Chaudhuri, G. (1999). Availability of a system with gamma life and exponential repair time under a perfect repair policy. Statist. Prob. Lett. 43, 189–196.CrossRefGoogle Scholar
Sarkar, J., and Sarkar, S. (2000). Availability of a periodically inspected system under perfect repair. J. Statist. Planning Infer. 91, 77–90.CrossRefGoogle Scholar
Scarsini, M., and Shaked, M. (2000). On the value of an item subject to general repair or maintenance. Europ. J. Operat. Res. 122, 625–637.CrossRefGoogle Scholar
Vaurio, J. K. (1999). Availability and cost functions for periodically inspected preventively maintained units. Reliab. Eng. Systems Safety 63, 133–140.CrossRefGoogle Scholar
Wortman, M. A., and Klutke, G. A. (1994). On maintained systems operating in a random environment. J. Appl. Prob. 31, 589–594.CrossRefGoogle Scholar
Yang, Y. J., and Klutke, G. A. (2000). Improved inspection schemes for deteriorating equipment. Prob. Eng. Inf. Sci. 14, 445–460.CrossRefGoogle Scholar
Yeh, L. (1995). An optimal inspection–repair–replacement policy for standby systems. J. Appl. Prob. 32, 212–223.CrossRefGoogle Scholar