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On bounds for some optimal policies in reliability

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Jie Mi
Jie Mi*
Affiliation:
Florida International University and Anhui University
*
∗ Postal address: Department of Statistics, Florida International University, University Park, Miami, FL 33199, USA. Email address: mi@fiu.edu
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Abstract

Often in the study of reliability and its applications, the goal is to maximize or minimize certain reliability characteristics or some cost functions. For example, burn-in is a procedure used to improve the quality of products before they are used in the field. A natural question which arises is how long the burn-in procedure should last in order to maximize the mean residual life or the conditional survival probability. In the literature, an upper bound for the optimal burn-in time is obtained by assuming that the underlying distribution of the products has a bathtub-shaped failure rate function; however, no lower bound is available. A similar question arises in studying replacement policy, warranty policy, and inspection models. This article gives a lower bound for the optimal burn-in time, and lower and upper bounds for the optimal replacement and warranty policies, under the same bathtub-shape assumption.

Keywords

Bathtub-shaped failure ratemean residual lifeα-percentile residual lifeage replacement policyblock replacement policyminimal repairwarranty policyinspection model

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 491 - 502
Copyright
Copyright © Applied Probability Trust 2002 

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References

Barlow, R. E., and Proschan, F. (1965). Mathematical Theory of Reliability. John Wiley, New York.Google Scholar
Block, H. W., and Savits, T. H. (1997). Burn-in. Statist. Sci. 12, 1–13.Google Scholar
Block, H. W., Borges, W. S., and Savits, T. H. (1985). Age-dependent minimal repair. J. Appl. Prob. 22, 370–385.Google Scholar
Block, H. W., Jong, Y. K., and Savits, T. H. (1999). Bathtub function and burn-in. Prob. Eng. Inf. Sci. 13, 497–507.CrossRefGoogle Scholar
Haines, A. L., and Singpurwalla, N. D. (1974). Some contribution to the stochastic characterization of wear. In Reliability and Biometry, eds Proschan, F. and Serfling, J., SIAM, Philadelphia, pp. 47–80.Google Scholar
Joe, H., and Proschan, F. (1984). Percentile residual life functions. Operat. Res. 32, 668–678.Google Scholar
Leemis, L. M., and Beneke, M. (1990). Burn-in models and methods: a review. IIE Trans. 22, 172–180.CrossRefGoogle Scholar
Mi, J. (1993). Discrete bathtub failure rate and upside-down bathtub mean residual life. Naval Res. Logistics 40, 361–371.Google Scholar
Mi, J. (1994). Burn-in and maintenance policies. Adv. Appl. Prob. 26, 207–221.Google Scholar
Mi, J. (1995). Bathtub failure rate and upside-down bathtub mean residual life. IEEE Trans. Reliab. 44, 388–391.Google Scholar
Mi, J. (1996). Minimizing some cost functions related to both burn-in and field use. Operat. Res. 44, 497–500.Google Scholar
Mi, J. (1997). Warranty policies and burn-in. Naval Res. Logistics 44, 199–209.Google Scholar
Mi, J. (1998). Some comparison results of system availability. Naval Res. Logistics 45, 205–218.Google Scholar
Mi, J. (2002). Age-replacement policy and optimal work size. J. Appl. Prob. 39, 296–311.Google Scholar
Rajarshi, S., and Rajarshi, M. B. (1988). Bathtub distributions: a review. Commun. Statist. Theory Meth. 17, 2597–2621.Google Scholar
Ross, S. (1996). Stochastic Processes. John Wiley, New York.Google 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
Yang, Y., and Klutke, G.-A. (2000). Improved inspection schemes for deteriorating equipment. Prob. Eng. Inf. Sci. 14, 445–460.Google Scholar