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On bounds for some optimal policies in reliability

Part of: Special processes Operations research and management science

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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