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May, 1991 Stochastic Order for Inspection and Repair Policies
Philip J. Boland, Emad El-Neweihi, Frank Proschan
Ann. Appl. Probab. 1(2): 207-218 (May, 1991). DOI: 10.1214/aoap/1177005934

Abstract

Inspection and repair policies for (nr+1)-out-of-n systems are compared stochastically with respect to two partial orderings b1 and b2 on the set of permutations of {1,2,,n}. The partial ordering b1 is finer than the partial ordering b2. A given permutation π of {1,2,,n} determines the order in which components are visited and inspected. We assume that the reliability of the ith independent component is given by Pi, where P1P2Pn. If π and π are two permutations such that πb1π, then we show that the number of inspections necessary to achieve minimal or complete repair is stochastically smaller with π than with π. We also consider three policies for minimal repair when the components are each made up of t "parts" assembled in parallel. It is shown that if πb2π, then the number of repairs necessary under π is stochastically smaller than the number necessary under π, but that in general this is not true for the finer ordering b1. The results enable one to make interesting comparisons between various inspection and repair policies, as well as to understand better the relationship between the orderings b1 and b2 on the set of permutations.

Citation

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Philip J. Boland. Emad El-Neweihi. Frank Proschan. "Stochastic Order for Inspection and Repair Policies." Ann. Appl. Probab. 1 (2) 207 - 218, May, 1991. https://doi.org/10.1214/aoap/1177005934

Information

Published: May, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0737.62089
MathSciNet: MR1102317
Digital Object Identifier: 10.1214/aoap/1177005934

Subjects:
Primary: 62N05
Secondary: 60G40 , 62N10 , 90B35

Keywords: -out-of- systems , complete repair , Inspection policy , minimal repair , partial orderings , permutation , stochastic order

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.1 • No. 2 • May, 1991
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