Multivariate stochastic comparisons of inspection and repair policies

✍ Scribed by Taizhong Hu; Ying Wei

• Book ID: 104301704
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 118 KB
• Volume: 53
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00088-8

✦ Synopsis

For a system consisting of n independent components, inspection and repair policies are compared in the sense of the usual multivariate stochastic order with respect to the partial orderings ¿ b 1 and ¿ b 2 on the set of permutations of {1; : : : ; n}. A given permutation of {1; : : : ; n} determines the order in which components are visited and inspected. We assume that the reliability of the ith component is given by Pi, where P1 6 P2 6 • • • 6 Pn. If and are two permutations such that ¿ b 1 , we show that inspecting the system with is better than with in the sense that more failed components are encountered or less time is used in completing an inspection. If each component is made up of t parts assembled in parallel, it is shown that, for three types of repair policies, the rank of preference of inspection procedures is consistent with the partial ordering ¿ b 2 on the permutations. Our main results strengthen those in Boland, El-Neweihi and Proschan (Ann. Appl. Probab. 1 (1991) 207).