Multivariate stochastic comparisons of inspection and repair policies

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 greater than or equal tob(1), and greater than or equal tob(2) on the set of permutations of {1,...,n}. A given permutation pi 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 P-i, where P-1 less than or equal to P-2 less than or equal to ... less than or equal toP(n). If pi and pi' are two permutations such that pi greater than or equal to b(1) pi', we show that inspecting the system with pi is better than with pi' 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 greater than or equal tob(2) on the permutations. Our main results strengthen those in Boland, El-Neweihi and Proschan (Ann. Appl. Probab. 1 (1991) 207). (C) 2001 Elsevier Science B.V. All rights reserved.