Progressive Type II censored order statistics for multivariate observations

For a sequence of independent and identically distributed random vectors X-i = (X-i(1) X-i(2)..... X-i(p)), i = 1. 2..... n, we consider the conditional ordering of these random vectors with respect to the magnitudes of N(X-i), i = 1, 2.... n, where N is a p-variate continuous function defined on the support set of X-1 and satisfying certain regularity conditions. We also consider the Progressive Type II right censoring for multivariate observations using-conditional ordering. The need for the conditional ordering of random vectors exists for example, in reliability analysis when a system has it independent components each consisting of p arbitrarily dependent and parallel connected elements. Let the vector of life lengths for the ith component of the system be X-i = (X-i(1), X-i(2)....,X-i(p)), i = 1, 2...., n. where X-i(j) denotes the life length of the jth element of the ith component. Then the first failure in the system occurs at time min{max(X-1(1),X-1(2).... X-1(p)), max(X-2(1), X-2(2),.... X-2(p))..., max(X-n(1). X-n(2). X-n(p))}, and for this case N(X-i) = max(X-i(1), X-i(2)...,X-i(p)). In this paper we introduce the conditionally ordered and Progressive Type II right-censored conditionally ordered statistics for multivariate observations and to study their distributional properties. (C) 2005 Elsevier Inc. All rights reserved.