Progressive Type II censored order statistics for multivariate observations

Abstract

For a sequence of independent and identically distributed random vectors. . , 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 n 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

Multivariate stress–strength reliability model and its evaluation for coherent structures

“…, f n (x), respectively. The following theorem generalizes Theorem 1 of [1]. The proofs of the results are presented in the Appendix.…”

“…In this case the reliability of a system can be represented in various forms depending on the structure of a system. If, for example the system has a series structure then the reliability corresponds to R = P Y < X (1) , where X (r ) denotes the r th smallest (1 ≤ r ≤ n) in X 1 , X 2 , . .…”

“…Bairamov [1] introduced the conditionally ordered order statistics for multivariate observations. Let X 1 , X 2 , .…”

Asymptotic properties of the number of near minimum-concomitant observations in the case of progressive type-II censoring

“…was considered in Bairamov andStepanov (2010, 2011). The limit β(y) in (4.1) was used for studying the asymptotic behaviour of the number of near minimumconcomitant observations.…”

“…One can refer, among others, to Nelson (1982), Lawless (1982), Cohen and Whitten (1988), , Balakrishnan and Cohen (1991), Viveros and Balakrishnan (1994), Sandhu (1995, 1996), Aggarwala and Balakrishnan (1997), Balakrishnan et al (2001a,b), Bairamov and Eryilmaz (2005), and Balakrishnan and Stepanov (2008). To the best of our knowledge, the Progressive type-II censoring in the bivariate case was addressed only in Balakrishnan and Kim (2005), and Bairamov (2006).…”