RELIABILITY AND IMPORTANCE MEASURES OF WEIGHTED-k-OUT-OF-n SYSTEM

Recently many popular reliability systems are being extended to weighted systems where weight associated with each component refers to load/capacity of that component. The simplest k-out-of-n system extended under this concept is known as weighted-k-out-of-n system. A weighted-k-out-of-n: G(F) system consists of n components each one having a positive integer weight w(i), i = 1, 2,..., n such that the total system weight is w and the system works (fails) if and only if the accumulated weight of working (failed) components is at least k. In this paper, we introduce the concept of Weighted Markov Bernoulli Trial (WMBT) {Xi, i = 0} and study the distribution of S-n(w), the total weight of successes in the sequence of n WMBT and conditional distribution of S-n(w) given that uth trial results in failure/success. We refer the distribution of S-n(w) as Weighted Markov Binomial Distribution (WMBD). Further we discuss application of WMBD and conditional WMBD in evaluation of reliability, Birnbaum reliability importance (B-importance) and improvement potential importance of weighted-k-out-of-n: G/ F system. The numerical work is included to demonstrate the computational simplicity of the developed results. Further we compare our study with the existing results in terms of efficiency and find that our results are efficient for large values of k.