Reliability Analysis of Weighted- k-out-of- n: G System Consisting of Two Different Types of Nonidentical Components Each with its Own Positive Integer-Valued Weight

Abstract

This paper introduces a special case of weighted-k-out-of-n:G system formed from two types of nonidentical components with different weights. This system consists of n nonidentical components each with its own positive integer-valued weight which are categorized into two groups with respect to their duties and services. In fact, we have a system consisting n components such that n1 of them each with its own weight 𝜔 i and reliability p1i and n2 of them each with its own weight 𝜔 * i and reliability p2i. If the total weights of the functioning components exceeds a prespecified threshold k, the system is supposed to work. The reliability of system is obtained based on the total weight of all working components in both group. The survival function and mean time to failure are presented. Also, the component importance of this system are studied.

Reliability Structures Consisting of Weighted Components: Synopsis and New Advances

“…On the other hand, Mahmoudi and Meshkat (2020) extended the case of the weighted k-out-of-n: G structure with 2 distinct kinds of units (Group 1 and Group 2), by assuming that the units are nonidentical. Proposition 3.9 provides a nice formula for determining its operating probability.…”