Reliability Analysis and Optimization Problems for a Weighted-k-out-of-n: G System with Multiple Types of Components

Abstract

This paper addresses critical gaps in the reliability modeling of weighted k-out-of-n:G systems, which are widely used in safety-critical and fault-tolerant applications. Traditional models typically assume component homogeneity and independence, limiting their applicability to complex real-world systems. To overcome these limitations, we propose a generalized framework that (i) allows for an arbitrary number of distinct component types, (ii) models dependencies among components arising from shared resources, environmental conditions, or common-cause failures, and (iii) avoids computational inefficiencies by deriving a non-recursive reliability formula. Additionally, we introduce three practical optimization models to support system design decisions: cost minimization under reliability constraints, reliability maximization under budget constraints, and optimal system replacement timing. The proposed framework offers significant improvements in computational efficiency, modeling realism, and decision support for large-scale engineering systems. These contributions extend the applicability of weighted k-out-of-n systems to domains such as power grids, telecommunications, and industrial manufacturing where component heterogeneity and dependencies are prevalent.