Applications of quadrivariate exponential distribution to a three-unit warm standby system with dependent structure

Abstract

Two-unit warm standby systems have been elaborately dealt within the literature. However, the study of standby systems with more than two units, though very relevant in state-of-the-art practical situations, has received little attention because of mathematical intricacies involved in analyzing them. Also, such systems have been studied assuming: (i) the lifetime or repair time of the units to be exponential, or (ii) the lifetime and repair time to be independent. The present contribution is an improvement in the state-of-the-art in the sense that three-unit warm standby system with dependent structure is shown to be capable of comprehensive analysis.

A New Analytical Method of Standby System Reliability Model

“…When () Kt enters the macrostate n again, the system is shut down. Hence, the state space 3 H is the one-dimensional absorption state of system work time.…”

“…In the design of ship equipment, standby is often a favored guarantee for system reliability [1][2][3] . In a cold standby system, it is assumed that the failure rate of standby unit is zero, so its reliability analysis is normally easier than that of warm standby system [4][5][6] .…”

Reliability analysis of a two-unit‏ ‏standby system under Marshall–Olkin dependency

“…the failure of a component affects the failure rate of the remaining components in the system. However, there are few publications in the literature on standby systems with a dependent structure; for instance, some works are in (Harris, 1968; Ramanarayanan and Subramanian, 1981; Yuge et al ., 2016; Yadavalli et al ., 2017; Yaghoubi and Gholami, 2021). These authors considered dependency among system components in their models.…”