k ‐out‐of‐ n Systems

Abstract

A k ‐out‐of‐ n system is a system with n components which functions or works if at least k out of the n components work. Parallel and series systems are special cases of a k ‐out‐of‐ n system. There are many different arrangements of the components in a k ‐out‐of‐ n system and many assumptions that can be made about the lifetimes of the components. In this chapter, the lifetimes of the components in the system are assumed to be independent and identically distributed. The reliability function of the system is found by calculating the probability that at least k components out of the n components work. The mean time to failure of the system is also found for the case of components with exponential distributions of lifetimes. In addition, the reliability function for a linear and circular consecutive k‐out‐of‐n system is given.

Renewable k-Out-of-n System with the Component-Wise Strategy of Preventive System Maintenance

“…Consider a renewable k-out-of-n system that consists of n components running in parallel that fails if at least k of them fail [47]. After each component failure (before the k-th one), it is repaired by a unique repair unit within a random repair time.…”