The number of failed components in a\xa0coherent working system when the lifetimes are discretely distributed

Krzysztof Jasiński

doi:10.1007/s00184-021-00817-2

Abstract

In this paper, we study the number of failed components of a coherent system. We consider the case when the component lifetimes are discrete random variables that may be dependent and non-identically distributed. Firstly, we compute the probability that there are exactly i, i=0,ldots ,n-k, failures in a k-out-of-n system under the condition that it is operating at time t. Next, we extend this result to other coherent systems. In addition, we show that, in the most popular model of independent and identically distributed component lifetimes, the obtained probability corresponds to the respective one derived in the continuous case and existing in the literature.

Highlights

Coherent systems are of special importance in reliability theory since they have been widely used to model mathematically sophisticated technical devices composed of simple elements
Asadi and Berred (2012) determined the probability that there are exactly i, i = 0, . . . , n − k, failures in the k-out-of-n system under the condition that it is operating at time t and the component lifetimes are independent and identically distributed (IID) absolutely continuous rvs
Our aim is to compute this probability in the case of k-outof-n systems and coherent systems consisting of n components whose discrete lifetimes are possibly dependent and not necessarily identically distributed (DNID) rvs

Summary

Introduction

Coherent systems are of special importance in reliability theory since they have been widely used to model mathematically sophisticated technical devices composed of simple elements. N − k, failures in the k-out-of-n system under the condition that it is operating at time t and the component lifetimes are independent and identically distributed (IID) absolutely continuous rvs Several properties of this probability were considered. Our aim is to compute this probability in the case of k-outof-n systems and coherent systems consisting of n components whose discrete lifetimes are possibly dependent and not necessarily identically distributed (DNID) rvs.

Results on failed components in k-out-of-n systems

Results on failed components in coherent systems

Summary and conclusions