Reliability modelling for linear and circular k -out-of- n : F systems with shared components

Reliability analysis for k -out-of- n systems has received much attention in the field of reliability due to its practical importance. In this work, models for linear and circular k -out-of- n : F systems with shared components, consisting of m subsystems, are discussed. The finite Markov chain imbedding approach cannot be used directly to derive reliability of the considered systems because of the common area existing between adjacent subsystems. For this reason, we first derive the probability that the number of failed components is a given value in the m common areas. Then, all disjoint cases, each of which is regarded as a series system consisting of m subsystems with different initial state probability distributions, are obtained, with which the n i th step transition rate matrix is calculated by using the Markov chain technique, for i = 1 , 2 , … , m . Finally, the reliability of the system is obtained by summing the reliabilities of all cases along with the finite Markov chain imbedding approach. Some numerical examples are presented to illustrate the efficiency of the proposed reliability evaluation method.