Reliability modeling for repairable circular consecutive-[formula omitted]-out-of-[formula omitted]: F systems with retrial feature

Abstract

In this paper, we consider a repairable circular consecutive-k-out-of-n: F retrial system, which can be used to simulate the intelligent closed recurring water cooling automation system in industrial production. We assume that the working time and retrial time of each component obey exponential distributions, and the repair time obeys a general distribution. Based on the generalized transition probability and the key component priority repair rule of the retrial system, the availability and reliability indices of the general repairable circular consecutive-k-out-of-n: F retrial system are derived by using the methods of supplementary variable and Laplace transform. Furthermore, we calculate the explicit expressions of the above indices when n and k are fixed at definite values in the system. The repair time is assumed to follow a Weibull distribution in examples demonstration, and the influence of various parameters on system reliability, steady-state availability and other indices are obtained. The sensitivity and relative sensitivity analysis of the steady-state availability, steady-state failure frequency and mean time to first failure (MTTFF) of the system are also performed.