Uncertain block replacement policy with no replacement at failure

Abstract

In this paper, we consider a block replacement policy with no replacement at failure and apply it to a system consisting of a new type of units. Due to the absence of historical data of lifetimes of new units, we fail to obtain the probability distribution of lifetimes. In this case, some domain experts are invited to provide belief degree of lifetime to estimate its distribution. However, human beings often overestimate unlikely events, which makes the variance of belief degree is much greater than that of the frequency. In order to deal with this problem, we assume the lifetime of the unit to be an uncertain variable. An uncertain block replacement model with no replacement at failure is proposed, and the existence condition of the optimal replacement time is given. Finally, a numerical example and sensitivity analysis are provided to illustrate the utility of the proposed model in practice.