Stochastic comparisons of replacement policies in coherent systems under minimal repair

Abstract

In this paper we study stochastic comparisons of the coherent systems obtained under different repair policies. We consider minimal repairs of the components, that is, a failed component is replaced by another component which is similar (i.e. it has the same distribution) to the replaced one and with the same age. Under these assumptions, we study how to determine the best replacement policies. Two general methods are proposed, one for systems with identically distributed components and another one for systems with ordered (in different stochastic senses) components. Both methods can be applied to systems with independent or dependent components. We use these methods to determine the optimal repair policies in some particular cases. We pay special attention to series and parallel systems with independent or dependent components. An algorithm to find the optimal replacement policy (when it exists) is provided.