Optimal age and block replacement policies for a multi-component system with failure interaction

In this paper we consider a generalized age and block replacement policy for a multicomponent system with failure interaction. The i-th component (1 less than or equal to i less than or equal to N) has two types of failures. Type I and type II failures are age dependent. Type I failure (minor failure) is removed by a minimal repair, whereas type II failure (catastrophic failure) induces a total failure of the system (i.e. failure of all other components in the system) and is removed by an unplanned (or unscheduled) replacement of the system. For an age replacement maintenance policy, planned (or scheduled) replacements occur whenever an operating system reaches age T, whereas in the block replacement case, planned replacements occur every T units of time. The aim of this paper is to derive the expected long-run cost per unit time for each policy. The optimal T* which would minimize the cost rate is discussed. Various special cases are detailed. A numerical example is given to illustrate the method.