ABSTRACT
We assume the single component system comprises a component and socket which together perform an operational function (Ascher and Feingold, 1984). By replacement we mean the replacement of the existing component in the socket by a new component. On replacement the system is considered to be new (renewal). Components have a lifetime or time to failure distribution F(t) (and corresponding reliability R(t) = (1 − F(t)). The system fails if and only if the component fails. We suppose that the lifetime distribution of a component is a mixture: F(t) = pF1(t) + (1 − p)F2(t); p is the mixing parameter. Thus, we suppose that components arise from a mixed population of “weak” and “strong” components. The reliability characteristics of such mixtures have been extensively studied (Jiang and Murthy, 1998), although maintenance policies have been studied to a lesser degree (Scarf et al., 2009).
