On the Number of Maintenance Cycles in Systems With Critical and Noncritical Components

We present a novel mathematical framework for computing the number of maintenance cycles of a system component [referred to as “noncritical” (NC)] until another reference system component [referred to as “critical” (CR)] fails for the first time. Whenever the NC component experiences a failure, it receives necessary corrective maintenance in terms of replacement or minimal repair, as long as the CR component is still in operation. The lifetime of the CR component is assumed to be independent of that of NC and the first failure of CR is assumed to mark the end of the cycle counting process. That is, the CR component is never correctively repaired but it can optionally be fully replaced in an opportunistic maintenance fashion every time the NC component fails. This study broadens the scope of existing renewal theory (whether standard or generalized) by computing the average number of renewals for the NC component within the limited lifetime of the CR component. Closed-form approximations for the proposed “bounded” renewal processes (BRPs) are also given. Simulation results on a variety of distributions for the component lifetimes, including actual distributions for components of wind turbines, show that the approximations follow closely the real processes. In addition, we demonstrate, using actual costs for replacement and repair of wind turbine components, the difference in maintenance cost estimation that the proposed BRPs make with respect to standard and generalized renewal theories, and exemplify the decision point for selecting a particular BRP to minimize maintenance cost.