Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives

Novel replacement policies that are hybrids of inspection maintenance and block replacement are developed for an n component series system in which the component parts used at successive replacements arise from a heterogeneous population. The heterogeneous nature of components implies a mixed distribution for time to failure. In these circumstances, a hybrid policy comprising two phases, and early inspection phase and a later wear-out replacement phase, may be appropriate. The policy has some similarity to burn-in maintenance. The simplest policy described is such a hybrid and comprises a block-type or periodic replacement policy with an embedded block or periodic inspection policy. We use a three state failure model, in which a component maybe good, defective or failed, in order to consider inspection maintenance. Hybrid block replacement and age based inspection and opportunistic hybrid policies will also arise naturally in these circumstances and these are briefly investigated. For the simplest policy, an approximation is used to determine the long run cost and the system reliability. The policies have the interesting property that the system reliability may be a maximum when the long-run cost is close to its minimum. The failure model implies that the effect of maintenance is heterogeneous. The policies themselves imply that maintenance is carried out more prudently to newer than to older systems. The maintenance of traction motor bearings on underground trains is used to illustrate the ideas in the paper.