On Reliability of a Multi-Socket Repairable System

Consider a set of the so‐called sibling components in a multi‐socket repairable system. In the case of an automobile, for example, these siblings would be spark plugs, light bulbs, tires, that is, identical components that are coded with the same part number. When field data are analyzed, a dilemma arises as to how to interpret a recurrent replacement of a sibling component: as a secondary failure of the component that has already been replaced once, or as the first failure of the component's sibling(s)? From the stand point of root‐cause analysis, the task is to understand whether recurrent failures are related to (i) a particular sibling, which might be operating in inauspicious conditions relative to other siblings, or (ii) to all siblings on the vehicle. One could attribute Scenario 1 to a system‐level (e.g. system interaction) problem, and Scenario 2 to a component‐level (supplier quality) problem. We first review a statistical procedure that solves the above‐mentioned dilemma in the framework of ordinary renewal process (ORP) and then extend the discussion to the non‐homogeneous Poisson process (NHPP) and the g‐renewal process (GRP). We also propose advanced Monte Carlo procedure for estimating GRP in this context.