Availability analysis of opportunistic age replacement policies

This research develops the availability function for a two component series system in which a component is replaced because of component failure or because it reaches a prescribed age. Also each component replacement provides an opportunity for the replacement of the other component. This last maintenance policy is called an opportunistic replacement strategy.

The system functions only if the both components of the system are functioning. The system fails if either of the components fails. Component i is replaced if it fails before attaining age T_i since it was last replaced or maintained. The component i is preventatively maintained if is has not failed by the age T_i. This type of replacement plan is called age replacement policy. When component 1 is being replaced or preventatively maintained, if the age of component j ≠ i exceeds τ_j then both components i and j are replaced at the same time. This type of replacement is called opportunistic replacement of component j and τ_j is called the opportunistic replacement time for component j. The time dependent and long run availability measures for the system are developed.

A nested renewal theory approach is used is used to develop the system availability function. The nesting is defined by considering the replacement of a specific one of the components as an elementary renewal event and the simultaneous replacement of both components as the macroscopic renewal event. More specifically, the renewal process for the system represents a starting point for the entire system and is in fact a renewal process. The intervals between system regeneration points are called “major intervals".

The age replacement time T_i and opportunistic replacement time τ_i are treated as decision parameters during the model development. The probability distribution of the major interval is developed and the Laplace transform of the system availability is developed.

Four replacement models are obtained from the main opportunistic age replacement policy. These are a failure replacement policy, an opportunistic failure model, a partial opportunistic age replacement policy and an opportunistic age replacement policy. These models are obtained as specific cases of the general model.

The long run availability measure for the failure replacement model is proven to be the same measure as that developed by Barlow and Proschan. This proof validates the modeling approach.