A general multiple-repair-attempt process and its application to optimal age replacement

Abstract

Considerable attention in reliability literature has been given to studying various repair models. These models are often described under the assumption of minimal repair. However, repairs of a failed system can be unsuccessful and, therefore, should be repeated until a successful attempt. At certain instances, the assumption of minimal repairs is too restrictive, as the repair can be worse than minimal due to adverse effects of the previous repair attempts, external and internal shocks to a system, insufficient quality of repair, etc. Therefore, in this paper, we use the generalised Polya process to define and derive useful properties for a more general multiple-repair-attempt process with the worse than minimal repair. This has the minimal repair model as a special case. As an application, the corresponding age replacement policy for the general multiple-repair-attempt model is defined and the optimal solutions are obtained. Detailed numerical illustrations support our findings.