Optimal number of major failures before replacement

When the repair cost of a failed system is random, it is no longer meaningful to expend more than the replacement cost on a catastrophic failure. This paper presents a mathematical model that uses two cost limits to combine and extend the replacement models based on minor-failure number8] and constant repair cost limit5] for general time-to-failure distributions. When the failed system requires repair, it is first inspected and the repair cost is estimated. Minimal repair is only then undertaken if the estimated cost is less than the minor repair-cost limit; or if the estimated cost is less than the replacement cost and the predetermined major-failure number is not reached. An example with a Weibull time-to-failure distribution and a negative exponential distribution of estimated repair cost is given to illustrate the computational results.