Nonparametric adaptive opportunity-based age replacement strategies

We consider opportunity-based age replacement using nonparametric predictive inference (NPI) for the time to failure of a future unit. Based on n observed failure times, NPI provides lower and upper bounds for the survival function for the time to failure Xn+1 of a future unit, which lead to upper and lower cost functions, respectively, for opportunitybased age replacement based on the renewal reward theorem. Optimal opportunity-based age replacement strategies for unit n+1 follow by minimising these cost functions. Following this strategy, unit n + 1 is correctively replaced upon failure, or preventively replaced upon the first opportunity after the optimal opportunity-based age replacement threshold. We study the effect of this replacement information for unit n + 1 on the optimal opportunitybased age replacement strategy for unit n + 2. We illustrate our method with examples and a simulation study. Our method is fully adaptive to available data, providing an alternative to the classical approach where the probability distribution of a unit’s time to failure is assumed to be known. We discuss the possible use of our method and compare it with the classical approach, where we conclude that in most situations our adaptive method performs very well, but that counter-intuitive results can occur.