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A Comparison Between a Frequentist, Bayesian and Imprecise Bayesian Approach to Delay Time Maintenance

Delay time models are stochastic maintenance decision aid tools that divide the failure time of a system into the appearance of a defect and its evolution towards a breakdown. In this study, an imprecise Bayesian approach to delay time modelling has been developed and compared with the frequentist and precise Bayesian approach based on a virtual maintenance problem. The conditional failure rate was the unknown parameter that had to be estimated via eight samples of failure times of increasing size. The goal was to minimise two loss functions related to the downtime and cost. The frequentist and precise Bayesian methods converge towards the optimal decision as the sample size grows but are strongly sub-optimal when no or only few data are available. The imprecise Bayesian approach based on E-admissibility returns large decision intervals in the lack of data, thereby straightforwardly representing the crucial difference between knowledge and ignorance.