Sensitivity of optimal replacement policies to lifetime parameter estimates

This paper analyzes three time-based replacement policies when the parameters of the time-to-failure distribution are unknown. Under the hypothesis of a large sample data, the unknown parameters are estimated via maximum likelihood method. The uncertainty around the point estimates impacts the maintenance decision rules. Based on the asymptotic normality of the parameter estimators and delta-method, the asymptotic distribution of the optimal decision parameter and the average cost is derived. This distribution permits to measure the uncertainty around the optimal maintenance decision rule induced by the point estimates. The sensitivity analysis of the replacement policies to the maintenance unit costs and lifetime distribution parameters is carried out. Application to two time-to-failure distributions is provided.