Inference for a gradually deteriorating system with imperfect maintenance

This article develops inferential methods for a gradually deteriorating system in the presence of imperfect corrective maintenance. The gamma process is adopted as the degradation model and two cases are discussed: degradation-based and age-based inference. The likelihood function related to each of these cases deals with dependent random variables and is scarcely discussed in the literature. Its derivation is detailed and the profile likelihood are numerically illustrated. An application of the developed inference results for replacement planning is proposed. A numerical example by using Monte-Carlo simulation is presented for the maintenance policy under consideration.