Parameter estimation in an ARD ∞ Wiener degradation and maintenance model under different observation schemes

This paper develops a statistical inference study within a degradation model featuring imperfect maintenance for technological or industrial devices. Degrading systems undergo maintenance that only partially reduces their degradation level. The underlying degradation process of the system is modelled by using an univariate Wiener process with drift. The imperfect maintenance is modelled by using an Arithmetic Reduction of Degradation of infinite order model ( ARD ∞ ). The system is observed at different times and the degradation level of the system is recorded. The estimation study explores five different observation schemes. Our work focuses on the estimation of the model parameters under these observation schemes, deriving maximum likelihood estimators for each case. A simulation study assesses the quality of the estimators and compares the different observation schemes.