Statistical inference for a Wiener-based degradation model with imperfect maintenance actions under different observation schemes

This paper studies the statistical inference in a degradation model with imperfect maintenance. Technological or industrial devices subject to degradation undergo maintenance actions that reduce their degradation level. The underlying degradation process is a Wiener process with drift. Maintenance effects are assumed to be imperfect, described by an Arithmetic Reduction of Degradation (ARD1$$ AR{D}_1 $$) model. The system is regularly inspected and the degradation levels are measured. Four different observation schemes are considered so that degradation levels can be observed between maintenance actions as well as just before or just after maintenance times. The paper studies the estimation of the model parameters under the four observation schemes. Maximum likelihood estimators are derived for each scheme. The quality of the estimations is assessed and the observation schemes are compared through an extensive simulation and performance study.