Semi-parametric estimation of Brown–Proschan preventive maintenance effects and intrinsic wear-out

A system subject to corrective and preventive maintenance actions is considered. Corrective Maintenance (CM) is done at unpredictable random times and is assumed to have As Bad As Old (ABAO) effects. Preventive Maintenance (PM) is supposed to be done at deterministic predetermined times and to follow a Brown–Proschan (BP) model, i.e., each PM is As Good As New (AGAN) with probability p and ABAO with probability 1−p. In this context a semi-parametric estimation method is proposed: nonparametric estimation of the first time to failure distribution and parametric estimation of the maintenance effect p. This work is original in considering that BP effects (ABAO or AGAN) are unknown or unobserved.