Optimum sequential preventive maintenance first or last policies with imperfect maintenance for a system subject to shocks

This paper proposes and analyses the generalized sequential preventive maintenance policies for an operating system that works at random processing times and subject to shocks. The shocks arrive according to a non homogeneous Poisson process (NHPP) with varied intensity function in each maintenance interval. As a shock occurs, the system suffers two types of failures with number-dependent probabilities: type-I (minor) failure, which is rectified by a minimal repair, and type-II (catastrophic) failure, which is removed by a corrective maintenance. The imperfect maintenance is carried out to improve the system failure characteristic due to the altered shock process. The preventive maintenance-first and preventive maintenance-last policies are defined as that the system is maintained before any type-II failure occurs at a planned time T-i or at the completion of a working time in the i-th maintenance interval, whichever occurs first and last, respectively. At the N-th maintenance, the system is replaced rather than maintained. This paper aim is to minimize the mean cost rate as a measure of policy by determining optimal sequential maintenance parameters for each preventive maintenance policy. All discussions are presented analytically and determined numerically in terms of its existence and uniqueness.