Optimal scheduling imperfect maintenance policy for a system with multiple random works

This paper investigates a scheduling imperfect maintenance policy for an operating system that works at random times for multiple jobs (n tandem jobs or n parallel jobs). We consider the system suffers from type-I failure which is corrected by a minimal repair, or type-II failure, which is disaster and is eliminated by a corrective maintenance. To control the deterioration process, preventive maintenance is design to go through at a scheduling time T or the completion of multiple jobs, whichever occurs last. Each maintenance is performed imperfectly, the system improves yet its failure characteristic is also changed after maintenance. Lastly, the system is displaced at the N-th maintenance. On the basis minimizes the mean cost rate, this paper derived the optimal scheduling parameters (T*, n*, N*) analytically and numerically, according to its existence and uniqueness. The models we proposed will provide a general structure for maintenance theory of reliability.