Some maintenance models and availability with imperfect maintenance in production systems

Minimal repair and perfect repair, discussed extensively in the reliability and maintenance literature, represent two extreme types of repairs. Many repair or maintenance activities may not fall into these two extreme cases. A periodic maintenance model, in which both preventive and corrective maintenance are imperfect, and two other imperfect maintenance models are proposed in this paper. Unlike other imperfect maintenance models, imperfect maintenance in this work is mainly treated in such a way that successive operating times of a system are independent and decreasing by a fraction and successive maintenance times are independent and increasing by a fraction. The limiting expected maintenance cost rate and availability are derived and optimum maintenance policies are discussed for these three maintenance models. Based on the obtained maintenance cost rate and availability, a class of optimization problems with nonlinear programming formulations is demonstrated and a numerical example is presented.