Optimal production lot-sizing and condition-based maintenance policy considering imperfect manufacturing process and inspection errors

In this paper, we propose an integrated Economic manufacturing quantity (EMQ) model combining both the concepts of condition-based maintenance (CBM) and imperfect manufacturing process. The manufacturing process is modelled by two indicators. One possesses binary state, indicating whether the manufacturing process is in-control or not. The other one is modelled by a homogeneous Gamma process, representing the degradation of the manufacturing equipment. The system is inspected at the end of each production run, upon which, the deterioration level can be perfectly observed, while two types of errors may occur in revealing the state of the manufacturing process. Defective products can be fabricated when the manufacturing state degrades. An integrated production and CBM policy is proposed. The objective is to develop the optimal production lot-sizing and preventive maintenance threshold in order to minimize the expected cost rate in the long-time horizon. We model the problem in the framework of a semi-Markov decision process. The successive-approximations method is applied to solve the problem numerically. The applicability of the proposed model and some sensitivity analysis are presented in a numerical illustration. It can provide theoretical reference to the decision-maker in production and maintenance planning.