Joint optimization of maintenance and spare ordering policy for a competing failure system considering product quality

This paper proposes an integrated framework for maintenance, spare parts ordering, and quality control planning within a multi-state production system that is subject to two competing modes of failure: hard failure and soft failure. Hard failures occur suddenly and without any prior warning, whereas soft failures develop following the onset of a defect. The quality of the product is significantly influenced by the state of the system, as a defective system typically leads to an increase in non-conforming products. To address this, periodic inspections are conducted to detect defects early, and preventive replacements (PR) are scheduled upon identification of a defective state, which acts as a crucial quality control indicator. Corrective replacements (CR) become necessary when either a hard or soft failure occurs. The timeliness of these replacements is contingent upon spare part availability; thus, we implement a hybrid spare ordering policy to enhance responsiveness. PR and CR are executed promptly when time-based ordered spares are accessible, while a condition-based order is triggered in the event of shortages in time-based orders. To determine the optimal inspection interval and time-based spare ordering point, we analyze the renewal scenarios of the system with the objective of minimizing the expected cost rate. We propose an optimization algorithm and a simulation procedure to validate the effectiveness of our policy through numerical experiments. The results highlight the significant potential of our approach in reducing unit losses related to non-conforming products while effectively minimizing the expected cost rate.