Optimal economic production quantity policy for a parallel system with repair, rework, free-repair warranty and maintenance

Hot standby redundancy maintains the working order of a system, repairs offer restoration in case of failure, and preventive maintenance (PM) prevents trouble. Warranties provide assurance to customers, and a superior warranty signifies higher product quality. The running costs of redundancy, maintenance and warranties influence decisions during product manufacture. Therefore, this paper presents an economic production quantity (EPQ) model for a parallel system with maintenance, production, and free-repair warranty (FRW) programmes. The production system begins with a basic unit and produces conforming items. PM is performed after the production run period and is classified as imperfect or perfect. If the basic unit fails, it is repaired and returned to operation after perfect PM; the spare unit is online only during the repair time of the basic unit. The spare will produce some number of defective goods, which are reworked in the same inventory cycle. The hot spare is minimally repaired if it fails in its standby or online mode. In this study, an inferior item is defined as one that satisfies specifications on inspection and is usable but is likely to incur postsale servicing costs when sold under an FRW. The total cost of this EPQ model includes setup, holding, PM, restoration, minimal repair, and warranty costs. The optimal production runtime is determined by minimising the total cost. Several cases are discussed in this paper, and the proposed model is illustrated using a numerical example and sensitivity.