مدل مقدار تولید اقتصادی به صورت شکست تصادفی در فرایند تولید با حداقل تعمیر و نگهداری ناقص

This study applies periodic preventive maintenance (PM) to economic production quantity (EPQ) model for a randomly failing production process having a deteriorating production system with increasing hazard rate: minimal repaired and reworked upon failure (out of control state). The minimal repair performs restorations and returns the system to an operating state (in-control state). It is assumed that, after each PM, two types of PM are performed, namely imperfect PM and perfect PM. The probability that PM is perfect depends on the number of imperfect maintenance operations performed since the last renewal cycle. Mathematical formulas for the expected total cost are obtained. For the EPQ model, the optimum run time, required to minimize the total cost, is discussed. Various special cases are considered, including the maintenance learning effect. Finally, a numerical example is presented to illustrate the effect of PM and setup, breakdown and holding cost.

To be globally competitive, manufacturers require a production policy that also manages inventory levels in the face of uncertainty regarding production failure and demand. Production policies have been extensively investigated with the aim of reducing production costs by Chelbi and Ait-Kadi (2004), Islam (2004), Jaber et al. (2009), Piñeyro and Viera (2010) and Ouyang et al. (2002). The economic production quantity (EPQ) model is a useful inventory control model that has been extensively investigated (Chung, and Huang, 2003). Notably, however, the quality of a product used to be inspected only at the final stage of production. Therefore, many non-conforming products have already been manufactured by the product inspection stage (Salameh and Jaber, 2000). Incorporating complete inspection into the production process has become possible with the automation of manufacturing. Hence, when the system shifts into “out-of-control” state, repair and reworking can be immediately performed to restore the state of the production process and satisfy product specifications or requirements.

This study described a integrate EPQ model that incorporates EPQ and maintenance programs. The model for optimizing the time T⁎ was examined. The nature of a PM process and policy produces the hypothesis that the probability of perfect PM being obtained depends on the number of imperfect PM performed since the previous renewal cycle. The results of investigating the optimal policy conditions demonstrate that such a policy is more general and flexible than policies already reported in the literature. Special cases were examined in detail. The optimum run times T⁎ were found in special cases, with reference to an example. Analysis reveals the effect of the input parameters on the solution, and also obtains some further insights. If the PM learning rate is estimated based on the actual data, analysts can use the learning curves to project the PM costs in the integrate EPQ model. This information can be used to estimate training requirements, and develop PM plans. Possible extensions of this work can be done in machine learning. For example, we can use historical maintenance data to find failure behavior by machine learning (data mining) and determine optimal maintenance policy to reduce total production cost.