Lot sizing in a deteriorating production system under inspections, imperfect maintenance and reworks

The paper studies the joint effect of shift, inspections, imperfect preventive maintenance (PM) and imperfect rework of defective items on optimal decisions for a deteriorating production system. At the time of inspection during a production run, either PM or restoration is done depending on the state of the production process. There is a probability that PM action may shift the process from 'in-control' state to 'out-of-control' state. During the 'out-of-control' phase, the system produces some defective items which go for rework at the end of the production run. A portion of the reworked items may also fail repairing. The model is formulated for the case of general inspections and analyzed under two well known inspection policies-periodic inspection policy and constant cumulative hazard inspection policy. For numerical examples, a comparison of the outcomes of the model with and without reworks under these two inspection policies is made. It is observed that the periodic inspection policy performs better than the constant cumulative hazard policy.