An extended production and inspection model with nonrigid demand

This paper extends a previous production and inspection (PI) model in relation to market demand that is nonrigid to consider an imperfect process that has a general hazard rate instead of a constant failure rate. Products are produced by an imperfect process that may shift randomly from the IN state to the OUT state. When the process is in the OUT state, it has a higher probability of producing a nonconforming product than when it is in the IN state. To achieve the zero defects policy, all products before delivery to the market should be inspected and the inspection order follows their production sequence. Furthermore, the inspection information from all previous products is used to decide either that the next candidate product should be inspected or that the inspection procedure for the current production lot should be terminated. When the inspection procedure is terminated, the remaining unmet demand is regarded as a shortage. An algorithm is developed to determine an optimal PI policy that minimizes the expected total cost, which includes the cost of inspection, of shortage, and of production.