A study on negative binomial inspection for imperfect production systems

Production systems continuously deteriorate with age and usage due to corrosion, fatigue, and cumulative wear in production processes, resulting in an increasing possibility of producing defective products. To prevent selling defective products, inspection is usually carried out to ensure that the performance of a sold product satisfies the customer requirements. Nevertheless, some defective products may still be sold in practice. In such a case, warranties are essential in marketing products and can improve the unfavorable image by applying higher product quality and better customer service. The purpose of this paper is to provide manufacturers with an effective inspection strategy in which the task of quality management is performed under the considerations of related costs for production, sampling, inventory, and warranty. A Weibull power law process is used to describe the imperfection of the production system, and a negative binomial sampling is adopted to learn the operational states of the production process. A free replacement warranty policy is assumed in this paper, and the reworking of defective products before shipment is also discussed. A numerical application is employed to demonstrate the usefulness of the proposed approach, and sensitivity analyses are performed to study the various effects of some influential factors.