It is common that a production system deteriorates subject to different manners and terms of usage during the production process. In such a case, an increasing defect rate is anticipated, which may damage the reputation of the manufacturer, thus a sound inspection schema is essential to ensure the quality of products and also reduce the production and the warranty costs. In this paper, a Weibull power law process was deemed to be appropriate in describing the deterioration of the production system, and a realistic inspection schema with the manipulation of negative binomial sampling was devised. The proposed schema periodically examines the system after each production cycle. Once an out-of-control status is recognized, a process of product inspection starts which inversely inspects from the last product of the corresponding production lot in turn and stops when an optimal number of conforming products have been collected. The determination of this optimal number is crucial and discussed in detail. Finally, a practical application was employed to demonstrate the usefulness of this study, and sensitivity analyses were performed to study the various effects of some influential factors.
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