Evaluating statistically constrained economic design for monitoring the average number of non-conformities with adaptive sampling schemes

Recent researches have shown that control charts with adaptive sampling schemes are faster than the static control charts in detecting process shifts. In this article, based on the Markov chain concepts, adaptive sampling schemes of U control chart are designed for monitoring the average number of non-conformities per unit in the process. Also, the economic statistical design of U control chart with two cost functions has been developed. These economic models considered features such as the cost of false alarms, the cost of detecting assignable causes and repairing, the cost of producing defective items when the process is in-control and out-of-control states and the cost of sampling and inspection. At the end, numerical examples for comparison and demonstrating the applicability of purposed schemes are solved. The results show the significant improvement of the adaptive sampling schemes as compared to the classic scheme based upon the statistical and cost criteria.