Design of cumulative count of conforming charts for high yield processes based on average number of items inspected

Purpose - This paper aims to propose a new approach to setting the control limits to promote the control performance of the cumulative count of conforming chart (CCC-r chart), in terms of the average number of items inspected (ANI). Design/methodology/approach - In contemporary high-yield manufacturing processes, the CCC-r chart is often an alternative of p charts or np charts for monitoring the fraction nonconforming (p). When a CCC-r chart is used, the traditional approach based on the equal-tail probabilities to setting control limits demonstrates a poor performance in terms of ANI as p deviates upward from its nominal value p(0). To improve the performance of CCC-r charts, this research uses a search method based on some analytical results to find the control limits such that the in-control ANI (ANI(0)) is near-maximal and near-unbiased. Findings - Analytical validation confirms that the proposed approach outperforms the traditional one in terms of the maximum and the unbiasedness of ANI(0). When p(0) is not given, simulation results show that the minimum-variance unbiased estimator tends to perform better than the maximum likelihood estimator. Originality/value - This study numerically shows that the use of the proposed approach achieves the goal of the near-maximal and near-unbiased ANI(0), and hence improves the performance of CCC-r charts. In addition, because the proposed approach is computational intensive, this study also develops a Visual Basic project to help practitioners obtain the control limits using the proposed approach.