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

Abstract

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.