Control limits based on the narrowest confidence interval

In statistical process control (SPC), if the traditional 3-sigma control limits or probability limits are adopted, some points with relatively high occurrence possibility may be excluded; however, some points with relatively small occurrence possibility may be accepted for asymmetrical or multimodal distributions. Motivated by the highest posterior density credibility interval, we propose control limits based on the narrowest confidence interval to solve the problem, where the narrowest confidence interval denotes the confidence interval with the shortest width. The proposed control limits will not only meet the false alarm requirement, but also ensure that each in-control data point has relatively high occurrence possibility. Some properties of the proposed control limits and its relation to the existing two control limits are presented in the end.