Control Limits Based on the Narrowest Confidence Interval

Abstract

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.

Multivariate control chart based on the highest possibility region

“…When p = 1, the proposed method reduced to that of Yang et al [30]. In the next section, the calculation of HPR's control limit will be introduced.…”

“…From the decision procedure of a control chart [30], the decision is carried out by comparing each plotted data point with the control limits. In other words, the corresponding hypothesis test is actually conducted based on single data.…”

“…the average run length which is reciprocal to the false alarm level, for asymmetrical or multimodal distributions. Nevertheless, there might be some out-of-control points with relatively high occurrence possibility and some in-control points with relatively low occurrence possibility [30]. This phenomenon does not coincide with quality control in practice, since producers only want to exclude the bad states of the processes and maintain the good ones.…”

“…This phenomenon does not coincide with quality control in practice, since producers only want to exclude the bad states of the processes and maintain the good ones. As mentioned in the co-author's recent work [30], the null hypothesis of control chart should focus on the occurrence possibility of each data point besides the false alarm requirement, where the possibility means the density function for continuous distributions and the probability mass function for discrete distributions, respectively.…”

Repetitive Model Refinement for Questionnaire Design Improvement in the Evaluation of Working Characteristics in Construction Enterprises

“…Other statistical confidence interval based studies include Tryon [22], who employed a graphical inference confidence interval approach in analyzing independent and dependent approaches for statistical difference, equivalence, replication, indeterminacy, and trivial difference. Yang et al [23] proposed control limits based on the narrowest confidence interval to analyze problems, if the traditional three-sigma control limits or probability limits were adopted and some points with relatively high probability of occurrence were excluded; yet, some points with relatively small probability of occurrence may still be accepted in asymmetrical or multimodal distributions. Bonett and Price [24] proposed an adjusted Wald interval for paired binomial proportions that was shown to perform as well as the best available methods.…”