A monitoring process and assessing process capability under a hierarchial model, Part 1.

In this paper we discuss the practical problems involved in following the rational subgrouping principle for control charting as many processes exhibit variation that exceeds the within subgroup variation. As an example we consider simple models for processes where the two extremes ‘high frequency variation’ and ‘low frequency variation’ both contribute to inherent process variation. We emphasize the importance of distinguishing between charting aimed at identifying situations where minor process adjustments are needed to compensate for process disturbancies, and charting aimed at demonstrating a state of ‘statistical control’ with a predictable long-term distribution of process output. For the latter purpose we discuss the modelling of process variation by means of a hierarchical model for normally distributed measurements. The approach is illustrated by a case from the pharmaceutical industry. We finally discuss the assessment of process capability under a hierarchical model for process variation.