(54i) Determining Product Specification for Count Data

In order to ensure that a business can produce minimum amount of out of specification product, it is critical to include the statistical knowledge of its process and measurement capability in determining the product specification. This can be done by following “Big Data” concepts, utilizing historical process and/or lab data. As a standard six-sigma methodology, the capability of measurement is commonly evaluated from P/T ratios. However, the evaluation of P/T ignores within-product variation, and is inadequate for non-normal data distributions and/or concentration-dependent standard deviations. We propose a more generally applicable approach, in which we focus on confidence levels (or “critical fallout values“) rather than on P/T ratios. Our approach allows for product variation and for all possible data distributions, including discrete distributions.

At The Dow Chemical Company, we have started to apply our generalized approach to the evaluation of method capability in the case of Poisson-distributed data. We will illustrate the merits of our approach from our experiences in this specific application.