Process Capability Analysis Methodologies for Zero-Bound, Non-Normal Process Data

The original Japanese process capability indices and Shewhart quality control charts (1939) were designed for use with independent, normally distributed data. When tracking inherently non-normal processes that tend to exhibit multiplicative rather than additive error variation, the options for statistical process monitoring and capability estimation are more limited. In particular, for zero-bound process variables such as flatness or parallelism, the normality of the process data is significantly distorted as the process improves and approaches its desired level of zero. In this article, we propose a process capability index estimation methodology for C-p and C-pk for the case of non-normal, zero-bound process data using the delta distribution, a variant of the lognormal distribution. This approach utilizes quantile estimates derived from a proposed modification of lognormal quality control charts (originally introduced by Morrison 1958 and Ferrell, 1958), thus allowing statistical control to be tracked and achieved before index estimation. When process data are skewed, these process control and capability estimation techniques are superior to those that rely on normality assumptions; when the skewed data are also zero-bound, these techniques provide additional benefits over traditional quantile transform techniques.