Non-Normal CpK: Process Capability for Skewed Data
The Principle of Non-Normal CpK
Skewed data (such as lifetimes, strengths and interval times) violate the normality assumption, and using the normal formula directly over- or under-estimates capability. Two approaches exist: first, transform the data to approximate normality with Box-Cox or Johnson transformations before calculating; second, fit a distribution such as Weibull or lognormal directly and compute capability from distribution quantiles (for example, the 0.135% and 99.865% percentiles) instead of mean +- 3 sigma. The tool runs a normality test first to tell you whether this tool is needed.
When to Use Non-Normal CpK
Use it to evaluate process capability when the data are clearly skewed or truncated (strength, lifetime, concentration, interval times); when the normality test fails and cannot be improved by routine transformation; and for PPAP and customer submissions of non-normal data. The tool runs a normality test first and prompts you to switch to this tool when the p-value is below 0.05, automatically trying several transformations and distribution fits. If the skew is severe, it guides you into the non-normal workflow.
How to Read the Results
The tool tries multiple transformations automatically, selects the best fit and compares the capability indices before and after transformation, while giving goodness-of-fit statistics (AD value/p-value) to judge whether the transformation or distribution fit succeeded. The report should state the transformation method or distribution type used for customer traceability and audit, avoiding disputes over unclear definitions. If the methods disagree widely, the data have an unusual shape and the choice rationale should be documented; record the goodness-of-fit statistics as well and keep the reporting convention consistent.
Precautions
Transformation changes the unit of measurement, so interpret capability indices in the transformed space. Distribution fitting is unreliable with small samples (fewer than 20). Agree on the non-normal capability convention (for example, 1.5 sigma shift adjustments) with the customer in advance. After transformation, confirm with a control chart that the process is stable before interpreting capability, and save the transformation parameters and raw data so the customer can recompute with the same convention, stating the limitations when the sample size is insufficient.