Non-Normal Capability Analysis evaluates process capability when data do not follow a normal distribution and normal Cp/Cpk assumptions are not appropriate.
Definition
Non-Normal Capability Analysis assesses how well a process meets specification limits when the output distribution is skewed, bounded, multimodal, or otherwise non-normal. It may use distribution fitting, transformations, percentile methods, or nonparametric approaches.
The goal is the same as normal capability analysis: estimate customer risk and process performance. The method changes because the distribution assumption changes.
History
Capability analysis grew from quality engineering and statistical process control. As practitioners applied it to cycle time, strength, chemical, reliability, and transactional data, non-normal methods became necessary.
When to Use
Use non-normal capability analysis when normality tests, histograms, probability plots, or process knowledge show that normal capability indices would misrepresent risk. It is common for bounded measurements, time data, wear data, and one-sided specifications.
Step-by-Step
- Confirm measurement system adequacy.
- Verify process stability with control charts.
- Review histogram and probability plots.
- Test or assess distribution fit.
- Choose transformation, fitted distribution, percentile, or nonparametric method.
- Estimate capability and defect risk.
- Interpret with process knowledge and customer requirements.
- Document assumptions and update if the process changes.
Examples
- Cycle time: Right-skewed service times require percentile-based capability.
- Reliability: Weibull behavior is analyzed with a fitted distribution.
- Flatness: One-sided bounded data may not be normal.
Common Pitfalls
- Forcing normal Cp/Cpk on skewed data.
- Ignoring process instability.
- Using transformations without explaining meaning.
- Fitting distributions with too little data.
- Mixing multiple populations.
- Reporting indices without defect-risk interpretation.