How the distribution affects capability analysis results

Minitab provides capability analyses based on both normal and nonnormal probability models. The analyses that use a normal probability model provide a more complete set of statistics, but your data must approximate the normal distribution for the statistics to be appropriate for the data.

For example, Normal Capability Analysis estimates expected PPM (parts per million) out-of-spec using the normal probability model. Interpretation of these statistics depends on two assumptions: that the data are from a stable process, and that they follow an approximately normal distribution.

Similarly, Nonnormal Capability Analysis calculates PPM (parts per million) out-of-spec using a nonnormal distribution that best fits your data. In both cases, the validity of the statistics depends on the validity of the assumed distribution.

If the data are severely skewed, the estimated proportion of defective items may be greatly over or under estimated. In this case, it is better to either transform the data to make the normal distribution a more appropriate model, or choose a nonnormal probability model for the data. With Minitab, you can transform the data using Johnson distribution system or Box-Cox transformation or use nonnormal probability model.