Statistical process control (SPC), process performance indices (Ppk), and acceptance sampling by variables (ANSI/ASQ Z1.9, or formerly MIL-STD 414) rely on the assumption that the process data follow the normal or bell curve distribution. This distribution is far more common in textbooks than in the real world. Generally accepted and off the shelf methods are however available for SPC and process performance analysis for non-normal distributions.

While we are not aware of formal sampling plans for non-normal distributions, it is however possible to get a confidence limit for the nonconforming fraction in a homogeneous production lot. As an example, we can be 95% confident that the nonconforming fraction is no greater than a certain percent depending on the sample data and sample size.

Attendees will learn the generally accepted, and off the shelf, methods for using SPC and carrying out process performance studies for non-normal distributions, and also confidence limits for the nonconforming fraction in a homogenous production lot. The latter is a potential alternative for non-normal distributions where ANSI/ASQ Z1.9 cannot be used.

The traditional Shewhart control chart has a 0.00135 (0.135%) false alarm risk at each control limit, but this assumes that the data follow a normal distribution. When the distribution is non-normal, the risk may be considerably higher, especially when there is a one-sided specification for the quality characteristic in question. This is especially true when there is a physical limit, such as the fact that it is impossible to get less than zero impurities, particles, trace metal concentrations, and so on. If the bell curve extends below zero, it models a physically impossible situationâ€”and the population fraction in question will instead be toward the upper control limit. If the actual distribution is known, however, control charts can be set up that have the traditional false alarm risk.

If SPC uses sample averages, the Central Limit Theorem will mitigate against the effects of non-normality, but individual measurements rather than averages are in or out of specification. This means we must identify the correct underlying distribution to perform a valid process performance study. If we assume wrongly that the distribution is normal, the estimated nonconforming fraction can be off by orders of magnitude; a purported Six Sigma process might not even be capable. Again, however, generally accepted and off the shelf methods are available to handle these situations.

ANSI/ASQ Z1.9 relies explicitly on the assumption that the measurements in the production lot follow the normal distribution. If they do not, the producer and customer cannot rely on the standard to assure the specified level of quality. It is however possible to calculate a 90%, 95%, or whatever is desired confidence limit for the nonconforming fraction based on (1) the sample data and (2) the sample size if we know the underlying statistical distribution.