Webinar On "What to Do When it's Not a Bell Curve"

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.

1. Statistical Process Control
   • SPC charts for non-normal distributions can be set up by calculating the 0.00135 and 0.99865 quantiles of the distribution in question, and setting the control limits accordingly. The false alarm risks will then be identical to those of a traditional Shewhart control chart.
   • Traditional Shewhart charts might be usable for sample averages due to the Central Limit Theorem, which says averages for large enough sample sizes will follow a roughly normal distribution regardless of the underlying distribution.
2. Process Performance Studies
   • The traditional calculations for capability and performance indices rely on the assumption that the process follows a normal or bell curve distribution. Application of the same mathematical formulas to non-normal data will deliver grossly inaccurate results.
   • Off the shelf methods are however available with which to calculate meaningful performance indices for these processes. If for example a non-normal process has an estimated nonconforming fraction of 0.00135 beyond its upper specification limit, its PPU equals 1 (the same as for a normally distributed process with the same nonconforming fraction).
     1. This approach is described in the Automotive Industry Action Group's SPC manual.
     2. Minitab and StatGraphics perform the necessary calculations automatically.
3. Acceptance Sampling

Manufacturing and quality engineers and technicians

William A. Levinson, P.E., FASQ, CFPIM, is the owner of Levinson Productivity Systems PC. He holds professional certifications from the American Society for Quality, APICS, and Society of Manufacturing Engineers.