What to Do When It's Not a Bell Curve - 2017

Overview:

Statistical textbooks, manuals, and even most software rely on the assumption that processes conform to the normal or bell curve distribution. When the real world process does not cooperate with this assumption,

• Statistical process control charts will have numerous false alarms that waste people's time and undermine confidence in SPC
• Estimates of process capability or process performance indices can be highly misleading, and off by orders of magnitude in terms of the actual nonconforming fraction. As an example, a centered "Six Sigma" process, which should deliver two nonconformances per billion opportunities, might not even be capable.
• ANSI/ASQ Z1.9 is not usable.

This presentation will show how to test the assumption that a process follows the normal distribution. While we can never prove that a process follows the normal (or any other) distribution, we can prove beyond a quantifiable reasonable doubt that it does not. This tells us to look for a better model, and models can be selected according to the nature of the process and also precedents that involve similar processes. We cannot overemphasize the need to include tests for distributional fit with any process capability or process performance report. These tests include qualitative graphical techniques such as the histogram (does it look like a bell curve?) and normal probability plot, and quantitative methods such the chi square test for goodness of fit and the Anderson-Darling test.

The latter is readily available in statistical software packages such as Minitab and StatGraphics. This assures the internal or external customer that the statistical model has in fact been tested for validity. Once we have identified the correct distribution, it is very straightforward to create SPC charts that reflect the underlying distribution. It is also very straightforward to calculate accurate process performance indices that reflect the actual ability of the process to meet the specifications.

Why should you Attend:

Almost all traditional industrial statistical methods rely on the assumption that the critical to quality (CTQ) characteristic follows the normal or bell curve distribution. The bell curve is far more common in textbooks than it is in real factories, where processes often follow other distributions.

The ANSI/ASQ Z1.9 (formerly MIL STD 414) standard for acceptance sampling by variables says very clearly that the sampling plans assume that the data follow a normal distribution, which means this standard will not work for non-normal data. Traditional process capability calculations, the kinds on which companies might claim to have Six Sigma processes, also rely on this assumption. If the underlying distribution is non-normal, then the estimated nonconforming fraction (defects per million opportunities) can be off by orders of magnitude, and a "Six Sigma" process might not even be capable.

Statistical process control (SPC) charts might similarly have much higher than the expected false alarm risk (0.27% two-sided risk for the traditional Shewhart chart). Production workers will therefore experience the equivalent of the boy who cried wolf, where they look for special or assignable causes in processes that are actually under control.

Areas Covered in the Session:

• The normal or bell curve distribution is far more common in textbooks than it is in real factories.
  • As but one example, undesirable random arrivals such as particles and impurities (measured on a continuous scale) apparently follow the highly skewed gamma distribution rather than the normal distribution. Minitab also applied this model successfully to snowfall in Boston
• Subjective and quantitative methods exist to test the assumption that data follow the normal (or other selected) distribution.
  • Histogram.
  • Chi square test for goodness of fit
  • Quantile-quantile test, of which the normal probability plot is one application.
• Know when the distribution might be non-normal. Processes with unilateral specification limits at one end and physical limits at the other-e.g. an upper specification limit for an impurity and the fact that it is impossible to get less than zero impurities-often signifies that the distribution will not be a bell curve.
• SPC charts can be created that work properly for non-normal distributions and have the same false alarm risk as the traditional Shewhart chart for a normal distribution.
• Process performance indices can be calculated that reflect accurately the nonconforming fraction (or defects per million opportunities) for non-normal distributions.

Who Will Benefit:

• Manufacturing
• Quality Engineers
• Managers

Speaker Profile

William Levinson is the principal of Levinson Productivity Systems, P.C. He is an ASQ Fellow, Certified Quality Engineer, Quality Auditor, Quality Manager, Reliability Engineer, and Six Sigma Black Belt. He holds degrees in chemistry and chemical engineering from Penn State and Cornell Universities, and night school degrees in business administration and applied statistics from Union College, and he has given presentations at the ASQ World Conference, TOC World 2004, and other national conferences on productivity and quality.

Levinson is also the author of several books on quality, productivity, and management. Henry Ford's Lean Vision is a comprehensive overview of the lean manufacturing and organizational management methods that Ford employed to achieve unprecedented bottom line results, and Beyond the Theory of Constraints describes how Ford's elimination of variation from material transfer and processing times allowed him to come close to running a balanced factory at full capacity. Statistical Process Control for Real-World Applications shows what to do when the process doesn't conform to the traditional bell curve assumption.

Others Details

For more details and updates please visit webinar website