Intervals & Tests
by Paul A. Keller, CQE CQA
The Non-Normal Distributions in the Real World article by Tom Pyzdek provides many examples and sound reasoning for the existence of Non-normal data. Tom elaborates on the implications of non-normality, particularly as they relate to capability calculations. As Tom suggests, when processes are sufficiently non-normal we will need to estimate the shape of the distribution to calculate process capability or control limits for individuals data. Most SPC products, including SPC-PC IV, SPC IV Excel, and SPC Explorer from Quality America, allow users to fit curves to data using the Johnson family of distributions. A key requirement for defining distributions is that the data be from a controlled process. This makes sense, as the lack of statistical control indicates the presence of multiple distributions. When rational subgroups of size greater than one can be formed, an X-Bar chart can be used to evaluate process control. When rational subgroups are limited to single observations, Individual-X charts would seem the natural choice for evaluating process control. However, we need to define the distribution in order to calculate the proper control limits for these individual data values. This is a problem, since we cannot define the distribution unless the process is in control. It seems we are in a "Catch 22" scenario.
Fortunately, there are other charts for individuals data. The EWMA chart and Moving Average chart are popular choices for this situation. Since the plotted statistic is an average (an exponentially weighted average or a moving average, respectively), the Normal distribution is used to define control limits. We can establish control using the EWMA or MA chart, then define the distribution using the Johnson methods. This fitted curve can be used to calculate process capability and control limits for the Individuals chart.
Learn more about the Statistical Inference tools for understanding statistics in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Intro. to Statistics short course (only $89) or his online Black Belt certification training course ($875).