Quality Digest

INITIAL POSTING: I've read that when determining process capability for a non-normal distribution, the process spread can be evaluated by finding the 0.135 and 99.865 percentile points using a probability plot. From this, I infer that the sigma value to be used in the capability calculations would be 1/6 of the spread. Using Minitab 14, I generated a column of data and then used the Individual Distribution Identification macro to obtain the percentile points. That macro concurrently reports the descriptive stats. (The generated data was Weibull 3-parameter, and the Identification macro was set to evaluate for this distribution). In this case, the std dev was reported as 2.25, while 1/6 of the "process spread" was 2.77. Moreover, the Minitab non-normal capability analysis (again selecting 3-parameter Weibull) reports only Ppk (1.22) due to 1-sided tolerance setup; Cpk is absent. Now, when the data is evaluated using a Box-Cox transform, Ppk drops to 1.00, and a Cpk value is given. So, my question is: Which is the better way to calculate process capability for non-normal data? It would appear that, in this case, the quantile method would yield a more optimistic result.

RESPONSE: For your type of question I typically ask the question "how long have you been working within the quality arena." Even though the specific responses may differ the typical response is a long period of time.

I then respond with something like, "If a smart person like you is confused and you have been working with this a long time, how do you think the line worker and CEO would feel? Do you think that they might be confused too?"

Sigma quality level calculations, Cp, Cpk, Pp, and Ppk can lead to a lot of confusion. My take is that we need to speak a language that everyone understands.

My approach is to track the output of the process at the 30,000-foot-level so that typical input variation experienced by the process is viewed as common cause. If this process tracking is considered predictable over time, we would then combine all the and make a statement about the percentage (or PPM rate) non-conformance; if a specification is no prevalent, we could then report the 80% frequency of occurrence. This approach applies to both normally distributed and non-normally distributed data.

With this approach, it is easy to understand the process capability/performance metric not only from the past but also a predictaion of the future, unless something either impacts the process either in a negative or positive (i.e., a Six Sigma project) way.

For more information see my Quality Progress 3.4 parts per million article "Control Charting at the 30,000-foot-level" (November 2003). FYI I am to also have a followup article in the November 2004 Quality Progress that expands upon the concept.

Contact me if you would like to discuss further.

Forrest Breyfogle
512-918-0280
forrest@smartersolutions.com
www.smartersolutions.com