To transform or not when creating a control chart for non-normal data is question that is often asked. However, I suggest broadening this “control chart non normal distribution” question to a general question of how-to best determine and report process stability and capability of a process; i.e., not “control” the process. With this re-scoped question, the non-normality issue has a different perspective.
The initial control chart non normal distribution situation has been a controversy where it has been my experience that a strong position is taken either on one of the question or the other side. Several years ago Don Wheeler and I wrote several articles on this topic in Quality Digest, where we each presented their opinion on the question. Don was taking a position using traditional control charting methods (i.e., truly controlling a process with no capability assessment), where I was suggesting a process evaluation from a much higher point of view; i.e., 30,000-foot-level perspective.
Linkage to a 30,000-foot-level metric reporting peer-review article,which addresses these issues, is available at the end of this webpage.
A recent Linkedin discussion resurfaced that addressed the non-normal control charting question. Actually the transformation issue is the tip of the iceberg. The real question is much broader.
Control chart non normal distribution and process stability with capability assessment
In Lean Six Sigma training, control charts and capability analyses are taught; however, a larger question to consider is: do traditional taught control charting and process capability analyses have issues relative to lean Six Sigma project report-outs?
I am suggesting that there are issues with these tools relative to their suggested usage in Lean Six Sigma. Perhaps this is the reason that this form of metric reporting (i.e., control charts and process capability reporting) often do not appear in Lean Six Sigma project report-outs (this has been my experience from seeing a variety of organizational general report-outs).
Traditional control charts have their place; however, what is usually needed in Lean Six Sigma is not traditional control charting, where one is attempting to truly “control” a process; e.g., a manufacturing process. A different primary need exists for all improvement projects.
What I am suggesting is that Lean Six Sigma projects create a 30,000-foot-level baseline that not only assesses process stable from a high-level point of view but provides a process capability statement in words that everyone can easily understand – in the same chart. For example, a process capability statement could be a predicted non-conformance rate (if a specification is provided and the process indicates stability from a high-level point of view). With 30,000-foot-level reporting, process capability indices such as Cp and Cpk are not used. Process capability indices reporting is not only confusing but can be a function of how the process is sampled.
If a high-level process capability statement is not satisfactory, then this common-cause metric improvement need “pulls” for improvement efforts. If enhancements were truly made to the process so that a response difference was made through a LSS project, the 30,000-foot-level individuals chart would transition to an enhanced level of performance.
Control chart non normal distribution and process stability with capability assessment: Application and Details
It should be highlighted that the approach I am suggesting is also applicable to the tracking of organizational Key Performance Indicators (KPIs) and typically provides additional insight beyond traditional KPI report-outs. The reason for this is that 30,000-foot-level reporting is from a high-level process-output point of view.
Among other things, for this reporting it is important to consider the following:
- Transformations need to make physical sense. A normal distribution is to be able to experience values from minus to plus infinity. In the real world, this often does not physically occur. For example, hold time in a call center cannot have negative numbers; i.e., time less than zero. A log-normal distribution often fits this situation for assessing stability when using an individuals chart and provide a capability assessment through a log-normal probability plot.
- If one has common cause variability that occurs between subgroups, the mathematics behind the control limits calculation indicate that x-bar&R, P-charts, C-charts, and U-charts can generate false signals. For these charts, variability between subgroups has NO impact on the calculation of control limits. On the contrary, with individuals chart variability between subgroups is part of this control chart’s limits calculation. An example of this subgrouping situation is when there is raw material lot-to-lot variability (which may or may not cause a problem) and a new lot arrives every day. An x-bar and R chart subgrouped by day can indicate out of control conditions. This can occur even when the overall process output is quite capable of meeting customer needs.
Control charts are to “control” a process at a “low” process level; e.g., an individual machine output. Traditional control chart mathematical relationships address this desire. 30,000-foot-level charting is higher level and is to address stability when the output of a process has multiple machines, operators, time differences (e.g., day of the week), lot differences, various input differences, etc.
One should note for lean Six Sigma project metric and KPI tracking 30,000-foot-level stability assessment with a customer prediction statement is more applicable than traditional control charting and process capability reporting.
For more explanation on control charting mathematics see:
- x-bar and R control chart (high-level) issues and resolution
- p-chart (high-level) issues and resolution
- c-chart (high-level) issues and resolution
- Transformation of non-normal data considerations
- Process capability indices reporting, issues and resolution
- Predictive performance reporting using 30,000-foot-level metrics
Control chart non normal distribution and process stability with capability assessment: Additional Information and “Proof”
The “proof” for making the above statements is described in a 30,000-foot-level peer-reviewed article that is available for download through the link at bottom of page.
For those who are open minded when reading this article, they should start to seeing issues with many current control charting methodologies and organizational KPI reporting that they have experienced. The article also covers what can be done to address these issues.
I recently had the comment in one of my lean Six Sigma Master Black Belt training sessions that made me feel good. Forrest, you have shown me what I have been doing for the last 20 years has issues and what I should do differently to overcome these shortcomings. Yes, the methodology I am suggesting has differences but it is very powerful.
A comment that I often receive is that the concepts you are describing should be taught in business schools. The overall system of Integrated Enterprise Excellence (IEE) includes 30,000-foot-level reporting and more. Jim Bennett has referenced IEE as lean Six Sigma 2.0. The details and implementation of IEE is described in Smarter Solutions’ Lean Six Sigma Master Black Belt training, where attendees do not need to have a belt certification to take the workshop, if they have adequate experience.
If someone does not understand a concept that is stated in the above 30,000-foot-level article, let me know and we can discuss.
ASQ Six Sigma Forum February 2014 published peer-reviewed-article titled “30,000-foot-level Performance Metric Reporting” by Forrest Breyfogle describes the reporting of measurements from an airplane point of view. Downloaded this article through the following link.Download