Process Behavior Charts for Non-normal Data: A 30,000-foot-level Perspective

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Process behavior charts for non-normal data at the 30,000-foot-level provide not only an assessment of process stability (from a high-level point of view) but can also provide a process capability statement (in easy to understand wording) — in one chart.

Process Behavior Charts for Non-normal Data: When Do Non-normal Data Situations Occur?

In the real world, the output of some processes are bounded by zero or some other value.  For example, the time it takes to execute a phone-call-response in a help-desk call center or the flatness of a part cannot be minus numbers.  In both these illustrations, the physical boundary is zero.

For these situations (unless data are distant from the zero boundary condition) a normal distribution does not provide an accurate representation of the population response for the process.

A log-normal distribution often fits this type of data situation and has a shape appearance of:

 

 

Process Behavior Charts for Non-normal Data: A 30,000-foot-level Perspective

Let’s consider the situation where someone wants to observe the output of a process and does not desire to “control the process”.

For a hold-time in a call center, one might want to evaluate this metric over many locations that receives calls, in one chart.  For this determination, one needs to assess process stability from a high level point of view first and then, if the process is stable, provide an easy-to-understand statement of how the process is performing (e.g., hold time) — not only now but what is expected in the future (unless something were to change in the process).

When non-normally distributed data are tracked over time at the 30,000-foot-level, process stability is to be assessed and a predictive statement provided, when appropriate. However, to make these assessments, a transformation that makes physical sense for the situation may be needed. If this is not done for an underlying log-normal situation, false “out-of-control” signals can occur and a process capability statement could be very erroneous. 

In the 30,000-foot-level output below, the left indiviudals chart assesses process stability and the right probability plot provides a process capability determination.  In the individuals chart, a Box-Cox Transformation with lambda zero is a log-normal transformation of the data, which indicates process stability for this situation since no data are above/below the red upper and lower control limits.

Raw data from the individuals chart is then used to create the lognormal probability plot, which indicates for a lower specification limit of 0.5 that there is an estimated non-conformance rate of  34.77% (an easy to understand statement made at the bottom of the 30,000-foot-level output.

 

 

Additional Information: Process Behavior Charts for Non-normal Data

The article link below describes the use of an appropriate transformation from a physical point of view when deciding which actions or non-actions are most appropriate.

Chapters 12 and 13 of the book Integrated Enterprise Excellence Volume III, Improvement Project Execution: A Management and Black Belt Guide for Going Beyond Lean Six Sigma and the Balanced Scorecard provides more details on benefiting from 30,000-foot-level reporting for both continuous and attribute data.

 

process behavior charts for non-normal data book

 

A free Minitab add-in is also available for the easy creation of 30,000-foot-level charts.

The 30,000-foot-level metric is one component of the Integrated Enterprise Excellence enhanced business management system.

 

Contact Us to set up a time to discuss with Forrest Breyfogle how your organization might gain much from an Integrated Enterprise Excellence (IEE) Business Process Management System and its process behavior charts for non-normal data (and normal data too).

 

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