Control Chart for Non-Normal Data Example: Log-normal Distribution with Negative Values

Enhanced control chart for non normal data plotting can include a process capability statement when a 30,000-foot-level reporting format is used.    With 30,000-foot-level reporting, log-normal data can even be assessed from a stability and predictability point of view even if there are negative value. In a 30,000-foot-level report, the process capability statement can be predictive using wording that is easy to understand in one chart.

Control limits for non normal data is an important consideration when calculating control chart upper and lower control limits.  An individuals statistical process control (SPC) chart is not robust to non normal data. When data are not normally distributed and no transformation is conducted, false signals can occur with an individuals chart. When making any data transformation, the data adjustment needs to make physical sense.

ASQ Quality Progress published article titled ″Control Charting at the 30,000-foot-level″ (Part 4) by Forrest Breyfogle addresses the use of a three-parameter lognormal control chart for log normal data that has negative values.

Statistical Process Control (SPC) textbooks and training typical state that an individuals control chart (X) or an individuals and moving range chart (XmR) control chart is appropriate and should be used when tracking individuals time-series process-output data. However, false signal issues can occur when data do not follow a normal distribution; e.g., a log-normal distribution transformation may be appropriate.

Control Chart for Non normal data: Issues and Resolution

The PDF document below elaborates on the technical issues that can occur when an appropriate data transformation is not made with the data. A log-normal distribution often is beneficial when addressing skewed data; e.g., when there is a natural boundary such as zero.  However, whenever negative values occur a 3-parameter log-normal transformation may be appropriate.

An illustration of the need for a transformation is days sales outstanding (DSO) is shown below where there is a lower boundary of about -40 days. The PDF illustrates how a data transformation would indicate that there are no out of control signals.

control chart for non normal data

A 30,000-foot-level reporting system addresses this transformed-data need and other issues. Described also in this PDF article is the creation of a 30,000-foot-level process capability index statement that is easy for others to understand.

General information about 30,000-foot-level reporting is described in a video: 30,000-foot-level Performance Reporting Introduction (5 Minutes)

How to create 30,000-foot-level charts for a variety of performance measurement situations is described in:

For more information about how 30,000-foot-level reporting addresses issues with non-normal data when there are negative values and easy-to-understand response process capability reporting, download the published ASQ Quality Progress November 2006 published article titled “Control Charting at the 30,000-foot-level, Part” (Part 4) PDF article. 

 

Contact Us to set up a time to discuss with Forrest Breyfogle how your organization might gain much from IEE 30,000-foot-level predictive performance reporting.