XmR Control Charts and Data Normality

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The importance of an XmR control charts and data normality consideration is that if data are not normally distributed false special-cause signals may occur in a control chart without a data transformation.

It needs to be highlighted that data transformations needs to make physical sense.  For example, the time to execute a processes cannot be less than zero.  If data are near zero, then a log-normal transformation may be appropriate.

XmR Control Charts and Data Normality: Article Described Issues and Resolution

The purpose of the link-provided paper below is to illustrate that XmR control charts are not robust to non-normally distributed data. An alternate control charting approach is presented in this document along with a procedure to describe process capability/performance reporting in terms that are easy to understand and visualize.

XmR Control Charts And Data Normality - lognormal distribution

Resolution to control charting issues that can arise from not transforming data is described in the article below.


XmR Control Charts and Data Normality: Article Described 30,000-foot-level Reporting Resolution Illustration

In addition, to addressing process stability, a 30,000-foot-level report-out can provide a predictive process capability statement in terms that everyone can easily be understood.

An example 30,000-foot-level report-out is:


XmR Control Charts And Data Normality, 30,000-foot-level alternative


A 30,000-foot-level report out consists of two steps:

  1. The left chart is an individual chart that assesses process stability for this process output data that has a natural boundary and is fitted well by a log-normal distribution (i.e., Box Cox Transformation of zero).
  2. From the straight-line log-normal probability plot on the right for the specifications of 0.5-7.0, one can estimate a non-conformance rate of 34.772%, which is stated at the bottom of the chart in easy to understand language. NOTE: this statement applies for not only now but the FUTURE unless the process were enhanced.


XmR Control Charts and Data Normality: Additional Information

The reporting techniques of 30,000-foot-level can be also applied in business scorecards in the Integrated Enterprise Excellence (IEE) business management system.  Among other things, IEE structurally links predictive 30,000-foot-level metrics with the processes that created them.

For additional information about 30,000-foot-level reporting and the IEE system, CLICK HERE


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 methodology to address process stability, even when data are not normally distributed.