Make Valid Control Chart and Subgroup Assumptions

Control Charts Subgrouped By Personnel Shifts
In one of my consulting assignments I was explaining to participants the use of control charts and how they are only able to distinguish between process special causes and common causes. During these discussions one of the participants enthusiastically explained how they had implemented control charts in a continuous process and wanted to know whether the method applied was correct.

The participant explained that there is one particular parameter in the process that is critical and is monitored on an hourly basis. They collected data with a subgroup of eight, representing one shift, and based on the resulting calculations created their control charts. These control charts were updated every eight hours at which time the process capability was calculated.

What is your assessment of this situation?

There were a few mistakes in the method used. Without getting into any statistical analysis, the first mistake that can be discovered through common sense is that the organization is plotting one point every eight hours. That means that they can detect a special cause only every eight hours. The question I raised with the participant was whether the process stable enough that they can wait for eight hours to detect a special cause! And if the process is stable enough to wait eight hours, why measure and collect the parameter values every hour? In the statistical terms, the organization possesses an extremely high beta risk.

Why was the participant using this type of analysis method? Had the participant understood the key assumptions in the formation of the X bar R control chart subgroups, this type of mistake might not have been committed. The key assumption in the formation of subgroups is that the variation within the subgroups is only due to common causes. This assumption must be carefully considered in order to eliminate potential control chart mistakes.

If properly trained in Six Sigma, the organization might have applied the control charts more appropriately and would have selected either the IMR Chart, Zone Chart, CUSUM chart or EWMA Chart. In doing so, they would have paid more attention to the engineering logic and the statistical assumption in the application of the charts rather than the calculations of plotting the charts.

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