Rational Subgrouping of Data for Control Charts

Control charts are a tool to evaluate the performance of a process over time.   Think of the process as a river that is flowing past the point where we will collect data.  We must decide what to measure, how to measure, where to measure and how often to collect data from the process.   The story that a control chart tells us about the process is dependent to a great degree on the data used to generate the chart.  Today we will discuss the concept of rational subgrouping of data for the purpose of generating control charts.

Whenever you look at a control chart, you should first ask yourself “What variation is this chart examining?”    Statistical Process Control is used to evaluate two types of variation in continuous data – within the subgroup (range or standard deviation control charts) and between subgroups (mean or average charts).    Using the Xbar and R charts as an example, the X bar control chart is monitoring the variation in the subgroup averages from subgroup to subgroup and the R chart is monitoring variation within the subgroup, from subgroup to subgroup.

There are two basic things to think about when subgrouping data.

First, you want to minimize the variation within a subgroup.  Rational subgrouping involves selecting samples that are relatively homogeneous, i.e. collected over a small region on time and space.  Items in a subgroup should represent the same set of process conditions.   Subgrouping methods can dramatically affect the measured variation within subgroups.  For this reason, samples in a subgroup are typically chosen consecutively from a process whenever possible to minimize within subgroup variation.

Second, you want to maximize the opportunity for variation to occur between subgroups.   Rational subgroups should also allow for quick identification of potential corrective actions once an out-of-control condition is detected.  For example, if we have three different machines making the same product and we mix the output together into one subgroup, we will not know which machine to look it if the process goes out of control.  A better approach will be to collect and analyze data by machine.

Finally, the frequency of sample collection has an impact on whether variation is identified as common cause or special cause by the control charts.   Increased sampling frequency will treat more causes of variation as special causes, whereas decreased frequency will treat more causes of variation as common cause.   For example, say that we start using a new lot of material every day.  If we collect sample data daily, the variation from lot to lot of material will more likely be identified as special cause variation.  If we collect data weekly or monthly, variation from lot to lot of material will more likely be identified as common cause variation.

Your comments or questions about this article are welcome, as are suggestions for future articles.  Feel free to contact me by email at roger@keyperformance.com.

About the author:  Mr. Roger C. Ellis is an industrial engineer by training and profession.  He is a Six Sigma Master Black Belt with over 50 years of business experience in a wide range of fields.  Mr. Ellis develops and instructs Six Sigma professional certification courses for Key Performance LLC.   For a more detailed biography, please refer to www.keyperformance.com.