## 2020

BACK TO BASICS

# Smart Charting

## Guidelines to manage processes effectively

by Peter J. Sherman

**This article was featured in January 2016’s Best Of Back to Basics edition.**

Control charts are at the foundation of Six
Sigma. Invented by Walter A. Shewhart while working
for Bell Labs in the 1920s, control charts serve as the primary tool to filter
out the probable noise (inherent variation or common cause) from the potential
signals (nonrandom variation or special cause).^{1}
From this, you know when and where to take action on a process.

Whenfirst learning about control charts, a few basic questions must be addressed:

- How many data points do you need?
- What length of time should be examined?
- When should you recalculate control limits?

Applying basic guidelines and common sense can help answer these questions.

### Data do’s

The number of data points needed in a control chart varies. For variable data used in an X-bar and range (R) chart, a minimum of three to five data points per sample and 20-25 groups of samples is appropriate.

With an individuals (I) and moving range (MR) chart, in which the sample size is one because data occur much less frequently, 12–24 values are reasonable to compute the control limits. For attribute charts (p-chart), the suggested sample size is at least 50.

Naturally, the more data you can collect during an extended period of time, the better it can be used to see how the process behaves. But the time and cost to collect a sample must be balanced with the amount of information needed.

Consider the process being observed. Does it operate in a fairly steady state? If so, a few weeks of historical data is sufficient.

Meanwhile, pharmaceutical companies often must collect tens of thousands of historical data points because they’re dealing with human lives. It’s important to understand the context of the process when deciding how much data to collect.

### Revision reminders

Revising control chart limits should be handled with similar care. Assume you collect data, and the control chart shows evidence of special causes (a point on or outside the limits). You know the process is not stable or predictable.

After you identify and remove the assignable cause(s), collect additional data and recalculate the mean and control limits. Observe the control chart to confirm it is in statistical control. Continue plotting new data but do not recalculate the control limits.

If the process does not change, the limits should not change. If you make changes to the process, recalculate the control limits to observe shifts in variation after the change.

For example, imagine you’re interested in improving monthly customer satisfaction scores. You collect scores from August to November 2009 and plot the data in time series using an I-chart. The chart measures the process mean, and the control limits are calculated:

UCL
represents the upper control limit, LCL is the lower control limit, and represents
the process mean. is the average moving range, and the constant d^{2}
is from the Shewhart table (n = 2).

You confirm the process is stable. Improvements are made in December 2009, and you continue plotting the data during the next year (see Online Table 1) using the same limits on the first control chart.

Notice the upward shift in the mean during the next 14 months. The process does not appear to be in statistical control given several points outside the UCL, as shown in Figure 1. But the improvements made in December 2009 changed the process. Recalculating the limits depicts that change (see Online Figure 1). The process is actually in statistical control.

Control charts are powerful tools for operational excellence professionals. Being aware of these guidelines and using common sense can ensure good decision making and allow control charts to be used effectively.

### Reference

- Donald J. Wheeler,
*Making Sense of Data*, SPC Press, 2003.

**Peter J. Sherman** is
director of process excellence at Cbeyond
Communications in Atlanta and lead instructor in Emory University’s Six Sigma
certificate program in Atlanta. He has a master’s degree in civil engineering
from the Massachusetts Institute of Technology in Cambridge, MA, and an MBA
from Georgia State University in Atlanta. A senior member of ASQ, Sherman is an
ASQ-certified quality engineer and a certified lean Six Sigma Master Black Belt
by Smarter Solutions Inc.

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