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Home » Control charts: Type of data plotted determines type of chart selected

February 1, 2004

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**Selection is critical to having correct control limits for the data**

*(Editor’s note: This is the second in a series of articles on control charts. In the first article, presented in our January 2004 issue, we defined control charts and described the types of situations that lend themselves to the use of control charts. This month, we examine the
process of selecting the most appropriate control chart.)
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Correct control chart selection is a critical part of creating a control chart, according to PQ Systems, an industry leader in the manufacturing of statistical process control (SPC) and quality control software based in Miamisburg, OH. "If the wrong control chart is selected, the control limits will not be correct for the data," states the company’s web site (www.pqsystems.com). "The type of control chart required is determined by the type of data to be plotted and the format in which it is collected."

"SPC is a methodology for charting the process and quickly determining when a process is out of control [e.g., a special cause variation is present because something unusual is occurring in the process]," according to **Sid Sytsma**, MSE, MBA, professor in the College of Business at Ferris State University in Big Rapids, MI, and an expert on SPC.

"The process is then investigated to determine the root cause of the out-of-control condition. When the root cause of the problem is determined, a strategy is identified to correct it. The investigation and subsequent correction strategy is frequently a team process, and one or more of the TQM [total quality management] process improvement tools are used to identify the root cause," he says.

Reduced variation, Sytsma explains, makes the process more predictable, with process output closer to the desired value.

According to **Steve David**, MBA, president and CEO of SkyMark, a Pittsburgh-based manufacturer of SPC software, all control charts have three basic components:

- a centerline, usually the mathematical average of all the samples plotted;
- upper and lower statistical control limits that define the constraints of common-cause variations;
- performance data plotted over time.

It is from those common points that the different types of control charts flow, dictated by the type of data and format.

The first determination that must be made in deciding what type of chart to use is whether you are dealing with attribute or variable data.

"In general, attribute data are* count* data," notes **Marilyn Hart**, PhD, of the University of Wisconsin-Oshkosh, who lectures and writes about health care and SPC. "You can *count* the number of patients attending the clinic each week, the number of patient falls, the number of C-sections, the number of births." Hart and her husband Robert Hart are co-authors of *Statistical Process Control for Health Care* (Pacific Grove, CA: Duxbury; 2002).*
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*"This is the first decision you need to make before plotting data," adds **Patrice L. Spath**, RHIT, a consultant with Brown-Spath & Associates, in Forest Grove, OR. "Attribute data usually are
the number of — i.e., surgical complications, C-sections, delinquent patient records."

PQ Systems adds this definition: "A standard is set and then an assessment is made to establish if the standard has been met. The number of times the standard is either met or not is the count. Attribute data never contain decimal places when they are collected; they always are whole numbers."

Variable data, Hart explains, are measurement data — sometimes called *continuous data*. "You measure, for example, the amount of time a laparoscopic cholecystectomy takes; you measure the amount of blood you’ve used; you measure the weight of the newborn infant," she says.

"It could include wait times in the emergency department," Spath adds; "actual surgical time less scheduled surgical time; dollar amount of accounts receivable; blood pressures of a patient over a 24-hour period — things that are measured, not counted."

"Generally, a measuring device such as a weighing scale or clock produces these data," according to PQ Systems. "Another characteristic of variables data is that they can contain decimal places."

As an illustration of the difference between the two types of data, **Judy Homa-Lowry**, RN, MS, president of Homa-Lowry Healthcare Consulting in Metamora, MI, refers to an example she used in the first article: monitoring refrigerators in a patient unit.

"If you are asking whether or not the temperature had been checked, that would be attribute data," she notes. "But it might be more important to know the range of temperatures, or to measure that range, and that would be variable data."

Determining whether you are working with variable or attribute data is fairly simple. As the decision tree shows, all other decisions flow from determining the type of data with which you are working.** (See decision tree, below and decision matrix,
below.)** After that, the process becomes a bit more complex.

Hart offers the following guidelines for control chart selection when you have variables data:

If the data occur one at a time (newborn weights, time for a lap chole procedure, etc.) the chart for individuals (sometimes called an X chart or an I chart) is best. (The moving range [MR] chart to monitor the change from one reading to the next may or may not be used.)

If the measurement data are grouped by month, for example, an Xbar and s chart is best. The Xbar and s chart also is appropriate when grouping the data by rational subgroups.

Some people also may suggest an Xbar and R chart when the data are grouped in small groups, for instance groups of five or less. However, that type of application happens so rarely and can be handled by an Xbar and s chart, that it does not seem worthwhile to learn the extra chart.

**Where it gets complicated**

Determining whether you are working with a rational subgroup is fundamental, Homa-Lowry says. "If you were monitoring a lab and looked at the number of errors, that would be a rational subgroup. You would start plotting them maybe by week, or by month; you could also look at the total number of procedures or discharges.

"If you have more than one observation per subgroup, you would use the Xbar chart. For example, looking at the turnaround for a daily sample of five lab orders: This might be good for a small hospital, since these things don’t happen very often. If you have more than 10 per month, you would have the s chart. The Xbar and R chart would be how many lab orders do we process each week," she continues.

"The control chart method is quite robust," Hart cautions. "That is, it will tolerate some departures from the normality assumption and still work rather well. So the data need only be near-normal for the control charts to work. If the data are badly skewed, which is often the case with data such as time intervals, misleading results will occur. Points may occur outside the control limits due to the skew of the data, not due to any special-cause variation.

"A pattern also will occur on the Xbar and s chart. In particular, if the data are skewed to the right, the values plotted on the Xbar chart will be in phase with the values plotted on the s chart. That is, they will go up and down together. If the data are skewed to the left, the values plotted on the Xbar chart will be 180° out of phase with the values plotted on the s chart — that is, when one goes up, the other goes down. A histogram and a probability plot must be made before a control chart is made to see if the data are badly skewed. If so, a transformation may be made to make the data near-normal before the control chart is made," she explains.

Hart notes that attribute data must be further subdivided into two categories.

"Each item has the attribute or it doesn’t," she observes. "One example could be C-sections. Each delivery either was a C-section or it wasn’t, and the number of C-sections cannot exceed the number of deliveries. Another would be mortality rates; there either was a mortality or there wasn’t."

In setting up your equation, the numerator is a subset of the denominator, so the count is limited by the number of units inspected, Hart continues. "This is governed by the binomial [two names] distribution, and the data are kept on a p chart."

Referring to Hart’s decision tree, "P," which stands for proportion, equals the number of items that have the attribute. "N" equals the total number in the P chart.

If the number of units inspected always is the same, it may be kept on an np chart, she adds. "This happens so rarely, however; and since the p chart will always work with this type of data, it may not be worth learning the np chart," she advises.

In the U chart, counts per unit are measured, and "C" stands for count. "Say we were looking at all the lab orders each week and wondering how many errors are observed; this would be plotted on a U chart," Homa-Lowry says, "because you can have a different number [of lab orders] each week. If there were 100 lab orders every week and you wanted to know how many errors were observed, you would use a C chart."

The second category of attribute data plots the number of occurrences, but the numerator (count of occurrences) and the denominator (area of opportunity) measure different things. The count is not limited by the area of opportunity. "This is governed by the Poisson distribution [named for the man who discovered it]," Hart notes. "It could depict the number of injuries, the number of chips in chocolate chip cookies, and so on, and is kept on a C chart if the area of opportunity is constant, and on a U chart if it is not."

An example, she says, would be the number of patient falls per patient day. "The count is the number of falls, and if there are 100 patients there one day, there theoretically could be more than 100 falls on that day. If the number of patients is constant (or at least relatively constant), a C chart could be kept just on the count of falls each day. If the number of patients varies from day to day, the data kept on a U chart are the number of falls divided by the number of patient days, or the number of patients times the number of days studied.

"You can’t have some falls that were *not* falls," Hart explains. "You can’t count how many times somebody *didn’t* fall."

Whatever it is you decide to depict, and whatever chart is most appropriate to use, Homa-Lowry offers these words of warning before you even begin:

"Make sure you have an operational definition for what you are doing — what it is you are going to collect, how you are going to collect it, the reasons for collecting it, and how you’re planning to use the data," she says. "If you don’t do that, you may go through this whole process and have something you can’t use."

**Need More Information?**

For more information, contact:

•** Patrice L. Spath**, Brown-Spath & Associates, P.O. Box 721, Forest Grove, OR 97116. Phone: (503) 357-9185. E-mail:
Patrice@brownspath.com.

•** Judy Homa-Lowry**, RN, MS, President, Homa-Lowry Healthcare Consulting, 7245 Provincial Court, Canton, MI 48187-2121. Phone: (810) 245-1535. E-mail:
105255.42@compuserve.com.

•** Steve David**, President/CEO, SkyMark, 7300 Penn Ave., Pittsburgh, PA 15208. Phone: (800) 826-7284 (USA and Canada); (412) 371-0680 (elsewhere). E-mail:
david@skymark.com. Web: www.skymark.com.

•** Marilyn Hart**, PhD, College of Business Admini-stration, University of Wisconsin Oshkosh, Oshkosh, WI 54901. Phone: (920) 424-7195.
E-mail: hart@uwosh.edu.

•** Sid Sytsma**, MSE, MBA, Professor, College
of Business, Ferris State University, Big Rapids, MI 49307. Phone: (231) 591-3594.

**Also, check out these resources: **

•** Shewhart W. Economic Control of Quality
of Manufactured Product,** Van Nostrand; 1931. (Available at www.amazon.com.) Waler Shewhart, a statistician at the Hawthorne plant at Western Electric, authored what is considered to be the foundation of modern statistical process control (SPC), and provides the basis for the philosophy of total quality management or continuous process improvement for improving processes.

•** SkyMark**, Pittsburgh. Web: www.skymark.com. SkyMark offers two software packages: PathMaker for Windows and ipathmaker for the web. Both applications make it very easy for nonexpert users to make correct control charts and many other commonly used charts. They offer the main chart types, all the standard control tests, and auto-calculate all the relevant statistics. Both packages also include a full
set of charting tools, plus brainstorm, affinity, flowchart, cause-and-effect diagram, voting, meetings, and more.

•** PQ Systems Inc.**, 10468 Miamisburg-Springboro Road, Miamisburg, OH 45342. Phone: (800) 777-3020. PQ offers software services to help its customers meet ISO and other standards to help them compete for the Baldrige Award and pursue Six Sigma efforts to improve quality. The company also provides training for SPC, measurement systems analysis, and quality improvement.

Healthcare Benchmarks and Quality Improvement 2004-02-01

February 1, 2004