Statistical Process Control

What is SPC?

Statistical Process Control (SPC) is the use of statistical tools and analyses to monitor, manage, and improve process performance. It provides easy, reliable, and proven techniques for evaluating trends and point values and determining variation in the process.

So what????? Why use it, we using statistics all the time??? SPC is too much trouble, too hard. You need to be a Ph.D. statistician to do the stuff!!!!

Consider the following:

• Your cesarean section rate has gone from 21% to 17% over the last four months. Is this the result of the C-section reduction team's hard work, some other factor, or a statistical fluke?
• Your Radiology Department's retake rate has gone up from 0.5% last month to 0.7% this month. Is this something you should worry about?
• Your accounts receivable days has fluctuated widely over the last six months. Do you know why?
• You are trying to create a meaningful balanced scorecard from a morass of indicators from all levels of the organization (and this ORYX thing - whatever that is - is giving your Quality Management folks fits). How do you collect, analyze, and act upon management information without improperly tampering with your systems and creating further chaos?

Each of these, and many other scenarios, are amenable to SPC. In each of them SPC would help you answer the Fundamental Management Question: do I have a problem, and what is causing it?

In its essence SPC applies simple graphical statistics tools to filter out the normal everyday variation inherent in every performance measure. This filtering process identifies the abnormal variation - both single events and trends - that indicates a 'problem' has occurred that requires managerial intervention.

In addition, SPC represents a shift in the way we think about measuring performance and analyzing data. The traditional approach, strongly emphasized in clinical research, collects data and then compares the data to either some past data set or a control group data set. While this is perfectly legitimate in clinical research trials, it is insufficient for measuring and improving performance in real time. Real time data collection and analysis means measuring, tracking, and assessing performance everyday. SPC provides the simplest and most powerful tools for real time performance assessment, that's what they were designed for: easy application by staff on the floor, without the PhD's.

The next few sections provide a brief introduction to SPC and provides some examples (we do the math for you) to help illustrate SPC's ease of use and power. All of the examples were done in Microsoft Excel using templates we developed. For more details, consider our SPC workshops where we bring your data to life in hands-on breakout sessions. The references at the end of this page are an excellent resource for your SPC education. Some are available through our Bookstore.

The Basics

Types of Data

Control charts are built around two data types:

• Variables Data - Quantitative data (temperature, blood pressure, widgets/hour, etc.) as measured or observed. Variables data is further categorized into continuous data - that can equal any numeric value - and discrete data - data restricted to integers.
• Attributes Data - Qualitative data ('abnormal', 'defective', etc.) or quantitative data derived from qualitative data (number of defects/part, abnormals/1000 pt. days, number of unplanned readmissions)

Variables data is generally preferred in SPC because it provides more information. For example, labeling a test result 'abnormal' does not convey any information about how abnormal the result was. At times, however, attributes data provides the only meaningful data. This is especially true in summary (or 'rolled up') data.

Process and Outcomes Indicators

It is important not only to measure outcomes from a process but relevant process measures as well. 'Relevant' in this case refers to those measures that indicate a process problem or predict outcomes measures - either as causal variables or risk factors. Thorough process knowledge, based on flowcharts and cause-effect diagrams, would readily identify important process measures. It is imperative, therefore, that this level of process knowledge is attained before establishing either process or outcomes measures.

Causes of Variation

The primary use of statistical process control is to determine the cause of variation in the indicator under study. SPC tools decompose variation into two causes:

• Special (or assignable) cause - Variation caused when some unusual or external cause occurs. When special cause occurs usually only one cause is at fault, the cause is identified and the data point removed to calculate true control limits. No process improvement effort is possible until the special cause is determined and removed. Attempting to improve a process containing special cause variation only increases the instability and variation in the process.
• Common cause - the normal day-to-day variation in the indicator of interest. When ONLY common cause variation is present no one cause is to blame for process performance; any process improvement effort must consider all sources of variation. A process with only common cause variation is also stable and predictable, with the control limits serving as a measure of process capability.

Determining Special Cause Variation: Control Charts

In this section we will discuss the four most common control charts and the rules for determining special cause variation. Click here for the full size printable version of a flowchart to help you select the proper control chart. Press the BACK button on the browser toolbar to return here.

More detailedinformation is available in the references below (especially Benneyan and Dooley). We also offer extensive SPC consulting and software to make your SPC program as effective and efficient as possible.

The primary rule for determining special cause variation are control limits set at plus/minus 3 standard deviations from the center line, usually the mean. With this in mind the most common control charts are:

Individuals control chart

 The individuals control chart is the easiest to construct and the most detailed, containing every data point. The individuals control chart is constructed as follows:

1. Calculate the average and standard deviation

2. Upper control limit (UCL) = Average + (3 x Std. Deviation)
3. Lower control limit (LCL) = Average - (3 x Std. Deviation) or 0, whichever is larger.

 An example, for Number of Procedures in One Procedure Room, appears to the left. In this example the daily volume data points are plotted sequentially; the average is plotted as the dashed line; and, the UCL and LCL are plotted as solid lines. In this example, one point (#15) is above the UCL signifying a special cause variation.

Once the special cause is identified the point is removed from the data (since it really is not a part of the normal process and inflates the standard deviation) and a new average and control limits are plotted. These new limits are used to monitor the process into the future, until further special cause variation occurs.

So what? Well...... If you were concerned about staffing this procedure room you could staff for the average of 10 procedures / day while being prepared for as many as 19 (perhaps with call-ins or per diem staff). If you were interested in this room's utilization you would investigate the out of control point. Why were we so busy on this day? What was the effect of the high utilization (overtime?)

All of the other days are within the normal process variation, nothing extraordinary happened on any of them. Any effort to improve this indicator would need to examineall of the factors that effect this room's volume,after identifying and dealing with the special cause point.

Averages control chart (or 'X-bar')

Another common control chart is the averages (or X-bar) control chart. It is used to analyze sequential subgroups (say weekly volume in the procedure room above) or simultaneous subgroups within the same process (say number of procedures by surgeon for the same month)
Using subgroup averages divides variation into two components: within subgroup variation and between subgroup variation. The process of analyzing subgroup average variation is, then a two stage process. First, the within subgroup variation is analyzed (and must not contain special cause variation!) and then the between subgroup variation (using the averages is analyzed).

Failing to analyze and understand the within subgroup variation is a leading misuse of averages control charts and a cause of subsequent error in the analysis. The within subgroup variation is analyzed one of two ways, depending on whether the subgroup sample sizes are constant. If the sample sizes are constant the Range control chart is used; if not, the Standard Deviation control chart is used.

The Range control chart equations are:

1. Collect at least 20 samples with an equal sample size (N= number of samples)
2. Calculate and plot (on separate graphs) the average and range of each sample
3. Calculate and plot the control limits:

Range:
R-bar = average of ranges = _Ri/N

UCLR = D4R-bar

LCLR = D3R-bar

Where,
Ri are the individual subgroup ranges,
D3 is a constant from statistical tables,
B4 is a constant from statistical tables,

Where,
Ri are the individual subgroup ranges,
D3 is a constant from statistical tables,


The Standard Deviation control chart equations are:

1. Collect at least 20 samples with an equal sample size (N= number of samples)
2. Calculate and plot (on separate graphs) the average and standard deviation of each sample
3. Calculate and plot the control limits:

Standard Deviation:S-bar = avg. of standard deviations = square root of ([(n-1)s2i]/(ni)-N))

UCLS = B4S-bar
LCLS = B3S-bar


Where,
s2i are the individual subgroup variances,
B3 is a constant from statistical tables,
B4 is a constant from statistical tables,

Average:
Grand Average = (_X-bari)/N

UCLX-bar = Grand Average + A3S-bar

LCLX-bar = Grand Average - A3S-bar

Again, the Average chart is meaningless unless the standard deviation chart is in control.

Percentage ('P') Control Chart

The final common control chart is the percentage control chart. This chart is very useful for tracking any rate based indicator (e.g.; percent of patients readmitted with 14 days of discharge). The chart is easy to construct, but does have variable control limits since the standard deviation of a percentage is based on the subgroup sample size.

1. Obtain at least 20 samples (of variable size ni)
2. Calculate the percentage for each subgroup (p=(_Xi/ni))
3. Calculate and plot:

p-bar = total units having characteristic/total units

sp = square root of (([p-bar x (1-p-bar)]/ni))

UCL = p-bar + (3 x sp)

LCL = p-bar - (3 x sp) , or 0 if LCL < = 0

Other Tests for Statistical Control

In addition to the three standard deviation limit other rules (often known as the Western Electric rules) are useful for identifying changes in process performance.

• Additional Standard Deviation Rules:
  • - 2 of 3 consecutive points above/below 2 standard deviation limits
  • - 4 of 5 consecutive points above/below 1 standard deviation limits
• 'Run' Tests:
  • Run of six or more points up or down.
  • Run of six or more points above or below median.
  • Run of 14 or more consecutive points in up/down sawtooth pattern.

The run tests in particular are valuable in identifying trends before they can generate a point outside the control limits.

Conclusion

Statistical process control (SPC) provides simple, yet powerful, for managing process while avoiding process tampering. A process 'in control' (i.e.; exhibiting no special cause variation) is ripe for breakthrough process improvement. A process still burdened with special cause variation is still in the problem solving stage.

Back to Table of Contents

Additional Resources On This Site

Our OnLine Consulting and OnLine Workshops both provide an opportunity for us to help you design and implement an SPC based performance measurement system. We have implemented SPC based systems and trained and lectured on the use of SPC in healthcare. .

Back to Table of Contents

References

Numerous excellent SPC books are in print. Below are several good ones, those available from Amazon.com are highlighted. Others are available from Amazon.com through our Bookstore.

• Douglas Montgomery. Introduction to Statistical Quality Control , ASQC Quality Press
• Edward R. Tufte. The Visual Display of Quantitative Information. Chesire, CT: Graphics Press.
• Edward R. Tufte. Envisioning Information. Chesire, CT: Graphics Press.
• Steven M. Zimmerman and R.N. Zimmerman. SPC Using Lotus 1-2-3©. ASQC Quality Press
• Thomas Pyzdek. Fundamentals (Pyzdek's Guide to SPC, Vol. 1) Vol 1
• H. James Harrington. Statistical Process Control Explained : The Easy-To-Understand Guide to SPC

Back to Table of Contents