Control Charts and Histograms for Stability and Capability Analysis

Jay Arthur
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303-756-9144
KnowWare International, Inc.
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Denver, CO 80224

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Process Stability vs Process Capability

Many people confuse control limits on control charts with specification limits used on histograms. Control limits are calculated from your data and are used to evaluate the stability of a process; spec limits are provided by your customers and are used evaluate the capability of a process. Here are the topics further discussed on this page:

• Analyzing Stability
• Choosing the Right Control Chart
• Common and Special Causes of Variation
• Quickly Detecting Process Shifts Using the Cusum Chart
• Analyzing Capability
• Other Tools for Analyzing Variation
• Common Confusion and Difficulties

  Analyzing Stability

A stable process produces PREDICTABLE RESULTS CONSISTENTLY. Process stability can be easily determined using control charts. A control chart is a line graph of your data (the same line graph used to identify and focus your problem) with average and sigma lines to determine stability. The average and sigma lines (+ 1, 2 and 3 sigma) are calculated from the data. The Upper Control Limit (UCL) is the +3 sigma line and the Lower Control Limit (LCL) is the -3 sigma line. 99.7% of all data points will fall between these two limits.

The QI Macros for Excel identify unstable points or trends for you and highlight them in red. QI Macros 2007 and later versions default to Montgomery's rules but also give you the flexiblilty to choose from other rules or define your own:

See our control chart rules article for instructions on how to change rules in the QI Macros.

Choosing the Right Control Chart

One area that many people struggle with is choosing the right control chart. The right chart is based on the type of data, attribute (counted) or variable (measured), and the sample size.

The QI Macros Control Chart Wizard can analyze your data and select the right control chart for you. Simply click and drag over your data to select it and then select Control Chart Wizard from the pull down menu. The wizard can select the right chart and only needs to ask one question when it is trying to determine between a p and u chart.

If you want to understand how to choose the right chart, consider the following:

• SPC Quick Reference Card
• SPC Simplified Book #215
• SPC Simplified 1 hour Training Video #267 Healthcare or Manufacturing, DVD.
• Control Chart Whitepaper

Common and Special Causes of Variation

Processes are never perfect. So, how can you tell if a process is stable? Common and special causes of variation make the process perform differently in different situations.

Common causes of variation happen all the time, every day. Getting from your home to school or work takes varying amounts of time because of traffic or transportation delays. Processes that are "out of control" need to be stabilized before they can be improved.

Special causes, require immediate cause-effect analysis to eliminate the special cause of variation. A blizzard, a traffic accident, a chemical spill or other freak occurrence would be a special cause of variation.

Quickly Detecting Process Shifts Using the EWMA and Cusum Charts

The Exponentially Weighted Moving Average (EWMA) and Cusum charts detect process changes more rapidly than regular control charts. So you might choose one of these charts to monitor for small subtle process shifts (less than 1.5 sigma).

Analyzing Capability

A capable process MEETS THE CUSTOMER'S REQUIREMENTS 100% OF THE TIME. The Upper and Lower SPECIFICATION limits (USL and LSL) are determined from the customer's requirements.

The histogram is the correct tool to analyze process capability. The QI Macros histogram will calculate the process capability measures (Cp, Cpk, Pp and Ppk) based on your data and on the specification limits. To run a histogram, select your data and then select histogram from the QI Macros pull down menu. The macro will prompt you for the spec limits:

If you don't know the specification limits, the QI Macros will calculate them for you. You can click ok to use the default, input your spec limit or click cancel if you have one-sided or uni-lateral spec limits.

Determining Capability Using Attribute Data

The capability of counted (i.e. attribute) data like defects, indivisible integers only, is zero defects. Customers hate defects, outages, etc. The capability of measured (i.e. variable) data like time, money, age, length, weight, etc. is determined using the customer's specifications and a histogram.

Determining Capability Using Variable Data

When a customer defines an upper and/or a lower specification limit for a product or service, whether it's the diameter of a shaft or the time in line at a fast food restaurant, all points within the two limits are considered "good."

• Use Cp and Cpk when your data represents a sample
• Use Pp and Ppk when your data represents the whole population
• The capability index (Cp) indicates how well the data would fit between the USL and the LSL if the process average were centered between the specification limits.
• Cpk on the other hand helps indicate how centered the data is within the range.
  If Cp = Cpk, the process is centered at the midpoint of the specifications.
  if Cp>Cpk, then the process is off-center.
• If both Cp and Cpk are greater than or equal to 1 then the process is considered capable.
• Cp and Cpk of:
  • 1.00 is equivalent to 3 Sigma
  • 1.33 is equivalent to 4 Sigma
  • 1.67 is equivalent to 5 Sigma
  • 2.00 is equivalent to 6 Sigma

Click here for more information about running histograms in the QI Macros. For more information about the formulas and how the capability indicies are calculated see our formulas page or Histogram Whitepaper.

You can calculate Cp, Cpk and Pp, Ppk without running a histogram using the Cp Cpk template. Access the template under Fill in the Blanks Templates, SPC Charts.

Other Tools for Analyzing Variation

The box-and-whisker and multivari chart can be used to show variation between different production lines, machines etc. You can run these charts using the QI Macros pull down menu. Test data is located at C/QIMacros/Testdata on your computer.

Common Confusion and Difficulties

1. Confusing Control Limits with Specification Limits. Many people confuse control limits on control charts with specification limits used on histograms. Control limits are calculated from your data; spec limits are provided by your customers.
   You can add specification limits to a control chart, but it isn't recommended as sound statistical practice.
2. Getting caught up in formulas and statistics behind the charts and forgetting to interpret the results. If you have questions regarding the detailed formulas behind the charts we have provided references in our test data files loaded on your computer at C/qimacros/testdata and detailed formulas on our website at http://www.qimacros.com/formulas.html
3. Getting caught up in drawing charts, but not using the information to monitor and improve your processes. We hear from far too many quality departments who become the chart drawing group for the company. They get caught up in drawing more and more charts, but they never get time to analyze the data and make needed improvements.

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