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Last Word
Michael J. Cleary

Capability Analysis Basics: Can the Elephant Dance?

Need help understanding the difference between Cp and Cpk?

When teaching an elephant to dance, one is less interested in the quality of the performance than in the fact that the elephant is dancing at all. A dance critic might find the performance flawed, but no one expected the elephant to dance in the first place.

 Sometimes manufacturing processes, like the elephant, are driven to produce beyond their capabilities, resulting in an output of uneven or poor quality. Customers, however, aren't too concerned with process capabilities--they aren't likely to be impressed by the mere fact that the elephant is dancing.

 Statistical tools can help you determine the capability of a system and prevent the waste that ensues from trial-and-error approaches. Capability analysis offers a set of statistical calculations that determine the capability of the system. Capability is a comparison between the system's ability to perform and its specification limits.

 A system is considered capable if it's producing close to 100 percent within specification limits. These limits are set by customers, engineers or managers and are sometimes referred to as requirements, goals, objectives or standards. Specification limits are the upper and lower boundaries within which the system must operate. They're not to be confused with control limits, which are based on the data collected from a system.

 Capability analysis is generally based on two assumptions: that data is normally distributed and that the system is stable, or in control. Control charts will indicate whether a system is stable--a critical point, because unstable systems produce unreliable information. Capability indexes allow us to monitor and report the improvement of any system over time.

 One area that can cause confusion is the relationship between Cp and Cpk. To test your understanding of this concept, consider whether the following statement is true or false: If Cpk and Cp are equal, the process is centered in the specifications.

 If you answered that the statement is true, you're right.

Example 1

 Examples may yield a better understanding of capability and of the relationship between Cp and Cpk in particular. In Example 1, the process is in control and the parts being produced reflect a normal distribution. The upper specification limit (USL) is 16, and the lower specification limit (LSL) is 4 .

 Since the process is centered, Cpk and Cp are equal.

 Now assume that we still have a stable (in-control) process and that the parts we're producing follow a normal distribution. The parameters for Example 2 are the same except for X, which is 11 instead of 10.

 In Example 2, the process is not centered in the specifications. Because of this, the Cpk is smaller (0.83), but the Cp has stayed the same (1.0). This is why some would say that a Cp is what the process could do if it were centered. A Cpk describes what the process is doing and reflects how far off center the process is.

Example 2

 These simple calculations help demonstrate the capability of a system to perform according to specifications and enhance opportunities for improvement.

 Now if we could just evaluate the capability of that elephant…


About the author

 Michael J. Cleary, Ph.D., founder and president of PQ Systems Inc. and professor emeritus of management science at Wright State University, is the author of A Data Analysis Handbook and developer of the Transformation of American Industry national training project. Contact him by e-mail at mcleary@qualitydigest.com .

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