When Cp is greater than Cpk, the mean is nearer to one specification limit or the other. So this is how Cp and Cpk work together: When the values are similar, the mean is close to the middle of the specification limits. Also, the further the mean moves away from the middle of the specification limits, the more different Cp and Cpk become. The further the sample mean is from the center of the specification limits, the lower Cpk becomes.
This mean is about 5 units higher than the midpoint of the specification limits. (I’ve removed one outlier where the supplier minimized the volume of ethanol.) Here’s some real data collected in 2010 by the National Renewable Energy Laboratory on the ethanol volume in E85 fuel. Plus, most people who buy E85 fuel think that they're buying fuel with volumes of ethanol close to 85. In the case of the volume of ethanol in E85 fuel, high ethanol content should reduce the use of non-renewable fuels and reduce certain emissions. But for some products, other goals compete with having the greatest number of units inside of the specification limits. If the only goal is to have the greatest number of units inside of the specification limits, having the process centered between the specification limits is great. The sample mean of this data is also 75.5 When the sample mean is halfway between the specification limits, Cp and Cpk are the same. Halfway in between the specification limits is 75.5. The specification limits here are 68 and 83, which are the limits that were in place for the volume of ethanol in E85 fuel in 2010. Minitab's capability analysis output shows both statistics together. Here's some data about the volume of ethanol in E85 fuel, which I've manipulated so that Cp and Cpk are the same.
In fact, under the right conditions, Cp and Cpk have exactly the same value. The smaller the standard deviation, the greater both statistics are. Often we describe Cpk as the capability the process is achieving whether or not the mean is centered between the specification limits. LSL stands for Lower Specification Limit and USL stands for Upper Specification Limit. The equation for Cpk is more complicated: / (0.5*NT). We often describe Cp as the capability the process could achieve if the process was perfectly centered between the specification limits. Traditionally, NT is 6 times the standard deviation. NT stands for Natural Tolerance, which is the width that should contain almost all of the data from the process. ET stands for Engineering Tolerance, which is the width between the specification limits.
The equation for Cp is often written ET / NT. A single letter that, by the way, doesn’t really explain anything about how these two statistics are different. Their names are different by only a single letter. Two capability statistics that are hard to keep straight are Cp and Cpk. But there are so many capability statistics that it's worth taking some time to understand how they’re useful together. These statistics tell you how well your process is meeting the specifications that you have. Capability statistics are wonderful things.