If you think about it, to evaluate any process you typically want to know its precision and accuracy. Look at the dart players in the Figure 1 below. The yellow player has good precision, but his accuracy is off. The green player has such poor precision, it is hard to tell if his accuracy is good. The yellow player will typically be easier to correct, as she just needs to change her aiming point.
Figure 1. The yellow player has greater precision. She only needs to change her aiming point.
Recently I was asked to evaluate several solder pastes to determine which printed better. We used transfer efficiency (the volume of the stencil printed solder paste “brick” divided by the stencil aperture volume) as the evaluation metric, expressed in percent. So 100 percent would be the target. The lower specification limit we choose was 50% and the upper specification at 150%.
Figure 2. Data from Pastes A and B.
A good result would be an average of 100% with a “tight” distribution. The “tightness” of the distribution being determined by the standard deviation. Figure 2 shows data from two pastes. Note that Paste A has an average of 100% and a standard deviation of 16.67%, whereas Paste B has an average of 80% and a standard deviation of 30%. Clearly, Paste A is superior to Paste B in both accuracy and precision. But what is the best way to express this difference? Is there one metric that will do it? Cpk is the answer.
Cpk is one metric that is sensitive to both the accuracy and precision. Cpk is defined as:
Where x is the average and S is the standard deviation.
Using these equations, we see that the Cpk of Paste A is 1.0, whereas the Cpk of Paste B is 0.333. Note that Paste B has a significant number of data points (about 17%) outside of the specification limits, however, Paste A has almost no data points out of specification.
So when evaluating most processes, Cpk tells it all!