Cpk Confidence Intervals

Cp and Cpk are point estimators of process capability. This means that it may be useful to understand the confidence intervals around these points. The width of confidence intervals around Cp and Cpk depend on the number of samples. As you can see from the following charts, confidence intervals can vary substantially around Cpk based on sample size.

Cpk 95% Confidence Intervals for n=25, 100 and 250

Cpk confidence intervals for n=25

Cpk confidence intervals for n=100

Cpk confidence intervals for n=250

Cpk 95% Confidence Interval by Sample Size

If we use Cpk=1.33, we could calculate the confidence interval around Cpk. It begins to flatten out around n=100:

Cpk confidence intervals for n=20-200

Cpk Confidence Interval Formulas for Normal Data

Cpk Confidence Interval Formulas
From Introduction to Statistical Quality Control (4th), Douglas Montgomery.

QI Macros versions dated after March 2016 will include the Cpk Confidence Intervals in the data calculations worksheet created by the Histogram macro. Look toward the bottom of the calculations page under the Observed / Expected PPM calculations:

cpk confidence interval

Note: This is assuming your data is normal. Also, as mentioned above, LCI and UCI change depending on your sample size. For instance, if your Cpk is 1.33 (Cpk > 1.33 is desirable), and you increase your sample size, your UCI will lower, while your LCI will rise, which creates a smaller window of Confidence – this is good, as it shows a minimizing in the degree of uncertainty associated w/ your samples.

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