The confidence interval is a range of likely values for a capability index. The confidence interval is defined by a lower bound and an upper bound. The bounds are calculated by determining a margin of error for the sample estimate. The lower confidence bound defines a value that the capability index is likely to be greater than. The upper confidence bound defines a value that the capability index is likely to be less than.
Minitab displays both a lower confidence bound and an upper confidence bound for %Defective, PPM Def, and Process Z.
Because samples of data are random, different samples collected from your process are unlikely to yield identical estimates of a capability index. To calculate the actual value of the capability index for your process, you would need to analyze data for all the items that the process produces, which is not feasible. Instead, you can use a confidence interval to determine a range of likely values for the capability index.
At a 95% confidence level, you can be 95% confident that the actual value of the capability index is contained within the confidence interval. That is, if you collect 100 random samples from your process, you can expect approximately 95 of the samples to produce intervals that contain the actual value of the capability index.
The confidence interval helps you to assess the practical significance of your sample estimate. When possible, compare the confidence bounds with a benchmark value that is based on process knowledge or industry standards.
For example, the maximum allowable defective rate for a manufacturing process is 0.50% defective. Using binomial capability analysis, analysts obtain a %defective estimate of 0.31%, which suggests that the process is capable. The upper CI for %defective is 0.48%. Therefore, the analysts can be 95% confident that the actual value of the %defective does not exceed the maximum allowable value, even when considering the variability from random sampling that affects the estimate.