Term | Description |
---|---|
USL | Upper specification limit |
LSL | Lower specification limit |
Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |
Between/within standard deviation |
The (1 -α) 100% confidence interval for Cp is calculated as follows:
where ν is approximated by
and
Term | Description |
---|---|
χ2α,ν | The α percentile of the chi-square distribution with ν degrees of freedom |
α | Alpha for the confidence level |
ν | Degrees of freedom |
Yij | The jth observation in the ith subgroup |
The ith subgroup average | |
The average across all subgroups | |
I | The number of subgroups |
ni | The ith subgroup size |
Term | Description |
---|---|
Average of the observations | |
LSL | Lower specification limit |
Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |
Between/within standard deviation |
Term | Description |
---|---|
USL | Upper specification limit |
Average of the observations | |
Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |
Between/within standard deviation |
The (1 -α) 100% confidence interval for Cpk is calculated as follows:
If the sigma tolerance value, say k, in the input is not the default 6, then 9 in the formula should be replaced by (k/2)**2.
Term | Description |
---|---|
N | The total number of observations |
α | Alpha for the confidence level |
v | The degrees of freedom. For information on the calculation of ν, see the topic on the Cp confidence interval for between/within capability analysis. |
Z1-α/2 | The 1-α/2 percentile from the standard normal distribution |
Minitab calculates CCpk based on known values of LSL, USL, and T.
Known value | CCpk |
---|---|
USL only | |
LSL only | |
LSL and USL |
where:
Term | Description |
---|---|
Estimator for the population mean | |
USL | Upper specification limit |
LSL | Lower specification limit |
Between/within standard deviation | |
Average of the observations | |
Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |