Cp
Notation
| Term | Description |
|---|---|
| USL | Upper specification limit |
| LSL | Lower specification limit |
| Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |
 | Within-subgroup standard deviation |
Cp confidence interval bounds
The (1 -α) 100% confidence interval for Cp is calculated as follows:
where ν is calculated based on the method used to estimate σ2within:
- Pooled standard deviation: ν = Σ (ni- 1)
- Average moving range and Median moving range: ν ≈ k – Rspan + 1
- Square root of MSSD: ν = k - 1
- Rbar: ν = 0.9 k (n - 1)
- Sbar: ν = fn k (n - 1), where fn is the adjustment factor that varies with n, as shown in the following table.
| n | fn |
|---|---|
| 2 | 0.88 |
| 3 | 0.92 |
| 4 | 0.94 |
| 5 | 0.95 |
| 6, 7 | 0.96 |
| 8, 9 | 0.97 |
| 10-17 | 0.98 |
| 18-64 | 0.99 |
| 65- | 1.00 |
Notation
| 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 |
| σ2within | Within-subgroup variance |
| ni | The ith subgroup size |
| k | Number of samples |
| Rspan | Length of the moving range |
| n | Average sample size (Σ ni / k). |
CPL
Notation
| Term | Description |
|---|---|
 | Process mean (estimated from the sample data or a historical value) |
| LSL | Lower specification limit |
| Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |
 | Within-subgroup standard deviation |
CPU
Notation
| Term | Description |
|---|---|
| USL | Upper specification limit |
 | Process mean (estimated from the sample data or a historical value) |
| Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |
 | Within-subgroup standard deviation |
Cpk
Cpk confidence interval bounds
The (1 -α) 100% confidence interval for Cpk is calculated as follows:
Notation
| Term | Description |
|---|---|
| N | The total number of observations |
| α | Alpha for the confidence level |
| v | The degrees of freedom based on the method used to estimate σ2within (for information on the calculation of v, see the section on Cp confidence interval bounds) |
| Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |
| Z1-α/2 | The 1-α/2 percentile from the standard normal distribution |
CCpk
Minitab calculates CCpk based on known values of LSL, USL, and T.
| Known value | CCpk |
|---|---|
| USL only |
 |
| LSL only |
 |
| LSL and USL |
 |
where:
Notation
| Term | Description |
|---|---|
 | Estimator for the population mean |
| USL | Upper specification limit |
| LSL | Lower specification limit |
 | Within-subgroup standard deviation |
 | Average of the observations |
| Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |
