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Process Capability: Cp, Cpk, Cpm & Target Adjustment

Calculate specification-width, centering and target-adjusted capability indices from a supplied process mean and positive standard deviation.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

With limits 18 and 26, mean 22, standard deviation 1 and target 22, Cp and Cpk both equal 4/3. Moving the mean to 23 lowers Cpk to 1 while Cp stays 4/3.

Cp = (USL − LSL)/(6s); Cpk = min(USL − mean, mean − LSL)/(3s); Cpm = (USL − LSL)/(6√[s² + (mean − target)²])

Worked example

Enter these known values and leave the other values blank.

Lower specification limit
18
Upper specification limit
26
Mean
22
Process standard deviation
1
Target
22
Potential capability Cp
1.333
Centered capability Cpk
1.33
Target-adjusted capability Cpm
1.3333
Cpk with target penalty (Cpmk)
1.3333

Assumptions and limitations

  • Supply all dimensions in a consistent measurement unit. Standard deviation must be positive and the upper specification limit cannot be below the lower limit.
  • Interpret conventional capability indices for a stable process under an appropriate distribution model. The calculator does not establish stability, normality or the quality of a sample estimate.
  • A mean outside the specification interval can produce negative Cpk and Cpmk. The sign is retained instead of clipping an out-of-specification process to zero.
  • The target-penalty output divides Cpk by √[1 + ((mean − target)/s)²]. These are point calculations without confidence intervals, defect-rate predictions or an automatic acceptance threshold.

Common questions

Why can Cp stay unchanged while Cpk falls?

Cp uses the total specification width and spread. Cpk also uses the distance from the mean to the nearer limit, so shifting the mean can reduce it without changing the spread.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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