Sensible limit values for process capability

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The calculation of the process capability in the form of the process capability index (Ppk or Cpk) sets the scatter of the individual results and the position of the mean value in relation to the specification limits. The higher the process capability index, the further away the individual results are from the specification limits.

Calculation of the process capability index:

The following parameters are included in the calculation of the process capability index:

Mean value (μ)
Standard deviation of the mean value (σ)
Upper and lower specification limit (OSG and USG)

The first step is to calculate the process capability indices “Cpo” and “Cpu” for the upper and lower specification limits:

_Cpo = (OSG – μ)/(3σ) OSG = upper specification limit

_Cpu = (μ – USG)/(3σ) USG = lower specification limit

_Cpk = min(_Cpo, _Cpu)

In a second step, the lower value (Cpk = smallest process capability value) of the two values is selected:

The calculation of meaningful Cpk values is only possible from 25 – 30 individual values.

Sample calculation:

Investigated quality characteristic: content of a medicinal product

Specification limits: 95 – 105 mg

Average value: 98 mg

Standard deviation: 0.5 mg

_Cpo = (105 mg – 98 mg)/(3×0.5 mg) = 4.7

_Cpu = (98 mg – 95 mg)/( 3×0.5 mg) = 2.0

_Cpk = min(_Cpo, _Cpu) = 2.0

But what do the Cpk values obtained mean?

Cpk = 1.00

If 1 million units are checked, 2699 faulty units would be found. The distance of the mean value to the next specification limit corresponds to 3 times the standard deviation (3σ) of the values.

Cpk = 1.33

If 1 million units are checked, 66 faulty units would be found. The distance of the mean value to the next specification limit corresponds to 4 times the standard deviation (4σ) of the values.

Cpk = 1.67

If 1 million units are checked, no faulty units would be found. The distance of the mean value to the next specification limit corresponds to 5 times the standard deviation (5σ) of the values.

Cpk = 2.00

If 1 million units are checked, no faulty units would be found. The distance of the mean value to the next specification limit corresponds to 6 times the standard deviation (6σ) of the values.

The limit values selected for the CpK value should be determined on a risk basis. This means that the more critical a quality characteristic is, the higher the acceptance criterion for the CpK value should be.

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