marposs Merlin - Capability Indices (Cp and CpK)

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Process natural tollerance
NOTE: The Cp index is calculated only if control charts are provided for the
characteristic.
CpK
This represents the process critical capacity. It is the reference index when the
statistical aim of the batch has been indicated as Process. It is calculated using
different methods, depending on the characteristic type:
Bilateral characteristic:
Cpk = Minimum value between:
(2 * (UTL – X)) / (6*σ)
(2 * (X – LTL)) / (6*σ)
where
UTL = Upper Tolerance Limit
LTL = Lower Tolerance Limit
X = mean measurement value
σ = estimated deviation of the measurements
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Capability indices (Cp)
The process capacity is used as the reference index when Process is selected as the
statistical scope of the batch. It is only calculated in the case of bilateral characte-
ristics, using the following formula:
Where
LST – LIT = Tolerance interval
6*σ = Process natural tolerance
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Natural Tolerance is an attempt to express the variability inherent in a given pro-
cess. The formula depends on how the measurements are distributed. As the aim
is to represent the variability of the process, we use the Sigma Hat, estimated
using the samples, rather than the Standard Deviation S used in the case of Natu-
ral Tolerance.
Bilateral or single limit characteristic
Process Natural Tolerance = 6 * σ
Where σ is the estimated process sigma
Unilateral characteristic
with upper limit: Process Natural Tolerance=Maximum between (6*σ) and (3*σ
+X)
with lower limit: Process Natural Tolerance=Minimum between (6*σ) and (3*σ-X)
Where: σ is the standard deviation of the measurements
X is the mean value of the measurements.
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