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Cp Cpk % out of tolerance

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Cp Cpk % out of tolerance
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To check if the production process is capable to produce within specification limits. The Cp and Cpk are used together with Control charts in Statistical process control (SPC)


Cp (Process capability if centered)

The Cp indicates if a process is capable to produce within the specification limits, if the process is centered between the specification limits. To get this quality (Cpk) the process needs to be tuned so that mean is moved to center of the tolerance borders. Therefore the Cp is always lower of equal compared to the Cpk value. This calculation assumes that the data is normally distributed this can be checked with the Anderson Darling normality test. If the cell with the Cp value is red the data set is not according the normal distribution.
The Cp value of a data-set is only calculated if the min and max tolerance are available.

Formula

formula
With a higher Cp value the variation is smaller and it is possible to produce with a higher quality.

Cpk (Process capability)

Calculates the Process capability value of a data-set. The higher the Sigma level the higher the quality (see table). This calculation assumes that the data is normally distributed this can be checked with the Anderson Darling normality test. If the cell with the Cpk value is red the data set is not according the normal distribution.

Formula

formula
With a higher Cpk value the data set is better within tolerance.

Two sided table
Cpk Sigma level % out of tolerance PPM out of tolerance
0.33 1.0 31.73 317310.508
0.50 1.5 13.36 133614.403
0.67 2.0 4.55 45500.264
0.83 2.5 1.24 12419.331
1.00 3.0 0.27 2699.796
1.17 3.5 0.05 465.258
1.33 4.0 0.01 63.342
1.50 4.5 0.001 6.795
1.67 5.0 0.0001 0.573
1.83 5.5 0.000004 0.038
2.00 6.0 0.0000002 0.002


% out of tolerance

Calculates how much % of the data set is statistical out of tolerance. Below 0.1% the value is displayed in PPM (Parts Per Million). This calculation assumes that the data is normally distributed this can be checked with the Anderson Darling normality test. If the cell with the "% out of tolerance" value is red the data set is not according the normal distribution.

Formula

formula calculate the formula value out of the t distribution.
formula calculate the formula value out of the t distribution.

% out of tolerance formula

Legend

formula = Mean
s = STDEV
USL = Upper specification limit
LSL = Lower specification limit

Minimum sample size Cp and Cpk

The minimum sample size to estimate the Cp and Cpk is 30 samples.

What if the process is not approximately normally distributed

All the Cp, Cpk and % out of tolerance assume that the data is according a normal distribution. This can be checked with the Anderson Darling normality test. If the data set is not normally distributed see "What to do with not normally distributed data". A solution is to transform the data and tolerance limits with a Box-Cox transformation. If the result of this transformation is a normally distributed data-set the Cp, Cpk and % out of tolerance can be used.

Example

From data-set in column A the CP is 1.2, Cpk 1.05 and statistical is 0.11% out of tolerance, this is visible in the rows: Cp, Cpk and % out of tol of the result array. The values will be calculated with the tolerance borders in Max Tol. and Min Tol.

Data file

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