Cp Cpk Pp Ppk and % out of tolerance To check if the production process is capable to produce within specification limits. The Cp Cpk Pp and Ppk are used together with Control charts in
Statistical process control (SPC) Show
The Cp and Cpk is calculated when the subgroup is set 1 or higher  The Cp and Cpk is used when a process is under statistical control. For not production environment (testing, new process or setting) use the Pp and
Ppk! 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. The Cp does not include the drift between the subgroups! If you want to included the drift use the Pp. 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. If the cell with the Cp value is Violet the process is probably not in control the difference between Cp and Pp is bigger as 15%. The Cp value of a data-set is
only calculated if the min and max tolerance are available. FormulaWith a higher Cp value the variation is smaller and it is possible to produce with a higher quality. Cpk (Process Capability Index)Calculates the Process capability value of a data-set. The Cpk does not include the drift between the subgroups! If you want to included the drift use the Ppk. The higher the Sigma level the higher the quality (see table). If the cell with the Cpk value is Violet the process is probably not in control the difference between Cpk and Ppk is bigger as 15%. FormulaWith a higher Cpk value the data set is better within tolerance. Sigma level table
Subgroups 0 is no subgroups the overall STDEV will be used and the Pp and Ppk will be calculated. What is a subgroup?If in a production process after every hour 5 measurements are done, the subgroup size is 5. When calculating the STDEV within data is ordered in groups of 5 to filter out the drift between the different groups. So the the following data is filtered
But it includes the short therm variation of the process. How to use subgroups?When subgroup size of 5 Data file LegendUSL = 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 The Cp and Cpk assume that the data is according a normal distribution, but due use of
subgroups less vulnerable for non normal overall data. The normally check is calculated on the overall data and does not use the subgroups! What if the process is not in control
Pp PpkThe Pp and Ppk is calculated when the subgroup is set 0 Pp (Process Performance if centered)The Pp 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 (Ppk) the process needs to be tuned so that mean is moved to center of the tolerance borders. Therefore the Pp is always lower of equal compared to the Ppk 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 Pp value is Red the data set is not according the normal distribution. FormulaWith a higher Pp value the variation is smaller and it is possible to produce with a higher quality. Ppk (Process Performance Index)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 Ppk value is Red the data set is not according the normal distribution. FormulaWith a higher Ppk value the data set is better within tolerance. Minimum sample size Pp and Ppk The minimum sample size to estimate the Pp and Ppk is 30 samples. % out of toleranceCalculates 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% out of tolerance Legends = STDEV USL = Upper specification limit LSL = Lower specification limit What if the process is not approximately normally distributed The Pp, Ppk 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 Pp, Ppk and % out of tolerance can be used. Example From data-set in column A the CP is 1.17, Cpk 1.03 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 are calculated with the tolerance borders in Max Tol. and Min Tol. Data file External links
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Cpk 1.67 몇 시그마
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