Cp Cpk in Minitab
Use Histogram Cp and Cpk to measure process capability
Histograms show the spread, or dispersion, of your data. The customer's upper specification limit (USL) and lower specification limit (LSL) set the boundaries or parameters that determine acceptable levels of variation in the process. When the process is between/within the USL and LSL then the process is said to be capable. The Minitab histogram uses variable data to determine process capability. With attribute data (defects), capability assumes that the process produces zero defects.
Cp Cpk for Process Capability Analysis
Cp > 1.0 Process is capable meaning measured process requirements fall between/within the customer's USL and LSL, 3-4 sigma (Cp=1.0 to 1.33)
Cpk > 1.0 Process is capable and centered between the LSL and USL, not shifted either direction. (Defects <-+-> Waste)
In observation 4 below we have a capable process with Cp 1.14 and Cpk 1.12 respectively.
(Minitab Output)
Cp values are not the best indicators of process capability. Cp is the ratio of the engineering tolerance (USL - LSL) to the natural tolerance (6s). The value of Cp does not take into account where the process is centered. Just knowing that a process is capable (Cp > 1.0) does not ensure that all the product or service being received is within the specifications. A process can have a Cp > 1.0 and produce no product or service within specifications. In addition, Cp values can't be calculated for one- sided specifications. A better measure of process capability is Cpk.
Cpk takes into account where the process is centered. The value of Cpk is the minimum of two process capability indices. One process capability is Cpu, which is the process capability based on the upper specification limit. The other is Cpl, which is the process capability based on the lower specification limit. Algebraically, Cpk is defined as shown in the figure.
Cpk Equation
Both
Cpu and Cpl take into account where the process is centered. The value
of Cpk is the difference between the process average and the nearest
specification limit divided by three times the standard deviation.
It should be noted that the standard deviation is the standard deviation
based on a R or s chart - not the standard deviation of the individual
measurements.
Cpk values above 1.0 are desired. This means that essentially no product
or service is being produced above USL or below LSL. If Cpk is less than
1.0, this means that there is some product being produced out of specification.
If there is only one specification, the value of Cpk is either Cpu or
Cpl, whichever is appropriate for the specification.
It should also be noted that Cp and Cpk levels (B/W Capability) should relate closely to Pp and Ppk levels (Overall Capacity) If Cp Cpk levels are substantially greater than Pp Ppk levels then your process is capable but not stable enough to reliably produce a consistent result.
If this is the case use corresponding control charts to measure process capacity and stability in tandem with the histogram to measure capability. In most quality settings this multi chart approach would be preferable to using the histogram alone.
In Minitab the capability 6 pack offers additional views of the capability scenario. Using the 6 pack you can see the correlation of other charts to the capability analysis in question.
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