Process capability index Cpk

Overview

Cpk (process capability index) is a typical indicator used in quality control and SPC (statistical process control). It evaluates how stably measurement data from a manufacturing process stays within the specification limits. Because it accounts for both the offset of the mean and the variation, it is widely used in process capability analysis and quality improvement. This page introduces a Cpk calculation function that can be used on the OMRON NX/NJ series.

• Difference from Cp:
  Cp shows the ideal capability assuming the data mean is at the "center of the specification." Cpk, on the other hand, accurately reflects the risk (how likely out-of-spec results are) when the mean is offset from the center.

One-sided defect rate

Normal distribution charts

3σ	4σ	5σ

The red vertical lines are the lower specification limit (LSL) and upper specification limit (USL)

Interpretation

If the Cpk value is 1.00 or more, the process capability is judged to be sufficient.

Calculation

This FB calculates as follows
The standard deviation (σ) is obtained using ArySD, a standard NJ function
\[ \sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}} \] Using this with the upper specification limit (USL) and lower specification limit (LSL), the process capability index Cp is calculated
\[ Cp = \frac{USL-LSL}{6\sigma} \] The one-sided Cpu and Cpl are calculated
\[ Cpu = \frac{USL - \bar{x}}{3\sigma} \] \[ Cpl = \frac{\bar{x}-LSL}{3\sigma} \] Cpk is calculated taking the offset into account (the smaller of Cpu and Cpl)
\[ Cpk = min(Cpu, Cpl) \]

Symbols

CalcCpk

In-out

Data

Array containing the target data

Input

Index

First element number of the array to calculate

Size

Number of elements

USL

Upper specification limit

LSL

Lower specification limit

Output

Cpk

Process capability index and variation

Cp

Process capability index

Cpu

Deviation between the upper specification limit and the process mean

Cpl

Deviation between the lower specification limit and the process mean

AVE

Mean

SD

Standard deviation

K

Bias (deviation between the midpoint of the specification limits and the process mean)

Example

Ladder logic

Calculates Cpk for elements 0 to 100 of the Data array

Source

CalcCpk

// Calculate the standard deviation AVE := AryMean(Data[Index], Size); SD := ArySD(Data[Index], Size); // Calculate Cpk Cp := (USL - LSL) / (6.0 * sd); K := ABS(AVE -((USL + LSL) / 2.0)) / ((USL- LSL) / 2.0); Cpk:= (1.0 - K) * Cp; CpU := (USL - AVE) / (3.0 * SD); CpL := (AVE - LSL) / (3.0 * SD);

FAQ

What is Cpk?

Cpk is a type of process capability index that evaluates conformance to specifications, taking into account process variation and the offset of the mean.

What is the difference between Cp and Cpk?

Cp is a capability index that assumes the process mean is at the center of the specification. Cpk also takes the offset of the mean into account, so it represents actual process capability more accurately.

What Cpk value is good enough?

Generally, a Cpk of 1.33 or more is considered sufficient process capability.

Can Cpk be calculated on OMRON NX/NJ?

Yes, using the CalcCpk function block published on this page.

Download

SampleCpk.zip

If you found this site helpful, your support would be greatly appreciated Donate