Process capability index

The process capability indices Cp and Cpk are indicators for the statistical evaluation of a process in the production technology. Indicate how safe the default as specified goals are achieved.

Definition

The CPK is defined as follows from the mean value, the associated standard deviation and the upper () and lower () specification limit:

The higher this value is, the more secure is the entire production within the specification.

The CP value is defined as:

The Cp value can only be calculated if both an upper and lower specification limit is defined.

During the Cp value specifies only the ratio of the predetermined tolerance to process variation, CPK value also includes the location of the mean value for the given tolerance middle. In the best case ( process mean lies exactly in the middle of the tolerance range ) is Cpk = Cp; otherwise CpK is < Cp.

Target values ​​for the process capability

Formerly a Cpk value of at least 1.00 was ( the distance of the nearest tolerance limit of the process mean is at least 3 standard deviations) is considered sufficient, later the requirement to 1.33 (4 standard deviations) was raised. Meanwhile, a p value of 2.00 is often (the width of the tolerance range corresponds to a spread of ± 6 standard deviations therefore Six Sigma ) combined with a CpK value of 1.67 ( the distance between the closest tolerance from the process mean is at least 5 standard deviations ) defined as a desirable goal.

Comparison table CpK - PPM

Under the assumption of a normally distributed process variable can be derived from the process capability index Cpk using the following formula, the expected number of errors per 1 million ( parts per million) calculate:

In this case the distribution function of the standard normal distribution. The following table gives some example values ​​for the two-sided probability:

Criticism of the process capability

The simplest means to enhance the process capability of a given process, is to relax the specification limits, the larger the difference between OSG and USG, the more standard deviations can be accommodated therein. The elimination of specification limits, an infinite process capability is achieved.

In order for the process capability remains a meaningful measure, the specification limits in no event may be influenced by the process owner.