Process capability study

In quality management , the process capability study examines the relationship between the frequency distribution of a measurable quality feature and the tolerance specified for this feature . The aim of the investigation is to make statements about the "quality capability" of the process that produces this feature.

method

Basic requirement for process stability

The generally recognized basic requirement for carrying out a process capability study is the stability of the process. Stability here means that the process produces consistent and predictable results from day to day, hour to hour. Proof of process stability is provided by the management and evaluation of a quality control card on which sample data from the process are shown.

If the process is not stable, the process must first be brought under control (controlled process, "under statistical control"). Only when the process delivers stable results can the process capability study begin.

Evaluation of control card data

If the process is stable over the entire observation period, the existing control card data is evaluated:

• Determination of the process mean value ( arithmetic mean value of all measured values),
• Mathematical estimate of the standard deviation of the process based on the control card data.

The process potential

The process potential C _p is then obtained as the quotient of the tolerance range and the process spread:

${\displaystyle C_{p}={\frac {\text{Toleranzbreite}}{\text{Prozessstreubreite}}}}$

The process spread is defined here as 6 standard deviations. A C _p value of 1.00 means that the difference between the upper and lower limit value for the characteristic is exactly six times as large as the observed standard deviation of the characteristic.

The mean observed for the characteristic is not included in this calculation. For this reason, the C _p index only reflects the potential of the process, i.e. the quality capability that would be observed if the mean value were centered exactly on the center of the tolerance range.

The process capability

The process capability index C _pK , which describes the actual quality capability of the process, now also takes into account the position of the process mean value in addition to the tolerance range and the process spread . It is defined as the smaller of the following two values:

${\displaystyle C_{\text{po}}={\frac {{\text{obere Toleranzgrenze}}-{\text{Prozessmittelwert}}}{\text{halbe Prozessstreubreite}}}}$

${\displaystyle C_{\text{pu}}={\frac {{\text{Prozessmittelwert}}-{\text{untere Toleranzgrenze}}}{\text{halbe Prozessstreubreite}}}}$

In the best case (process mean value is exactly in the middle of the tolerance range), C _pK = C _p ; otherwise C _pK <C _p .

Target values ​​for process capability

In the past, a C _pk value of at least 1.00 (the distance between the closest tolerance _{limit and the process mean} value is at least 3 standard deviations) was considered sufficient, later the requirement was raised to 1.33 (4 standard deviations). In today's thinking, a C _p value of 2.00 (the width of the tolerance range corresponds to a spread of ± 6 standard deviations, hence Six Sigma ) is combined with a C _pk value of 1.67 (the distance between the closest tolerance _{limit and the process mean} value is at least 5 standard deviations) as a desirable goal.

Alternative calculation methods for data that are not normally distributed

In the illustration above, it was assumed that the feature data is approximately normally distributed . There are alternative calculation methods for other forms of distribution.

Expressiveness

The calculated indices are of course only meaningful as long as the process works consistently (remains under control).

Even if the investigation is called a process capability investigation , it must also be taken into account that the calculated capability index only applies to one characteristic : the quality capability may be completely different for other characteristics generated by the same process.

literature

• Edgar Dietrich, Alfred Schulze: Statistical procedures for machine and process qualification . 6th, completely revised edition. Carl Hanser Verlag, Munich / Vienna 2009, ISBN 978-3-446-41525-6 .
• Tilo Pfeifer, Robert Schmitt (Ed.): Masing Handbook Quality Management , 6th revised edition. Carl Hanser Fachbuchverlag, Munich / Vienna 2014, ISBN 978-3-446-43431-8 .

Individual evidence

1. ↑ E. Dietrich, A. Schulze: Statistical procedures for machine and process qualification. Carl Hanser Verlag, Munich / Vienna 2009, ISBN 978-3-446-41525-6 , p. 246.
2. ↑ E. Dietrich, A. Schulze: Statistical procedures for machine and process qualification. 2009, p. 219.
3. ↑ E. Dietrich, A. Schulze: Statistical procedures for machine and process qualification. 2009, p. 323ff.
4. ↑ E. Dietrich, A. Schulze: Statistical procedures for machine and process qualification. 2009, p. 324.
5. ↑ E. Dietrich, A. Schulze: Statistical procedures for machine and process qualification. 2009, p. 326.
6. ↑ ^{a b} Thomas Pyzdek: Motorola's Six Sigma Program. (English).
7. ↑ E. Dietrich, A. Schulze: Statistical procedures for machine and process qualification. 2009, p. 312ff.
8. ^ Walter Masing (Ed.): Masing Handbuch Qualitätmanagement , Carl Hanser Verlag, Munich / Vienna 1998, ISBN 3-446-19397-9 , p. 265.