Change search
ReferencesLink to record
Permanent link

Direct link
Elliptical safety region plots for Cpk
Department of Mathematics, Luleå University of Technology.
Department of Mathematics, Luleå University of Technology.
2011 (English)In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 38, no 6, 1169-1187 p.Article in journal (Refereed) Published
Abstract [en]

The process capability index C pk is widely used when measuring the capability of a manufacturing process. A process is defined to be capable if the capability index exceeds a stated threshold value, e.g. C pk >4/3. This inequality can be expressed graphically using a process capability plot, which is a plot in the plane defined by the process mean and the process standard deviation, showing the region for a capable process. In the process capability plot, a safety region can be plotted to obtain a simple graphical decision rule to assess process capability at a given significance level. We consider safety regions to be used for the index C pk . Under the assumption of normality, we derive elliptical safety regions so that, using a random sample, conclusions about the process capability can be drawn at a given significance level. This simple graphical tool is helpful when trying to understand whether it is the variability, the deviation from target, or both that need to be reduced to improve the capability. Furthermore, using safety regions, several characteristics with different specification limits and different sample sizes can be monitored in the same plot. The proposed graphical decision rule is also investigated with respect to power.

Place, publisher, year, edition, pages
2011. Vol. 38, no 6, 1169-1187 p.
Keyword [en]
capability index, process capability plot, elliptical safety region, graphical method, safety region, hypothesis testing, power
National Category
Probability Theory and Statistics
URN: urn:nbn:se:umu:diva-47859DOI: 10.1080/02664763.2010.491858OAI: diva2:445018
Available from: 2011-09-30 Created: 2011-09-30 Last updated: 2011-11-15Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Vännman, Kerstin
In the same journal
Journal of Applied Statistics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 60 hits
ReferencesLink to record
Permanent link

Direct link