A Comparison of Decision Methods for C_pk When Data are Autocorrelated

ABSTRACT

In many industrial applications, autocorrelated data are becoming increasingly common due to, for example, on-line data collection systems with high-frequency sampling. Therefore, the basic assumption of independent observations for process capability analysis is not valid.

The purpose of this article is to compare decision methods using the process capability index C _pk when data are autocorrelated. This is done through a case study followed by a simulation study. In the simulation study the actual significance level and power of the decision methods are investigated. The outcome of the article is that two methods appeared to be better than the others.

KEYWORDS:

• autocorrelation
• C _pk
• capability index
• continuous process
• process industry

ACKNOWLEDGMENT

The authors are grateful for the financial support provided by Produktion Botnia. The authors also thank Swedish Steel AB for access to process data. Special thanks to Per Lagerwall at Swedish Steel AB for valuable support. Furthermore, thanks to Bjarne Bergquist and Erik Vanhatalo at Luleå University of Technology for valuable comments on earlier drafts.

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Murat Kulahci

Murat Kulahci is an associate professor in statistics at the Technical University of Denmark and at Luleå University of Technology, Sweden. He holds a bachelor's degree in chemical and industrial engineering, master's degrees in chemical engineering and finance, and a Ph.D. in industrial engineering. He is a member of the European Network for Business and Industrial Statistics.