Nonparametric Predictive Inference in Statistical Process Control

Abstract

Statistical process control (SPC) is used to decide when to stop a process as confidence in the quality of the next item(s) is low. Information to specify a parametric model is not always available, and as SPC is of a predictive nature, we present a control chart developed using nonparametric predictive inference. The proposed ‘extrema chart’, based on the extrema of a sample of observations from the process, is a generalisation of an existing nonparametric method, which controls a process using single observations. We examine the average run length (ARL) of both the one-sided and two-sided extrema chart, and a simulation study is presented to compare the extrema chart with the well known X¯ chart and CUSUM chart. The disadvantage of these charts is that when the process mean and variation of the in-control process have to be estimated, the ARL is biased. This is not an issue for the extrema chart, as no knowledge about the underlying distribution is required.

Key Words:

• Control limits
• exchangeability
• extrema chart
• reference set
• run length

Additional information

Notes on contributors

G. R. J. Arts

Gerda Arts Lecturer in Statistics at the Department of Mathematical Sciences, University of Durham. Dr. Arts received her Ph.D in Mathematics from the University of Twente (the Netherlands) in 1998. Her research interests lie in industrial and applied statistics. She is also active as a member of the departmental consultancy unit, offering statistical support to staff in other departments as well as to companies around the world.

F. P. A. Coolen

Frank Coolen Reader in Statistics at the Department of Mathematical Sciences, University of Durham. His main research interests are foundations of statistics and decision making, and reliability theory. Dr Coolen received his Ph.D in Mathematics from Eindhoven University of Technology (the Netherlands) in 1994. He serves as Associate Editor for Journal of Statistical Planning and Inference.

P. van der Laan

Professor van der Laan Received his Ph.D in Mathematics at the Eindhoven University of Technology in 1970, and has worked at the Mathematical Centre in Amsterdam, Philips, and as Full Professor of Statistics at the Agricultural University of Wageningen and, from 1990 till his retirement in 2003, at Eindhoven University of Technology. His research interests are in nonparametric statistics, selection methods, design of experiments and quality management. Professor van der Laan is an elected member of the International Statistical Institute.