Phase II control charts for autocorrelated processes

Abstract

A large amount of SPC procedures are based on the assumption that the process subject to monitoring consists of independent observations. Chemical processes as well as many non-industrial processes exhibit autocorrelation, for which the above-mentioned control procedures are not suitable. This paper proposes a Phase II control procedure for autocorrelated and possibly locally stationary processes. A time-varying autoregressive (AR) model is proposed, which is capable of dealing with the autocorrelation as well as with local non-stationarities of the temporal process. Such non-stationarities are induced by the time-varying nature of the AR coefficients. The model is optimized during Phase I when it is assured that the process is in control and as a result the model describes accurately the process. The Phase II proposed control procedure is based on a comparison of the current time series model with an alternative model, measuring deviations from it. This comparison is carried out using Bayes factors, which help to establish the in-control or out-of-control state of the process in Phase II. Using the threshold rules of the Bayes factors, we propose a binomial-type control procedure for the monitoring of the process. The methodology of this paper is illustrated using two data sets consisting of temperature measurements at two different stages in the manufacturing of a plastic mould.

Keywords:

• Autocorrelated processes
• binomial-type control procedures
• Phase II control charts
• statistical process control
• time series monitoring
• time-varying autoregressive model

Acknowledgements

We are grateful to two anonymous referees who provided helpful comments on an earlier version of the paper.

Disclosure statement

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of this article.

Funding information

This work is supported by the General Secretariat for Research and Technology (GSRT, Ministry of Education, Greece) research funding action ‘ARISTEIA II’.

Notes on contributors

Kostas Triantafyllopoulos, is a Senior Lecturer at the School of Mathematics and Statistics of the University of Sheffield. He holds a PhD in Statistics from the University of Warwick. Prior to Sheffield, he has worked as a Research Associate at the University of Bristol and as a Lecturer at the University of Newcastle upon Tyne. His research interests include time series analysis and statistical process control. He has published widely and is involved in research grants including the Nuffield Foundation and Engineering and Physical Sciences Research Council (UK). He has wide teaching experience in statistics and is the supervisor of 7 doctoral students and 30 masters students.

Sotiris Bersimis, holds a PhD in Statistics and Probability from the University of Piraeus, Department of Statistics and Insurance Science, a MSc in Statistics from the Athens University of Economics and Business and a BSc in Statistics and Insurance Science from the University of Piraeus. His PhD was funded by a scholarship from Hellenic General Secretary of Research and Technology. He also granted a post-doctoral fellow scholarship by the Hellenic State Scholarships Foundation. Currently he is a lecturer at the Statistics and Insurance Science of the University of Piraeus. He concentrated his personal research in stochastic modeling of industrial, business and biomedical processes as well as in applied analysis of multivariate data. He has published over 35 papers in peer reviewed scientific journals, three books (in Greek) while he has presented over 60 papers in international conferences.