Shewhart dispersion charts made easy for mild to moderately autocorrelated normally distributed data

ABSTRACT

The aim is to make it easier for users to implement dispersion monitoring plans when the data are autocorrelated. If the data follow a low-order ARMA model then the same threshold for the monitoring plan is applicable by revising the rational subgroup size. A robust plan for non-normal data is achieved in most cases by first transforming the data to an approximate normal distribution, and then applying the plan for normally distributed data. The dispersion plan is based on the robust regression estimator of the slope coefficient when regressing the ordered rational sub-group values against their “expected” in-control values.

KEYWORDS:

• continuous variables
• rational sub-group
• statistical process control
• time series
• volatility

About the author

Ross Sparks is a Statistician with over 38 years research and teaching experience at universities and research at CSIRO. He is currently based in Data 61, CSIRO, Australia and been with CSIRO for over 25 years. His role is in leading strategic and tactical research projects in Data61, CSIRO in the area of multivariate spatio-temporal monitoring and spatio-temporal modelling. He has published 82 papers in refereed journals, 10 book chapters, 19 papers in conference proceedings and 10 articles in trade magazines.

He has lectured at the University of Natal, University of Cape Town and University of Wollongong in Statistics and Applied Mathematics before joining CSIRO Australia. He has made a number of research contributions in the areas of (multivariate) process monitoring, spatio-temporal modelling and the handling of (partially) missing data. Specifically, he has contributed to topics in the variable selection in multivariate regression models, outlier detection in regression models, model validation and assessment, quality control and assurance, cluster analysis, dimension reduction methods and disease surveillance.

Acknowledgment

The author would like to thank Rob McGregor from InfoClear for his editorial help with this version of the article.