Statistical process control for autocorrelated data on grid

ABSTRACT

Assumptions of normality and independence are the key assumptions required in the development and use of control charts. The assumption of independence is hard to justify in many experimental data. The control charts for sample mean and sample standard deviation are obtained in this article when the observations are obtained over a grid on a two-dimensional surface. It is assumed that the observations follow a first order autoregressive process in both the directions. The results are applied to road pavement data on road course thickness observed on a two dimensional grid. The results from a simulation study are presented for the comparison of modified and unmodified control limits.

KEYWORDS:

• Autocorrelated data
• -chart
• s-chart
• AR(1) process

AMS SUBJECT CLASSIFICATION:

• 62M10
• 62P30

Acknowledgments

We are very grateful to David Griffiths and John Rayner for their valuable comments. We are also thankful to the editor and three anonymous referees for their constructive suggestions.