Information visualization about changes of process mean and variance on (¯x, s) control chart

Abstract

The $(\overline{x},s)$ control chart is one of simultaneous control charts to monitor process mean and variance on $\overline{x}-s$ coordinate. The primary purpose of the $(\overline{x},s)$ control chart has been the judgement of the process condition at the time of individual samplings. Then, for the purpose of identifying some process parameters which are responsible for an out-of-control signal in the $(\overline{x},s)$ control chart, a method based on Akaike Information Criterion (AIC) has been proposed in recent years. However, similar to other simultaneous control charts, a disadvantage of the $(\overline{x},s)$ control chart is that the time-ordered nature of the data is visually lost. In this research, we address a way of overcoming the disadvantage of the $(\overline{x},s)$ control chart by giving visual information on the time progress. At first, we locate areas indicating a caution and a warning of an out-of-control condition on the $(\overline{x},s)$ control chart using AIC. Then, a method of drawing a time series of the sample mean and standard deviation on the $(\overline{x},s)$ control chart is considered using some techniques of the information visualization. Based on the consideration above, the procedure of perceiving the track of changes in the process condition up to the out-of-control signal is proposed.

Keywords:

• $(\overline{x},s)$ control chart
• Akaike information criterion (AIC)
• caution and warning areas
• Kullback–Leibler information
• simultaneous monitoring schemes

Acknowledgements

The authors would like to thank the Editor and Reviewers very much for their helpful, useful and constructive comments and suggestions regarding this paper. Then, this work was supported by JSPS KAKENHI grant number 15K01191: ‘Proposal of quality management system based on the information and communication technology (ICT) towards the next generation production system’ and 17K01266: ‘An investigation of data visualization and its application to production and operation management’. We would like to appreciate the grants for our research.