The density control chart: a general approach for constructing a single chart for simultaneously monitoring multiple parameters

Abstract

The majority of the existing literature on simultaneous control charts, i.e. control charting mechanisms that monitor multiple population parameters such as mean and variance on a single chart, assume that the process is normally distributed. In order to adjust and maintain the overall type-I error probability, these existing charts rely largely on the property that the sample mean and sample variance are independent under the normality assumption. Furthermore, the existing charting procedures cannot be readily extended to non-normal processes. In this article, we propose and study a general charting mechanism which can be used to construct simultaneous control charts for normal and non-normal processes. The proposed control chart, which we call the density control chart, is essentially based on the premise that if a sample of observations is from an in-control process, then another sample of observations is no less likely to be also from the in-control process if the likelihood of the latter is no less than the likelihood of the former. The density control chart is developed for normal and non-normal processes where the distribution of the plotting statistic of the density control chart can be explicitly derived. Real examples are given and discussed in these cases. We also discuss how the density control chart can be constructed in cases when the distribution of the plotting statistic cannot be determined. A discussion of potential future research is also given.

Keywords:

• hypothesis testing
• likelihood function
• multiple parameters
• non-normal processes
• Shewhart control chart
• simultaneous control chart

Acknowledgments

The authors would like to thank Professor Alan H. Welsh for his valuable comments. They would also like to thank two referees for their comments and suggestions which improved the presentation of the article. This research work of H-CC and L-AC was partially supported by a grant from the National Science Council of the Republic of China (NSC 95-2118-M-009-007).