The Variable Parameters Control Charts for Monitoring Autocorrelated Processes

Abstract

The variable parameters (VP) control chart varies all control parameters from the current sample information, and results in more effective monitoring based on statistical and economic criteria. The usual assumption for designing a control chart is that the observations from the process are independent. However, for many processes, such as chemical processes, consecutive measurements are often highly correlated. In the present article, the observations are modeled as an AR(1) process plus a random error, and the properties of the VP charts are evaluated and studied under this model. Based on the study, the VP control scheme generally has better performance in detecting small mean shifts than the standard and the other adaptive charts. However, when the observations are highly autocorrelated, the complexity of the VP chart gives a negative effect on the performance.

Keywords:

• Autocorrelated process
• Control chart
• First-order autoregressive process
• Quality control
• Variable parameters

Mathematics Subject Classification:

• 62P30
• 60J20

Acknowledgment

This work was supported by the National Science Council of Taiwan, Republic of Chinese under the grant NSC97-2221-E-025-005.