Monitoring Variability of Multivariate Processes

• Activity Number: 235
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Quality and Productivity
• Author(s): Amit Mitra*+
• Companies: Auburn University
• Keywords: Multivariate process control ; Variance-covariance matrix ; time to first detection ; process variability

Abstract

Techniques to monitor and detect shifts in the mean of a multivariate process have received much attention. Here, the focus is on detecting and possibly identifying changes in the variability of response variables in multivariate processes. Traditional methods incorporate the determinant of the variance-covariance matrix of the response variables. This has an advantage of aggregating the variability of several variables into one index. However, it also has a drawback of failing to detect changes in variances since it is quite possible for different for different variance-covariance matrices to yield the same determinant. Decomposition of the variance-covariance matrix is investigated that may lead to better identification of changes in the variances of the response variables. Results of the suggested procedure are investigated through simulation. The performance measures are the mean and the standard deviation of the time to first detection.