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In previous simple cases generalized linear model (GLM)-based control charts have been shown to be very effective in detecting shifts in multivariate counts when input variables are measurable. This paper studies the effectiveness of GLM-based control charts on more complicated data sets with multiple inputs and outputs whose relationships are varied. Results show that the GLM-based charts were most effective in detecting changes in the means of overdispersed counts (when compared with counts with normal dispersion). The GLM-based charts were more effective than multiple C charts in detecting changes in the means of counts when multiple complicated relationships exist. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There are several multivariate extensions to the venerable cumulative sum (CUSUM) chart. This work provides a comparison of the advantages and disadvantages of each, as well as performance evaluations and a description of their interrelationships. A new derivation is also provided. Extensive simulation results that include initial and steady-state conditions are presented. Geometric descriptions are used, and names are proposed based on these geometric characteristics. As several of the key steps in the development of a multivariate extension to a CUSUM also appear in the construction of a two-sided CUSUM, some approaches to a two-sided CUSUM are also summarized. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A model-based scheme is proposed for monitoring multiple gamma-distributed variables. The procedure is based on the deviance residual, which is a likelihood ratio statistic for detecting a mean shift when the shape parameter is assumed to be unchanged and the input and output variables are related in a certain manner. We discuss the distribution of this statistic and the proposed monitoring scheme. An example involving the advance rate of a drill is used to illustrate the implementation of the deviance residual monitoring scheme. Finally, a simulation study is performed to compare the average run length (ARL) performance of the proposed method to the standard Shewhart control chart for individuals. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the robustness of the multivariate exponentially weighted moving average (MEWMA) control chart to non-normal data is examined. Two non-normal distributions of interest are the multivariate $t$ distribution and the multivariate gamma distribution. Recommendations for constructing MEWMA control charts when the normality assumption may be violated are provided. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate the use of control charts based on orthogonal contrasts for a semiconductor manufacturing process. The statistical performance of individuals control charts based on these contrasts and their exponentially weighted moving average counterparts is compared to that of the traditional approach. Contrast-based charts have superior detection capabilities than the traditional approach when targeted at specific process disturbances. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper shows that economic statistical design can provide for better statistical properties without significantly increasing optimal total costs. Cost comparisons between optimal economic statistical designs and optimal economic designs show no significant cost increases. The average run length (ARL) constraints added by economic statistical design significantly improve the statistical properties of the control chart scheme. False alarm frequency is limited while keeping good shift detection characteristics. In addition, the Multivariate Exponentially Weighted Moving Average (MEWMA) control schemes performed better from the cost standpoint than the benchmark pure statistical design—the Hotelling T2 control chart. This improvement held for unconstrained and constrained designs. Finally, cost comparisons at small values of n showed significant advantage for the MEWMA schemes. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Multivariate statistical process control (SPC) procedures are useful in cases where several process variables are monitored simultaneously. A significant disadvantage of these techniques is that the time required to detect a process shift increases with the number of variables being monitored. We show how the shift detection capability of one popular multivariate SPC scheme, the multivariate analogue of the exponentially weighted moving average control chart, can be significantly improved by transforming the original process variables to a lower-dimensional subspace through the use of a U-transformation. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The design of a CUSUM control chart typically involves choosing the subgroup size and sampling interval to achieve specified control chart performance. One can maintain a specified sampling intensity by using small subgroups at frequent intervals or larger subgroups at infrequent intervals. We use the average time to signal to investigate the performance of a CUSUM chart under alternative selections of the subgroup size and sampling interval. Recommendation are provided for both initial-state and steady-state performance. [ABSTRACT FROM AUTHOR]