Sentence examples for multivariate processes in from inspiring English sources

Zamba and Hawkins (2006) presented a model to estimate the time of step change in the mean vector of multivariate processes in situations where the parameters are unknown.

Qiu 2008 proposed a distribution-free technique to detect fluctuation in multivariate processes through the employ of a log-linear model to estimate the in-control distribution, and the use of a multivariate CUSUM chart to detect shifts.

Besides, some researchers used artificial neural networks for estimating the time of change in multivariate processes.

Allahyari and Amiri (2011) studied step change point estimation problem in multivariate processes using a clustering approach.

For example, El-Midany et al. (2010) proposed modular artificial neural networks (ANNs) to recognize abnormal patterns, to identify the variables responsible for out-of-control signal and classify the abnormal pattern parameters in multivariate processes.

Sullivan and Woodall (2000) based on a likelihood ratio statistic proposed a preliminary control chart for change point estimation in the multivariate processes with individual observations when the shift occurs in the mean vector, the covariance matrix or in both.

In this paper, we regroup all the tasks of the multivariate process monitoring in one approach.

Doğu and Kocakoc (2011) estimated the time of step change in the covariance matrix of multivariate normal processes, in which a multivariate control chart based on sample covariance is used for receiving out-of-control signals.

The Hotelling T2control chart was first introduced by Hotelling (1947) to come up with the correlation between the quality characteristics in monitoring multivariate processes.

However, due to the complexity of multivariate distributions, existing methods in univariate processes cannot be readily extended to multivariate processes.

In this chapter, we introduce the basics of SPC, providing an overview of different approaches for univariate and multivariate processes.