Monitoring bivariate process

Abstract

The 2 T chart and the generalized variance |S| chart are the usual tools for monitoring the mean vector and the covariance matrix of multivariate processes. The main drawback of these charts is the difficulty to obtain and to interpret the values of their monitoring statistics. In this paper, we study control charts for monitoring bivariate processes that only requires the computation of sample means (the ZMAX chart) for monitoring the mean vector, sample variances (the VMAX chart) for monitoring the covariance matrix, or both sample means and sample variances (the MCMAX chart) in the case of the joint control of the mean vector and the covariance matrix.Keywords: control charts; bivariate processes; mean vector; covariance matrix. ResumoOs gráficos de 2 T e da variância amostral generalizada |S| são as ferramentas usualmente utilizadas no monitoramento do vetor de médias e da matriz de covariâncias de processos multivariados. A principal desvantagem desses gráficos é a dificuldade em obter e interpretar os valores de suas estatísticas de monitoramento. Neste artigo, estudam-se gráficos de controle para o monitoramento de processos bivariados que necessitam somente do cálculo de médias amostrais (gráfico ZMAX) para o monitoramento do vetor de médias, ou das variâncias amostrais (gráfico VMAX) para o monitoramento da matriz de covariâncias, ou então das médias e variâncias amostrais (gráfico MCMAX) para o caso do monitoramento conjunto do vetor de médias e da matriz de covariâncias.Palavras-chave: gráficos de controle; processos bivariados; vetor de médias; matriz de covariâncias.

Cep Online: A Web-Oriented Expert System for Statistical Process Control

“…Interesting alternatives to the T 2 and generalized variance (|S|) control charts for monitoring bivariate processes (namely, the ZMAX, VMAX and MCMAX charts), are presented in [15].…”

Monitoring the mean vector and the covariance matrix of multivariate processes with sample means and sample ranges

“…Control charts more efficient than the |S| chart have been proposed. Recently, Machado (2008a, 2009), Machado and Costa (2008a) and Machado, De Magalhães and Costa (2008), Machado, Costa and Rahim (2008), Machado, Costa and Claro (2009) considered the VMAX statistic to control the covariance matrix of multivariate processes. The points plotted on the VMAX chart correspond to the maximum of the sample variances of the p quality characteristics.…”