A new chart based on sample variances for monitoring the covariance matrix of multivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Synthetic Control Chart Based on Two Sample Variances for Monitoring the Covariance Matrix

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The double sampling and the EWMA charts based on the sample variances

We propose a new statistic to control the covariance matrix of bivariate processes. This new statistic is based on the sample variances of the two quality characteristics, in short VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these two variances. The reasons to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar is its faster detection of process changes and its better diagnostic feature; that is, with the VMAX statistic it is easier to identify the out-of-control variable. We study the double sampling (DS) and the exponentially weighted moving average (EWMA) charts based on the VMAX statistic. (C) 2008 Elsevier B.V. All rights reserved.

A control chart based on sample ranges for monitoring the covariance matrix of the multivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A new chart for monitoring the covariance matrix of bivariate processes

In this article we consider a control chart based on the sample variances of two quality characteristics. The points plotted on the chart correspond to the maximum value of these two statistics. The main reason to consider the proposed chart instead of the generalized variance |S| chart is its better diagnostic feature, that is, with the new chart it is easier to relate an out-of-control signal to the variables whose parameters have moved away from their in-control values. We study the control chart efficiency considering different shifts in the covariance matrix. In this way, we obtain the average run length (ARL) that measures the effectiveness of a control chart in detecting process shifts. The proposed chart always detects process disturbances faster than the generalized variance |S| chart. The same is observed when the size of the samples is variable, except in a few cases in which the size of the samples switches between small size and very large size.

Control charts for monitoring the mean vector and the covariance matrix of bivariate processes

In this article, we propose new control charts for monitoring the mean vector and the covariance matrix of bivariate processes. The traditional tools used for this purpose are the T (2) and the |S| charts. However, these charts have two drawbacks: (1) the T (2) and the |S| statistics are not easy to compute, and (2) after a signal, they do not distinguish the variable affected by the assignable cause. As an alternative to (1), we propose the MVMAX chart, which only requires the computation of sample means and sample variances. As an alternative to (2), we propose the joint use of two charts based on the non-central chi-square statistic (NCS statistic), named as the NCS charts. Once the NCS charts signal, the user can immediately identify the out-of-control variable. In general, the synthetic MVMAX chart is faster than the NCS charts and the joint T (2) and |S| charts in signaling processes disturbances.

Gráfico de controle de VMAX para o monitoramento da matriz de covariâncias

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Gráfico de controle MCMAX para o monitoramento simultâneo do vetor de médias e da matriz de covariâncias

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Joint control charts for monitoring location and dispersion

The T-2 and the generalized variance vertical bar S vertical bar charts are used for monitoring the mean vector and the covariance matrix of multivariate processes. In this article, we propose for bivariate processes the use of the T-2 and the VMAX charts. The points plotted on the VMAX chart correspond to the maximum of the sample variances of the two quality characteristics. The reason to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar is the user's familiarity with the computation of simple sample variances; we can't say the same with regard to the computation of the generalized variance vertical bar S vertical bar.

Monitoring bivariate processes

The T2 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.

Gráficos de controle para monitoramento de processos multivariados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Determination of potassium and sodium in an ash sample by gamma-ray spectroscopy

Neutron activation analysis and gamma-ray spectroscopy were used to determine the quantity of potassium and sodium in an ash sample of Tabebuia sp bombarded with thermal neutrons. These techniques, widely applied in nuclear physics, can be used in the context of wood science as an alternative for the usual physical chemistry methods applied in this area. The quantity of K and Na in an 8.60 +/- 0.10 mg of ash was determined as being 1.3 +/- 0.3 mg and 11.0 +/- 1.8 mu g, respectively. The ratio of Tabebuia sp converted into ash was also determined as 0.758 +/- 0.004%.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dependence of the electrical conductivity and elastomeric properties on sample preparation of blends of polyaniline and natural rubber

Blend films (free-standing) containing 20% in volume of polyaniline (PANI) in 80% of natural rubber (NR) were fabricated by casting in three different ways: (1) adding PANI-EB (emeraldine base) dissolved in N-methyl-2-pyrrolidone (NMP) to the latex (NRL), (2) adding PANI-EB dissolved in in-cresol to NR dissolved in xylol (NRD), (3) overlaying the surface of a pure NR cast film with a PANI layer grown by in situ polymerization (NRO). All the films were immersed into HCl solution to achieve the primary doping (protonation) of PANI before the characterization. The main goal here was to investigate the elastomeric and electrical conductivity properties for each blend, which may be applied as pressure and deformation sensors in the future. The characterization was carried out by optical microscopy, dc conductivity, vibrational spectroscopy (infrared absorption and Raman scattering), thermogravimetry analysis (TGA), differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA), and tensile stress-strain curves. The results suggest that the NRL blend is the most suitable in terms of mechanical and electrical properties required for applications in pressure and deformation sensors: a gain of conductivity without losing the elastomeric property of the rubber. (c) 2005 Wiley Periodicals, Inc.