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.

Grafico misto de controle da media com amostragem em dois estagios

This paper proposes a new control chart to monitor a process mean employing a combined npx-X control chart. Basically the procedure consists of splitting the sample of size n into two sub-samples n1 and n2 determined by an optimization search. The sampling occur in two-stages. In the first stage the units of the sub-sample n1 are evaluated by attributes and plotted in npx control chart. If this chart signs then units of second sub-sample are measured and the monitored statistic plotted in X control chart (second stage). If both control charts sign then the process is stopped for adjustment. The possibility of non-inspection in all n items may promote a reduction not only in the cost but also the time spent to examine the sampled items. Performances of the current proposal, individual X and npx control charts are compared. In this study the proposed procedure presents many competitive options for the X control chart for a sample size n and a shift from the target mean. The average time to sign (ATS) of the current proposal lower than the values calculated from an individual X control chart points out that the combined control chart is an efficient tool in monitoring process mean.

Caracterização das perdas e distribuição de cobertura vegetal em colheita mecanizada de soja

O conceito de controle de qualidade nas operações inserido na agricultura é viabilizado por incidir diretamente nos principais objetivos do processo produtivo: retorno econômico e aumento da produtividade. A colheita mecanizada normalmente é realizada sem que haja controle efetivo para que a variabilidade das perdas fique dentro de padrões aceitáveis. Esta pesquisa teve o objetivo de determinar e caracterizar as perdas e a distribuição da cobertura vegetal após a colheita mecanizada da soja, por meio de ferramenta de controle estatístico de processo (cartas de controle). A média da perda de grãos total foi próxima do limite superior aceitável para a cultura da soja, apresentando alta variabilidade entre os pontos, tornando o processo fora de controle. A distribuição de cobertura vegetal manteve-se em processo controlado, com maior variabilidade onde o relevo foi mais inclinado. A utilização das cartas de controle foi eficiente na identificação dos pontos fora de controle e na avaliação da qualidade do processo de colheita.

Índice de capacidade do processo na avaliação da irrigação por aspersão

Analisar a qualidade da irrigação, além de avaliar seu bom funcionamento, é uma forma de verificar a viabilidade de sua implantação e operação. Como a uniformidade de distribuição é um dos parâmetros mais utilizados para essa avaliação, este trabalho objetivou utilizar técnicas de engenharia de qualidade, usando o índice de capacidade do processo (Cpl) para avaliar a uniformidade de distribuição de água em um sistema de irrigação por aspersão convencional. Os ensaios foram conduzidos no Núcleo Experimental de Engenharia Agrícola, UNIOESTE, com dois aspersores modelo Super10, marca NAANDAN, espaçados 9 m entre si, durante 25 irrigações de 1 h cada. Os dados climáticos foram coletados a cada 10 min, por uma estação meteorológica sem fio. Encontraram-se um CUC médio de 79,72% e velocidade do vento média de 1,85 m s-1. Foram aplicados os testes de controle de qualidade, elaborando os gráficos de controle de Shewhart e calculado o índice de capacidade do processo (Cpl), sendo que os resultados obtidos permitem afirmar que a utilização do índice de capacidade do processo torna-se uma ferramenta poderosa para classificar sistemas de irrigação em função de sua uniformidade de distribuição.

Gráficos adaptativos de controle por atributos e seu projeto na prática

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Planejamento do controle estatístico de processos com baixa fração não conforme restrito a amostras pequenas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Gráficos de controle de EWMA e de X-barra para monitoramento de processos autocorrelacionados

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

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)

O efeito da autocorrelação no planejamento das cartas de controle de x̄ e EWMA

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

An adaptive chart for monitoring the process mean and variance

Traditionally, an (X) over bar chart is used to control the process mean and an R chart is used to control the process variance. However, these charts are not sensitive to small changes in the process parameters. The adaptive ($) over bar and R charts might be considered if the aim is to detect small disturbances. Due to the statistical character of the joint (X) over bar and R charts with fixed or adaptive parameters, they are not reliable in identifing the nature of the disturbance, whether it is one that shifts the process mean, increases the process variance, or leads to a combination of both effects. In practice, the speed with which the control charts detect process changes may be more important than their ability in identifying the nature of the change. Under these circumstances, it seems to be advantageous to consider a single chart, based on only one statistic, to simultaneously monitor the process mean and variance. In this paper, we propose the adaptive non-central chi-square statistic chart. This new chart is more effective than the adaptive (X) over bar and R charts in detecting disturbances that shift the process mean, increase the process variance, or lead to a combination of both effects. Copyright (c) 2006 John Wiley & Sons, Ltd.

Monitoring the covariance matrix with the VMAX chart

In this article, we propose a new statistic to control the covariance matrix of bivariate processes. This new statistic is based on the sample vat-lances of the two quality characteristics, shortly 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 are faster detection of process changes and better diagnostic feature, that is, with the VMAX statistic It is easier to identify the out-of-control variable.

X̄ chart with variable sample size and sampling intervals

Recent theoretical studies have shown that the X̄ chart with variable sampling intervals (VSI) and the X̄ chart with variable sample size (VSS) are quicker than the traditional X̄ chart in detecting shifts in the process. This article considers the X̄ chart with variable sample size and sampling intervals (VSSI). It is assumed that the amount of time the process remains in control has exponential distribution. The properties of the VSSI X̄ chart are obtained using Markov chains. The VSSI X̄ chart is even quicker than the VSI or VSS X̄ charts in detecting moderate shifts in the process.

AATS for the X̄ Chart with Variable Parameters

A Fortran computer program is given for the computation of the adjusted average time to signal, or AATS, for adaptive X̄ charts with one, two, or all three design parameters variable: the sample size, n, the sampling interval, h, and the factor k used in determining the width of the action limits. The program calculates the threshold limit to switch the adaptive design parameters and also provides the in-control average time to signal, or ATS.

Economic design of a Vp X̄ chart

We develop an economic model for X̄ control charts having all design parameters varying in an adaptive way, that is, in real time considering current sample information. In the proposed model, each of the design parameters can assume two values as a function of the most recent process information. The cost function is derived and it provides a device for optimal selection of the design parameters. Through a numerical example one can foresee the savings that the developed model possibly provides. © 2001 Elsevier Science B.V. All rights reserved.

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.