Preliminary results concerning the VSS X- chart with unknow in-control parameters

The VSS X- chart is known to perform better than the traditional X- control chart in detecting small to moderate mean shifts in the process. Many researchers have used this chart in order to detect a process mean shift under the assumption of known parameters. However, in practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. In this paper, we evaluate the (run length) performances of the VSS X- control chart when the process parameters are estimated and we compare them in the case where the process parameters are assumed known. We draw the conclusion that these performances are quite different when the shift and the number of samples used during the phase I are small. ©2010 IEEE.

Gráficos de controle de Shewhart: Duas década de pesquisa

Esta tese apresenta, de forma compacta, os trabalhos mais importantes do autor, que são frutos de uma pesquisa de vinte anos sobre gráficos de Shewhart. O autor estudou os modelos que descrevem o tipo e o instante de ocorrência das causas especiais, propôs novos esquemas de amostragens e estatísticas de monitoramento. Mais recentemente, vem avaliando a capacidade dos gráficos de controle em sinalizar causas especiais quando as observações são autocorrelacionadas e propondo novas estatísticas para o monitoramento de processos mutivariados.

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Bivariate control charts with double sampling

In this article, we consider the T(2) chart with double sampling to control bivariate processes (BDS chart). During the first stage of the sampling, n(1) items of the sample are inspected and two quality characteristics (x; y) are measured. If the Hotelling statistic T(1)(2) for the mean vector of (x; y) is less than w, the sampling is interrupted. If the Hotelling statistic T(1)(2) is greater than CL(1), where CL(1) > w, the control chart signals an out-of-control condition. If w < T(1)(2) <= CL(1), the sampling goes on to the second stage, where the remaining n(2) items of the sample are inspected and T(2)(2) for the mean vector of the whole sample is computed. During the second stage of the sampling, the control chart signals an out-of-control condition when the statistic T(2)(2) is larger than CL(2). A comparative study shows that the BDS chart detects process disturbances faster than the standard bivariate T(2) chart and the adaptive bivariate T(2) charts with variable sample size and/or variable sampling interval.

Monitoring a wandering mean with an np chart

Este artigo considera um gráfico np x proposto por Wu et al. (2009) para controle de média de processo como uma alternativa ao uso do gráfico de. O que distingue do gráfico de controle np x é o fato das unidades amostrais serem classificadas como unidades de primeiro ou de segunda classe de acordo com seus limites discriminantes. O gráfico tradicional np é um caso particular do gráfico np x quando os limites discriminantes coincidem com os limites de especificação e unidade de primeira (segunda) classe é um item conforme (não conforme). Estendendo o trabalho de Reynolds Junior, Arnold e Baik (1996), consideramos que a média de processo oscila mesmo na ausência de alguma causa especial. As propriedades de Cadeia de Markov foram adotadas para avaliar o desempenho do gráfico np x no monitoramento de média de processos que oscila. de modo geral, o gráfico np x requer amostras duas vezes maior para superar desempenho do gráfico (enquanto que o gráfico tradicional np necessita tamanho de amostras cinco ou seis vezes maior).

Monitoring process mean and variability with one non-central chi-square chart

Traditionally, an (X) over bar -chart is used to control the process mean and an R-chart to control the process variance. However, these charts are not sensitive to small changes in process parameters. A good alternative to these charts is the exponentially weighted moving average (EWMA) control chart for controlling the process mean and variability, which is very effective in detecting small process disturbances. In this paper, we propose a single chart that is based on the non-central chi-square statistic, which is more effective than the joint (X) over bar and R charts in detecting assignable cause(s) that change the process mean and/or increase variability. It is also shown that the EWMA control chart based on a non-central chi-square statistic is more effective in detecting both increases and decreases in mean and/or variability.

The Variable Sample Size (X)over-bar Chart with Estimated Parameters

The VSS X chart, dedicated to the detection of small to moderate mean shifts in the process, has been investigated by several researchers under the assumption of known process parameters. In practice, the process parameters are rarely known and are usually estimated from an in-control Phase I data set. In this paper, we evaluate the (run length) performances of the VSS chart when the process parameters are estimated, we compare them in the case where the process parameters are assumed known and we propose specific optimal control chart parameters taking the number of Phase I samples into account.

Synthetic control charts with two-stage sampling for monitoring bivariate processes

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control bivariate processes. During the first stage, one item of the sample is inspected and two correlated quality characteristics (x;y) are measured. If the Hotelling statistic T1 2 for these individual observations of (x;y) is lower than a specified value UCL 1 the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the Hotelling statistic T2 2 for the sample means of (x;y) is computed. When the statistic T2 2 is larger than a specified value UCL2, the sample is classified as nonconforming. According to the synthetic control chart procedure, the signal is based on the number of conforming samples between two neighbor nonconforming samples. The proposed chart detects process disturbances faster than the bivariate charts with variable sample size and it is from the practical viewpoint more convenient to administer.

Gráficos de X com esquemas especiais de amostragem para o controle de médias que oscilam ou para o controle de processos que geram observações autocorrelacionadas

Pós-graduação em Engenharia Mecânica - FEG

Statistical methods for assessing agreement between double readings of clinical measurements

Statistical analysis of data is crucial in cephalometric investigations. There are certainly excellent examples of good statistical practice in the field, but some articles published worldwide have carried out inappropriate analyses. Objective: The purpose of this study was to show that when the double records of each patient are traced on the same occasion, a control chart for differences between readings needs to be drawn, and limits of agreement and coefficients of repeatability must be calculated. Material and methods: Data from a well-known paper in Orthodontics were used for showing common statistical practices in cephalometric investigations and for proposing a new technique of analysis. Results: A scatter plot of the two radiograph readings and the two model readings with the respective regression lines are shown. Also, a control chart for the mean of the differences between radiograph readings was obtained and a coefficient of repeatability was calculated. Conclusions: A standard error assuming that mean differences are zero, which is referred to in Orthodontics and Facial Orthopedics as the Dahlberg error, can be calculated only for estimating precision if accuracy is already proven. When double readings are collected, limits of agreement and coefficients of repeatability must be calculated. A graph with differences of readings should be presented and outliers discussed.

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)