Control de Variables Asociadas con la Calidad en el Proceso de Corrugado Mediante el Uso de Gráficos de Control Multivariante

El propósito de esta investigación es estudiar el proceso de producción de cartón corrugado en la empresa Productora Cartonera S. A. (PROCARSA). Para ello se evaluó el comportamiento de las variables de calidad resistencia al aplastamiento de borde (ECT) y Separación de espiga (PAT). Posterior al análisis descriptivo, a cada variable de calidad se le ajustó un diseño factorial, considerando como factores a evaluar Operador, Flauta, Liner (Papel externo del cartón) y Empaque. Se determinó que estos factores influyen de manera significativa sobre las variables de calidad. Para el caso de la variable ECT, todos los componentes del modelo resultan significativos, mientras que para la variable PAT, solo resultan significativos los efectos principales, algunas interacciones de orden dos y la interacción de orden cuatro. Se evaluó la correlación entre las variables de calidad, resultado estadísticamente significativa, lo que llevó a descartar el uso de gráficos de control univariantes para monitorear el proceso. Luego, se construyó un gráfico de control multivariante para determinar si el proceso está trabajando bajo control. En la fase 1 se presentó una señal fuera de control. Finalmente, se eliminó el punto fuera de control y se obtuvieron los límites finales de control. Estos límites se usarán en adelante para evaluar y monitorear el proceso. Palabra clave: Control, Multivariante, Hotelling, Calidad. Abstract The purpose of this research is to study the corrugated cardboard production process in the company Producer Carton S.A, PROCARSA. For this, the behavior of the quality variables resistance to edge crushing (ECT) and separation of dowel (PAT) was evaluated. After the descriptive analysis, a factorial design was adjusted to each quality variable, considering Operator, Flute, Liner, and Packaging as factors to be evaluated. It was determined that these factors have a significant influence on the quality variables. For the case of the ECT variable, all the components of the model are significant, while for the PAT variable, only the main effects, some interactions of order two, and the interaction of order four are significant. The correlation between the quality variables was evaluated, the result statistically significant, which led to discarding the use of univariate control charts to monitor the process. Then, a multivariate control chart was constructed to determine if the process is working under control. In phase 1 there was a signal out of control. Finally, the out-of-control point was eliminated and the final limits of control were obtained. These limits will be used from now on to evaluate and monitor the process. Keywords: Control, Multivariate, Hotelling, Quality.

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On multivariate control charts

Production ◽

10.1590/s0103-65132011005000010 ◽

2011 ◽

Vol 21 (2) ◽

pp. 235-241 ◽

Cited By ~ 8

Author(s):

Marianne Frisén

Keyword(s):

Control Chart ◽

Industrial Production ◽

Control Charts ◽

Multivariate Control Charts ◽

Multivariate Control Chart ◽

Multivariate Control

Industrial production requires multivariate control charts to enable monitoring of several components. Recently there has been an increased interest also in other areas such as detection of bioterrorism, spatial surveillance and transaction strategies in finance. In the literature, several types of multivariate counterparts to the univariate Shewhart, EWMA and CUSUM methods have been proposed. We review general approaches to multivariate control chart. Suggestions are made on the special challenges of evaluating multivariate surveillance methods.

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Comparison of short runs control chart and T2 Hotelling control chart for monitoring sunergy glass production process

Journal of Physics Conference Series ◽

10.1088/1742-6596/2106/1/012019 ◽

2021 ◽

Vol 2106 (1) ◽

pp. 012019

Author(s):

M Qori’atunnadyah ◽

Wibawati ◽

W M Udiatami ◽

M Ahsan ◽

H Khusna

Keyword(s):

Production Process ◽

Control Chart ◽

Mass Production ◽

Control Charts ◽

Manufacturing Industry ◽

Average Run Length ◽

Glass Production ◽

Short Run ◽

Multivariate Control Chart ◽

Multivariate Control

Abstract In recent years, the manufacturing industry has tended to reduce mass production and produce in small quantities, which is called “Short Run Production”. In such a situation, the course of the production process is short, usually, the number of productions is less than 50. Therefore, a control chart for the short run production process is required. This paper discusses the comparison between multivariate control chart for short run production (V control chart) and T2 Hotelling control chart applied to sunergy glass data. Furthermore, a simulation of Average Run Length (ARL) was carried out to determine the performance of the two control charts. The results obtained are that the production process has not been statistically controlled using either the V control chart or the T2 Hotelling control chart. The number of out-of-control on the control chart V using the the EWMA test is more than the T2 Hotelling control chart. Based on the ARL value, it shows that the V control chart is more sensitive than the T2 Hotelling control chart.

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NDA Based Hierarchical Classification Scheme for Identifying the Contributors to a Multivariate Control Chart

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.467-469.427 ◽

2011 ◽

Vol 467-469 ◽

pp. 427-432

Author(s):

H.Y. Huang ◽

Jong Chih Chien

Keyword(s):

Control Charts ◽

Classification Scheme ◽

Hierarchical Classification ◽

Property A ◽

Multivariate Control Charts ◽

Related Quality ◽

Control Event ◽

Multivariate Control Chart ◽

Multivariate Control ◽

Interpretation Problem

Many multivariate control charts have been proposed for monitoring several related quality characteristics simultaneously. However, even when an out-of-control signal is detected, the employed multivariate control charts generally do not provide any interpretable information associated with that signal. That is, the contributors of the out-of-control event can not be identified by the charts. Hence, how to tackle this interpretation problem effectively is an important issue in multivariate process control. One rarely addressed but very crucial property of this interpretation problem is that the number of possible outcomes can be very large. According to this key property, a nonparametric discriminant analysis (NDA)-based hierarchical classification scheme is proposed in this paper. A simulation experiment including several popular classification methods was conducted for evaluating the performance of the proposed method. The result shows that our proposed scheme is very competitive when measured against these popular methods.

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Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso

Quality Innovation Prosperity ◽

10.12776/qip.v25i1.1552 ◽

2021 ◽

Vol 25 (1) ◽

pp. 3-15

Author(s):

Takumi Saruhashi ◽

Masato Ohkubo ◽

Yasushi Nagata

Keyword(s):

Covariance Matrix ◽

Likelihood Ratio ◽

Control Chart ◽

Control Charts ◽

Ewma Chart ◽

Regularization Parameters ◽

Multivariate Control Chart ◽

Multivariate Control ◽

Mean Vector ◽

Variance Covariance Matrix

Purpose: When applying exponentially weighted moving average (EWMA) multivariate control charts to multivariate statistical process control, in many cases, only some elements of the controlled parameters change. In such situations, control charts applying Lasso are useful. This study proposes a novel multivariate control chart that assumes that only a few elements of the controlled parameters change. Methodology/Approach: We applied Lasso to the conventional likelihood ratio-based EWMA chart; specifically, we considered a multivariate control chart based on a log-likelihood ratio with sparse estimators of the mean vector and variance-covariance matrix. Findings: The results show that 1) it is possible to identify which elements have changed by confirming each sparse estimated parameter, and 2) the proposed procedure outperforms the conventional likelihood ratio-based EWMA chart regardless of the number of parameter elements that change. Research Limitation/Implication: We perform sparse estimation under the assumption that the regularization parameters are known. However, the regularization parameters are often unknown in real life; therefore, it is necessary to discuss how to determine them. Originality/Value of paper: The study provides a natural extension of the conventional likelihood ratio-based EWMA chart to improve interpretability and detection accuracy. Our procedure is expected to solve challenges created by changes in a few elements of the population mean vector and population variance-covariance matrix.

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Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection

Mathematics ◽

10.3390/math9212772 ◽

2021 ◽

Vol 9 (21) ◽

pp. 2772

Author(s):

Ishaq Adeyanju Raji ◽

Nasir Abbas ◽

Mu’azu Ramat Abujiya ◽

Muhammad Riaz

Keyword(s):

Control Chart ◽

Control Charts ◽

Real Life ◽

Robust Estimator ◽

Estimation Of Parameters ◽

Run Length ◽

Control Charting ◽

Shewhart Control ◽

Multivariate Control Chart ◽

Multivariate Control

While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho robust estimator (SDRE), whilst the process parameters are estimated from phase-I. Through intensive Monte-Carlo simulation, the study presents how the estimation of parameters and presence of outliers affect the efficacy of the Hotelling T2 chart, and then how the proposed outlier detector brings the chart back to normalcy by restoring its efficacy and sensitivity. Run-length properties are used as the performance measures. The run length properties establish the superiority of the proposed scheme over the default multivariate Shewhart control charting scheme. The applicability of the study includes but is not limited to manufacturing and health industries. The study concludes with a real-life application of the proposed chart on a dataset extracted from the manufacturing process of carbon fiber tubes.

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Propuesta de Carta de Control Multivariada utilizando la Media Winsorizada basada en la Carta |S| / Proposed Multivariate Control Chart using Winsorized Mean based on the |S| Chart

Revista Ingeniería ◽

10.15517/ri.v29i1.34379 ◽

2018 ◽

Vol 29 (1) ◽

pp. 65-79

Author(s):

Rister Junior Barreto Pombo ◽

Angellys Paola Ariza Guerrero ◽

Roberto José Herrera Acosta

Keyword(s):

Covariance Matrix ◽

Control Chart ◽

Control Charts ◽

Quality Monitoring ◽

Multivariate Control Charts ◽

Global Quality ◽

Simultaneous Evaluation ◽

Multivariate Control Chart ◽

Implementation Methodology ◽

Multivariate Control

Resumen— El monitoreo global de la calidad de un producto está sujeto a la evaluación simultánea de varias de sus características; es necesario bajo estas condiciones la implementación de las cartas de control tipo multivariadas. La variabilidad, en este caso la matriz de varianza covarianza, es sin duda el más importante de los estadísticos desde la perspectiva multivariada, que puede ser monitoreada con distintas cartas. Entre éstas se encuentran: las cartas Shewhart, CUSUM y EWMA. En este artículo se desarrolla una metodología de implementación de la Media Winsorizada en la carta de control multivariada de varianza efectiva |S|, encontrando una gran utilidad en procesos con valores extremos. El estudio muestra además una comparación entre la carta de control tradicional multivariante y la carta propuesta, que muestra mayor sensibilidad.Abstract— The global quality monitoring of a product is often subject to the simultaneous evaluation of several of its features; under these circumstances it is necessary to implement multivariate control charts. Variability, in this particular case, the variance-covariance matrix is indisputably the most important of the statistics from the multivariate perspective and it can be monitored with different charts, among these: Shewhart, CUSUM and EWMA. This article develops the Winsorized Mean in the effective variance multivariate control |S|-chart implementation methodology and it was demonstrated that the modification was more efficient when the sample hat outliers. This study shows a comparison between the traditional multivariate control chart and a proposed chart which was found to have more sensitivity.

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Use of multivariate control charts to assess the status of reef fish assemblages in the Northwestern Hawaiian Islands

PeerJ ◽

10.7717/peerj.3651 ◽

2017 ◽

Vol 5 ◽

pp. e3651 ◽

Cited By ~ 2

Author(s):

Atsuko Fukunaga ◽

Randall K. Kosaki

Keyword(s):

Reef Fish ◽

Control Charts ◽

Fish Assemblages ◽

Confidence Bounds ◽

Multivariate Control Charts ◽

National Monument ◽

Northwestern Hawaiian Islands ◽

The Status ◽

Multivariate Control Chart ◽

Multivariate Control

A distance-based multivariate control chart is a useful tool for ecological monitoring to detect changes in biological community resulting from natural or anthropogenic disturbances at permanent monitoring sites. It is based on a matrix of any distances or dissimilarities among observations obtained from species composition and abundance data, and bootstrapping techniques are used to set upper confidence bounds that trigger an alarm for further investigations. We extended the use of multivariate control charts to stratified random sampling and analyzed reef fish monitoring data collected annually on shallow (≤30 m) reefs across the Northwestern Hawaiian Islands (NWHI), part of the Papahānaumokuākea Marine National Monument. Fish assemblages in the NWHI were mostly stable, with exceptions in the south region (Nihoa, Mokumanamana and French Frigate Shoals) in 2012 and 2015 where changes in the assemblage structure exceeded the upper confidence bounds of multivariate control charts. However, these were due to changes in relative abundances of native species, and potentially related to the small numbers of survey sites and relatively low coral covers at the sites, particularly in 2015. The present study showed that multivariate control charts can be used to evaluate the status of biological communities in a very large protected area. Future monitoring of fish assemblages in the Papahānaumokuākea Marine National Monument should be accompanied by specific habitat or environmental variables that are related to potential threats to its shallow-water ecosystems. This should allow for more detailed investigations into potential causes and mechanisms of changes in fish assemblages when a multivariate control chart triggers an alarm.

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Multivariate Control Chart and Lee–Carter Models to Study Mortality Changes

Mathematics ◽

10.3390/math8112093 ◽

2020 ◽

Vol 8 (11) ◽

pp. 2093

Author(s):

Gisou Díaz-Rojo ◽

Ana Debón ◽

Jaime Mosquera

Keyword(s):

Control Chart ◽

Control Charts ◽

Causes Of Death ◽

Mortality Model ◽

Probability Of Death ◽

Multivariate Control Chart ◽

Model Residuals ◽

Multivariate Control ◽

Carter Model

The mortality structure of a population usually reflects the economic and social development of the country. The purpose of this study was to identify moments in time and age intervals at which the observed probability of death is substantially different from the pattern of mortality for a studied period. Therefore, a mortality model was fitted to decompose the historical pattern of mortality. The model residuals were monitored by the T2 multivariate control chart to detect substantial changes in mortality that were not identified by the model. The abridged life tables for Colombia in the period 1973–2005 were used as a case study. The Lee–Carter model collects information regarding violence in Colombia. Therefore, the years identified as out-of-control in the charts are associated with very early or quite advanced ages of death and are inversely related to the violence that did not claim as many victims at those ages. The mortality changes identified in the control charts pertain to changes in the population’s health conditions or new causes of death such as COVID-19 in the coming years. The proposed methodology is generalizable to other countries, especially developing countries.

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