multivariate control chart
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PurposeThis study aims to design a multivariate control chart that improves the applicability of the traditional Hotelling T2 chart. This new type of multivariate control chart displays sufficient information about the states and relationships of the variables in the production process. It is used to make better quality control decisions during the production process.Design/methodology/approachMultivariate data are collected at an equal time interval and are represented by nodes of the graph. The edges connecting the nodes represent the sequence of operation. Each node is plotted on the control chart based on their Hotelling T2 statistical distance. The changing behavior of each pair of input and output nodes is studied by the neural network. A case study from the cement industry is conducted to validate the control chart.FindingsThe finding of this paper is that the points and lines in the classic Hotelling T2 chart are effectively substituted by nodes and edges of the graph respectively. Nodes and edges have dimension and color and represent several attributes. As a result, this control chart displays much more information than the traditional Hotelling T2 control chart. The pattern of the plot represents whether the process is normal or not. The effect of the sequence of operation is visible in the control chart. The frequency of the happening of nodes is recognized by the size of nodes. The decision to change the product feature is assisted by finding the shortest path between nodes. Moreover, consecutive nodes have different behaviors, and that behavior change is recognized by neural network.Originality/valueModifying the classical Hotelling T2 control chart by integrating with the concept of graph theory and neural network is new of its kind.

A potential eco-friendly method without organic solvents is presented by integrating a chromatographic fingerprint and multivariate control chart based on Q residuals to differentiate grape juices from different farming practices. The sample preparation was only water dilution, and the mobile phase was water acidified with sulfuric acid, which can be readily neutralized before its disposal. The proposed method is shown to be a simple way to distinguish between organic and non-organic grape juices in a non-target way, successfully evaluating an external validation data set, where organic and non-organic samples were correctly assigned. Through the chromatographic profile, it is possible to suggest that one of the species responsible for this distinction may be from the anthocyanins class.

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.

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.

     A multivariate control chart is measured by many variables that are correlated in production, using the quality characteristics in any product. In this paper, statistical procedures were employed to find the multivariate quality control chart by utilizing fuzzy Hotelling  test. The procedure utilizes the triangular membership function to treat the real data, which were collected from Baghdad Soft Drinks Company in Iraq. The quality of production was evaluated by using a new method of the ranking function.

  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.