Multivariate Statistical Process Control (MSPC) seeks to monitor several quality characteristics simultaneously. However, it has limitations derived from its inability to identify the source of special variation in the process. In this research, a proposed model that does not have this limitation is presented. In this paper, data from two scenarios were used: (A) data created by simulation and (B) random variable data obtained from the analysed product, which in this case corresponds to cheese production slicing process in the dairy industry. The model includes a dimensional reduction procedure based on the centrality and data dispersion. The goal is to recognise a multivariate pattern from the conjunction of univariate variables with variation patterns so that the model indicates the univariate patterns from the multivariate pattern. The model consists of two stages. The first stage is concerned with the identification process and uses Moving Windows (MWs) for data segmentation and pattern analysis. The second stage uses Bayesian Inference techniques such as conditional probabilities and Bayesian Networks. By using these techniques, the univariate variable that contributed to the pattern found in the multivariate variable is obtained. Furthermore, the model evaluates the probability of the patterns of the individual variables generating a specific pattern in the multivariate variable. This probability is interpreted as a signal of the performance of the process that allows to identify in the process a multivariate out-of-control state and the univariate variable that causes the failure. The efficiency results of the proposed model compared favourably with respect to the results obtained using the Hotelling’s T2 chart, which validates our model.
Mixed-level designs have a wide application in the fields of medicine, science, and agriculture, being very useful for experiments where there are both, quantitative, and qualitative factors. Traditional construction methods often make use of complex programing specialized software and powerful computer equipment. This article is focused on a subgroup of these designs in which none of the factor levels are multiples of each other, which we have called pure asymmetrical arrays. For this subgroup we present two algorithms of zero computational cost: the first with capacity to build fractions of a desired size; and the second, a strategy to increase these fractions with M additional new runs determined by the experimenter; this is an advantage over the folding methods presented in the literature in which at least half of the initial runs are required. In both algorithms, the constructed fractions are comparable to those showed in the literature as the best in terms of balance and orthogonality.
El diseño de experimentos es una herramienta utilizada para descubrir como entran en juego distintas variables de un proceso en la obtención de un producto. Existen dos enfoques principales para realizar experimentación, el enfoque clásico y el enfoque de Taguchi. Los diseños de Taguchi son diseños ortogonales que se especializan en estimar efectos principales e interacciones de control por ruido, dejando en segundo plano las interacciones de control por control. Los arreglos ortogonales de Taguchi fueron diseñados de tal manera que un arreglo especifico puede ser utilizado para diferentes números de factores, por ejemplo, el L32 se utiliza cuando existen de 16 a 31 factores y requiere de 32 experimentos. Cuando el número de columnas disponibles excede al número de factores que se desea investigar, las columnas sobrantes se utilizan comúnmente para estimar interacciones. Sin embargo, en casos en que el investigador esta solo interesado en los efectos principales, correr el arreglo completo podría ser algo innecesario y costoso. La presente investigación tiene como objetivo fraccionar los arreglos ortogonales de Taguchi L8, L12, L16 y L32 de tal forma que la fracción generada sirva únicamente para estimar efectos principales y las corridas restantes se agreguen solo en caso de ser requeridas. El método propuesto se basa en búsqueda exhaustiva y utiliza como criterios de selección la D-optimalidad, los factores de inflación de varianza (FIV) y el índice de balance general (IBG). Solo arreglos ortogonales de Taguchi de dos niveles fueron considerados para esta investigación. Los resultados de la investigación se traducen en ahorros significativos de recursos, reducción del tiempo de experimentación y del numero de corridas.
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