Full-factorial designs consider all possible combinations of factor settings involved. However, as the number of factors increases, the number of experiments increases dramatically. In these cases, fractional factorial designs are used. The reduced number of runs associated with fractional factorials results in potential aliases among main effects and their interactions. To resolve this situation, fractional factorial designs are often augmented. This article presents an alternative way of augmenting resolution IV fractions using small sets of runs to decouple specific interactions in targeted alias chains. The new method is compared to its competitors, the complete foldover and the semi-fold.

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.

Recently, water has become a resource that generates controversy due to shortage alarms and high consumption by production companies. Making good use of water has become the main objective of government institutions. The food industry generates a large amount of wastewater, concentrating the largest number of contaminants originated in its processes. Wastewater from the food industry is characterized by having a large amount of organic matter, especially fats and oils, as well as suspended solids. The objective of this research is to carry out a characterization of effluents generated in a wastewater treatment plant in the food sector based on Mexican and international regulations to determine whether it is reusable. This article addresses Mexico’s lag in the reuse of treated wastewater in the face of the water crisis, highlighting the urgency of adopting these practices to mitigate water scarcity. For the development of this investigation, samples were collected at the discharge point produced by the company’s effluents, followed by an evaluation of their physical, chemical, and biological parameters, and finally, it was determined that the effluent follows the regulatory standards for discharge into the city sewer but outside the range for reuse in productive processes or irrigation of green areas.

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 $T^2$ chart, which validates our model.