Alias structures for two-level fractional designs are commonly used to describe the correlations between different terms. The concept of alias structures can be extended to other types of designs such as fractional mixed-level designs. This paper proposes an algorithm that uses the Pearson’s correlation coefficient and the correlation matrix to construct alias structures for these designs, which can help experimenters to more easily visualize which terms are correlated (or confounded) in the mixed-level fraction and constitute the basis for efficient sequential experimentation.

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.

Variability in manufacturing processes must be properly monitored and controlled to avoid incurring quality problems; otherwise, the probability of manufacturing defective products increases, and, consequently, production costs rise. This paper presents the development of a methodology to locate the source(s) of variation in the manufacturing process in case of a statistical deviation so that the user can quickly take corrective actions to eliminate the source of variation, thus avoiding the manufacture of out-of-specification products. The methodology integrates the multivariate cumulative sum control chart and the multilayer perceptron artificial neural network for the detection and interpretation of the source(s) of variation generated in the manufacturing processes. A case study was carried out with a printed circuit board manufacturing process, and it was possible to classify the origin of the variation with a sensitivity of 92.41% and specificity of 91.16%. The results demonstrate the viability of the proposed methodology to monitor and interpret the source of statistical variation present in production systems.

El presente estudio, aborda el problema del control de tolerancias cuando se va a fabricar una pieza de ensamble. Para este caso se escogió un borne eléctrico, conformado por un agujero y un eje de ajuste con juego; donde pequeñas variaciones dimensionales pueden afectar el correcto ensamblaje y funcionamiento del conjunto de la pieza. El objetivo principal consiste en determinar una combinación óptima de tolerancias que garantice el ensamblaje funcional de la pieza y minimice los rechazos de fabricación. Para lograrlo se utilizó el Método de Simulación Monte Carlo, mediante la herramienta de Microsoft Excel junto con la herramienta Solver que permitió analizar el impacto de la variación dimensional en una cota funcional crítica. La metodología está conformada de cinco pasos que detallan el procedimiento para la identificación del sistema complejo, las variables elegidas y el espacio de muestreo, así como, un diagrama de Pareto que muestra de manera clara y objetiva la solución al caso planteado. Se logro detectar las pequeñas variaciones dimensionales que comprometen la funcionalidad del ensamble entre eje y agujero, mediante la generación de números aleatorios. Los hallazgos encontrados contribuyen en mayor medida a la variabilidad del resultado, permitiendo proponer ajustes en las tolerancias con base en un análisis de sensibilidad tipo Pareto.