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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.