Abstract
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.
Highlights
The field of application of the model developed in this research is that of ControlCharts (CCs)
The first stage corresponds to the identification process, and the second stage refers to the process of attribution of patterns detected in the unified variable where frequencies and pattern association is achieved with the Bayesian Network
The first stage corresponds to the identification process and the second stage to the process of attribution of patterns detected in the Unified Multivariate Variable” (UMV)
Summary
The field of application of the model developed in this research is that of Control. Charts (CCs). The reasons for generating modifications to the Hotelling’s CCs are: (1) the limitation in its design since it can only detect out-of-control signals for the special pattern of “changes in the mean” when the process has lost stability due to non natural variation causes and, (2) its inability to detect the random variables that cause instability in the process and to identify the type of failure that occurs as discussed in [17] This means that there are no defined procedures for the interpretation of variation structures for MVPR. The random variables “p” that come from different measurement scales can be compared under the same scale, obtaining a way to compare these variations that originally have different magnitudes and units of measurement Another contribution is the use of Bayesian Networks to calculate the probabilities that a multivariate pattern with special variation presents and the probability that it comes from the presence of some pattern of some specific univariate variable.
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