Framework for monitoring process control with finite mixture distribution: Application in company of alimentary sector

Purpose. The main objective of this study is develop an application with finite mixture of probability distributions control charts, we selected a process of a company in the food sector, whose products consist of dough with wheat .based.

Design/methodology/approach. This article has an approach of the case study in company of alimentary sector with the following steps: i) to collect the master sample from different production batches; ii) with graphical methods verifying the quantity and the characterization of the number of mixing probability distributions in production batch; iii) to adjust the theoretical model of probability distribution of each subpopulation in production batch; iv) statistical model considering the mixture distribution of probability and assuming that the statistical parameters are unknown; v) with numerical methods finding the constant statistical K that results in a type I average error α = 0.27% when the process is under control. This study was applied to a food industry in which π subpopulations were identified to find the finite probability distributions, and, for after, we have been finding the K constant by type I error of 0,27%.
Findings. This search results in a complex graphic because it involves more parameters to be considered in its calculation. Nevertheless, it can help the practitioners to monitor on a single graph multiple streams of the production process with similar efficiency to the traditional control chart.
Originality/value. This article is contributing with a statistical graphic design for monitoring production
batches from different machines, processes or flows. Customers have applied this graphic design when they continuously receive product batches from a supplier and they need to monitor statistically the critical quality characteristics of the product. There is another practical situation that can affect the performance of control charts and it has only few studies about it.

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Mixture distributions, Control chart, Quality Management, Alimentary sector