Modelos ocultos de Markov: uma abordagem em controle de processos

Abstract

The hidden Markov model methodology is being widely used in all fields of knowledge these days. With its strong mathematical structure, this methodology is able to model several problems because it is very malleable and unrestricted, a fact that does not occur in the Markov chain methodology. This methodology can be seen as an extension of the Markov chain, since it can contain more than one Markov chain. Problems for monitoring control charts and online control can be modeled via the Markov chain, since the sampling interval is regular and the condition of the process to be Markovian is generally assumed. Dorea et al. (2012) assumed the existence of an unobservable internal system so that monitoring by online control is only part of the process. Based on this assumption, one can model this process via the hidden Markov model, since the process comprises two Markov chains (one observable and one non-observable). This work will present the methodology of the hidden Markov model and then apply the methodology in the planning of online statistical control in order to establish an estimate for the false alarm and non-detection probabilities.