  Industrial processes generate a massive amount of monitoring data that can be
exploited to uncover hidden time losses in the system, leading to enhanced
accuracy of maintenance policies and, consequently, increasing the
effectiveness of the equipment. In this work, we propose a method for one-step
probabilistic multivariate forecasting of time variables based on a Hidden
Markov Model with covariates (IO-HMM). These covariates account for the
correlation of the predicted variables with their past values and additional
process measurements by means of a discrete model and a continuous model. The
probabilities of the former are updated using Bayesian principles, while the
parameter estimates for the latter are recursively computed through an adaptive
algorithm that also admits a Bayesian interpretation. This approach permits the
integration of new samples into the estimation of unknown parameters,
computationally improving the efficiency of the process. We evaluate the
performance of the method using a real data set obtained from a company of a
particular sector; however, it is a versatile technique applicable to any other
data set. The results show a consistent improvement over a persistence model,
which assumes that future values are the same as current values, and more
importantly, over univariate versions of our model.
