In the field of Statistical Process Control (SPC) there are several different approaches to deal with monitoring of batch processes. Such processes present a three-way data structure (batches × variables × time-instants), so that for each batch a multivariate time series is available. Traditional approaches do not take into account the time series nature of the data. They deal with this kind of data by applying multivariate techniques in a reduced two-way data structure, in order to capture variables dynamics in some way. Recent developments in SPC have proposed the use of the Vector Autoregressive (VAR) time series model considering the original three-way structure. However, they are restricted to control approaches focused on VAR residuals. This paper proposes a new approach to deal with batch processes using the VAR model, but focusing on coefficients instead of residuals. Through a simulated batch process, we illustrate the better performance of our approach over the residual-based control charts in both offline and online context.

Information is a central notion for cognitive sciences and neurosciences, but there is no agreement on what it means for a cognitive system to acquire information about its surroundings. In this paper, we approximate three influential views on information: the one at play in ecological psychology, which is sometimes called information for action; the notion of information as covariance as developed by some enactivists, and the idea of information as minimization of uncertainty as presented by Shannon. Our main thesis is that information for action can be construed as covariant information, and that learning to perceive covariant information is a matter of minimizing uncertainty through skilled performance. We argue that the agent’s cognitive system conveys information for acting in an environment by minimizing uncertainty about how to achieve her intended goals in that environment. We conclude by reviewing empirical findings that support our view and by showing how direct learning, seen as instance of ecological rationality at work, is how mere possibilities for action are turned into embodied know-how. Finally, we indicate the affinity between direct learning and sense-making activity.