A method of operating an industrial process or a machine, comprising obtaining operating data from an operating historian database, said operating data containing a plurality of variables collected from an industrial process or machine during operation, characterized by executing by non-real time calculation-intensive background processing on a computing system over a longer period of time, in preparation for a real-time analysis, steps of: - preparing statistical models based on the obtained operating data, each of the statistical models describing non-linear relations between two or more variables among said plurality of variables, one of said two or more variables being a dependent variable and the other one or more of said two or more variables being an explanatory variable selected among said plurality of variables to best explain a variation in the dependent variable according to a predetermined statistical criterion, preferably a relative entropy, - organizing a plurality of operating variables into a hierarchical network of said prepared statistical models according a predetermined statistical criterion, preferably a relative entropy, calculated for each of said prepared statistical models, in which hierarchical network the statistical models are connected to each other through said variables of said statistical models such that a dependent variable of a statistical model of a hierarchically lower level according to the calculated statistical criterion thereof, preferably a relative entropy, is connected to the corresponding explanatory variable of a statistical model of a hierarchically higher level according to the calculated statistical criterion thereof, preferably a relative entropy, and storing said hierarchical network of statistical models in a database or like, executing, by real-time processing (83, 87) on a computer system of an automation system controlling the industrial process or machine, in response to operator actions the online analysis including steps of: - receiving, via a graphical human-machine interface of the automation system, a selection of one of said plurality of variables as a variable of interest for real-time analysis, - automatically selecting, based on said stored hierarchical network of statistical models, among said plurality of variables at least one explanatory variable which is best to explain a variation in said variable of interest in terms of said statistical criterion, preferably a relative entropy, when said variable of interest is a dependent variable - calculating based on said stored hierarchical network of statistical models and displaying on said graphical human-machine interface dependence of a value of said variable of interest from a value of said at least one explanatory variable when said variable of interest is a dependent variable, and controlling, through said graphical human-machine interface, said dependent variable in the industrial process or machine by adjusting one or more of said at least one explanatory variable based on information obtained from said online analysis. - preparing statistical models based on the obtained operating data, each of the statistical models describing non-linear relations between two or more variables among said plurality of variables, one of said two or more variables being a dependent variable and the other one or more of said two or more variables being an explanatory variable selected among said plurality of variables to best explain a variation in the dependent variable according to a predetermined statistical criterion, preferably a relative entropy, - organizing a plurality of operating variables into a hierarchical network of said prepared statistical models according a predetermined statistical criterion, preferably a relative entropy, calculated for each of said prepared statistical models, in which hierarchical network the statistical models are connected to each other through said variables of said statistical models such that a dependent variable of a statistical model of a hierarchically lower level according to the calculated statistical criterion thereof, preferably a relative entropy, is connected to the corresponding explanatory variable of a statistical model of a hierarchically higher level according to the calculated statistical criterion thereof, preferably a relative entropy, and storing said hierarchical network of statistical models in a database or like, - receiving, via a graphical human-machine interface of the automation system, a selection of one of said plurality of variables as a variable of interest for real-time analysis, - automatically selecting, based on said stored hierarchical network of statistical models, among said plurality of variables at least one explanatory variable which is best to explain a variation in said variable of interest in terms of said statistical criterion, preferably a relative entropy, when said variable of interest is a dependent variable - calculating based on said stored hierarchical network of statistical models and displaying on said graphical human-machine interface dependence of a value of said variable of interest from a value of said at least one explanatory variable when said variable of interest is a dependent variable, and