Qualitative trend analysis for process monitoring and supervision based on likelihood optimization: State-of-the-art and current limitations

In this study, two recently developed methods for qualitative trend analysis are applied and compared on the basis of two different data sets. One of the methods is globally optimal in the maximum likelihood sense but is computationally expensive. This method is based on shape constrained spline function. The second method is based on kernel regression and a Hidden Markov Model. This is more efficient but cannot be guaranteed to be optimal. Nevertheless, both methods deliver satisfying results with respect to the estimation of the location of inflection points as well as the corresponding tangent slopes. In contrast, only the globally optimal method appears useful to identify time series which do not satisfy a presupposed shape.