An Influence Gauge to Detect and Explain Relations between Measurements and a Performance Indicator

Abstract


 
 
 What about a software tool that behaves like a gauge able to estimate the quantity of information contained in a group of measurements? Then if we have a performance indicator or a defect rate, how may we compute the maximum performance explanation contained in our dataset? The first question may be answered by entropy and the second with mutual information. The present paper recalls a simple way to use those mathematical tools in an application one wants to launch each time a new dataset has to be studied. Often the PHM team in Snecma is asked to participate in special workforces to analyze sudden crisis. This methodology helps at the very beginning of the process to identify our mathematical capability to build an explanation model. This was the case during a small engine start crisis when some spark plugs were not working. Another time we used this tool to identify the flying condition when a gearbox was heating. This methodology was first developed for industry purposes like the optimization of machine tools or process recipes. Its success is in the simplifications of the computations that enlighten the interpretability of the results. Each signal is quantified in a way that improves the mutual information with the performance indicator. This is done signal by signal, but also for any small subsets of multivariate measurements until the confidence given by the quantity and quality of the data reaches its maximum. The segmentation of the data helps and boosts the computation of the integrals. Moreover, as this methodology uses quantified data as inputs it works as well with any sort of inputs such as continuous, discrete ordered and even categorized measurements. Once a best subset of measurements is selected a simple non-linear model is built using a relaxation algorithm. This model is a set of hypercubes that classifies the input space in a very simple and interpretable way. The methodology given below is a rough approach and may be replaced by more efficient regression algorithms if one only have continuous measurements but it has some advantages like a way to search a “best rule” according to some constraints and a graphic navigation tool very efficient to correct recipes.