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Describes a simple algorithm which has been developed for determining exact moments of top event failure probability from the moments of the basic events in a fault tree. This method requires neither Taylor series expansion of top event failure probability function nor its partial derivates to find these moments. This method has subsequently extended to systems with multistate components. Describes a general algorithm for the purpose. Provides several illustrations to highlight its usefulness.

A faulty gear affects the functionality of the machine. Thus, it is necessary to diagnose the faults at an initial stage so as to reduce the losses incurred. Vibration signals contain dynamic information about the health condition of a rotating machine. Many researches are based on FFT and have its own drawback with non-stationary signals like the ones from gears. Hence, there is a need for development of new methodologies to infer diagnostic information from such signals. The vibrations produced by gears from good and simulated faulty conditions can be used to detect the faults in these gears. In the present study, variational mode decomposition (VMD) was used as a new signal pre-processing technique along with decision trees which have provided good classification performance. The technique decomposes the signals into various modes by identifying a compact frequency support around its central frequency, such that adding all the modes reconstructs the original signal. Descriptive statistical features were extracted from VMD processed signals. J48 decision tree algorithm was used to identify the useful features and the selected features were classified using the decision trees namely, J48, random tree and decision stump algorithm. The performance analyses of various algorithms are discussed in detail.