Probabilistic information fusion with point, moment and interval data in reliability assessment

This study presents a general framework for probabilistic information fusion with point, moment, and interval data based on the principle of maximum relative entropy. Two types of interval information, namely, the independent interval and the correlated interval, are naturally incorporated in this framework for probability inference. The relative entropy is alternatively expressed using the hazard rate functions associated with the distributions. The probabilistic information fusion problem is recast into a hazard rate dynamics problem, which is solved using Euler-Lagrange method with point, moment, and interval data as boundary conditions. It provides a novel perspective on probabilistic information fusion such that the fusion mechanism is to seek an optimal hazard rate function in the functional space achieving the least action which is expressed as the relative information entropy. The geometry interpretation of the information fusion with point, moment, and interval data, and the effect of processing sequence are signified. An electronic component reliability problem is used to illustrate the basic idea of the method, followed by a fatigue reliability assessment problem demonstrating the overall method. The effectiveness of the method using limited samples and implicit interval information is emphasized using an aeroengine disk lifing application with a risk requirement in airworthiness.