Geometry on degradation models and mis-specification analysis by using [formula omitted]-divergence

Abstract

Information geometry has been productively used in different research fields involving machine learning, neural networks, optimization and statistics. It also applied in reliability analysis where time-to-failure data are available for study. For highly reliable products, however, it is difficult to obtain failure data in a reasonable time period. Degradation modeling and data analysis are effective tools to deal with the situation that no or very few failures are observed in a life testing experiment. In this paper, we investigate the geometry on the statistical manifold induced by a degradation model. Both the linear and non-linear degradation models are discussed in details, where the random parameter is distributed according to a Tsallis’s distribution. After the statistical manifold is constructed, the Amari–Chentsov structure on the manifold is discussed. The model mis-specification analysis is discussed by using the α-divergence as a measure of the difference between the true model and suggested models. The effects of model mis-specification are studied by considering the relative bias and relative variability. Finally, using a laser degradation dataset as an example, the numerical results of parameter estimation and simulation studies of the model mis-specification analysis are reported.