Geometry on the statistical manifold induced by the degradation model with soft failure data

摘要

Information geometry discusses the properties of a statistical manifold and is useful for different fields involving neural networks, signal processing, machine learning, optimization and statistics. The methods of information geometry are also employed to discuss the geometry on a statistical manifold induced by the reliability model and lifetime testing, where the time-to-failure data are available for analyzing. For highly reliable products, however, it is difficult to obtain failure data in a reasonable period of time. For some products there is a gradual loss of performance, then it is possible to derive degradation measurements over times. This paper investigates the geometry on a statistical manifold induced by the degradation model with few or no failure data. The statistical manifold is constructed based on the degradation model. The Fisher information metric, Amari-Chentsov structure, affine connection and a-connection on the manifold are discussed. Taking the linear model as an example, the main results are illustrated, where we find that the geometry quantities are closely related to the degradation threshold value, parameters of the model and the Euler's constant. The parameters are estimated by using the multi-step estimation method, and numerical results are reported. (C) 2019 Elsevier B.V. All rights reserved.