Information geometry has been attracting considerable attention in different scientific fields including information theory, neural networks, machine learning, and statistical physics. In reliability and survival analysis, methods of information geometry are employed to discuss the geometry on a reliability model. Most of the existing work of information geometry in reliability analysis focused on time-to-failure data. For highly reliable devices, it is difficult to obtain failure data in a reasonable period of time, and hence degradation measurements are used to extrapolate the failure time. In this paper, we investigate the geometry on a statistical manifold induced by the Wiener degradation process with nonlinear drift and diffusion coefficients, where the drift parameter is assumed to be a random variable to incorporate the unit-to-unit characteristics. The Fisher information metric, Amari–Chentsov tensor and $\alpha$-connection on the manifold for the degradation model are discussed. As an application in the design of engineering experiments, the information metric is employed to develop the optimal design of degradation experiments under a cost constraint. Monte Carlo simulation and a numerical study are used to illustrate the methodologies developed in this paper.

信息几何已经在包括信息论，神经网络，机器学习和统计物理学在内的不同科学领域中引起了相当大的关注。在可靠性和生存性分析中，采用信息几何方法来讨论可靠性模型上的几何。可靠性分析中信息几何的现有大多数工作都集中在失效时间数据上。对于高度可靠的设备，很难在合理的时间内获得故障数据，因此使用降级测量来推断故障时间。在本文中，我们研究了由维纳退化过程引起的具有非线性漂移和扩散系数的统计流形上的几何，其中漂移参数假定为随机变量，以合并单位到单位的特征。Fisher信息量度，Amari–Chentsov张量和$\alpha$讨论了退化模型在流形上的连接。作为工程实验设计中的一种应用，信息度量被用来开发在成本约束下降解实验的最佳设计。蒙特卡罗模拟和数值研究用于说明本文开发的方法。