The heterogeneous inverse Gaussian (IG) process is one of the most popular and most considered degradation models for highly reliable products. One difficulty with heterogeneous IG processes is the lack of analytic expressions for the Fisher information matrix (FIM). Thus, it is a challenge to find an optimum test plan using any information-based criteria with decision variables such as the termination time, the number of measurements and sample size. In this article, the FIM of an IG process with random slopes can be derived explicitly in an algebraic expression to reduce uncertainty caused by the numerical approximation. The D- and V-optimum test plans with/without a cost constraint can be obtained by using a profile optimum plan. Sensitivity analysis is studied to elucidate how optimum planning is influenced by the experimental costs and planning values of the model parameters. The theoretical results are illustrated by numerical simulation and case studies. Simulations, technical derivations and auxiliary formulae are available online as supplementary materials.

异构逆高斯 (IG) 过程是高度可靠产品最流行和最考虑的退化模型之一。异构 IG 过程的一个困难是缺乏 Fisher 信息矩阵 (FIM) 的分析表达式。因此，使用任何基于信息的标准以及终止时间、测量次数和样本大小等决策变量来找到最佳测试计划是一项挑战。在本文中，具有随机斜率的 IG 过程的 FIM 可以在代数表达式中显式推导，以减少由数值近似引起的不确定性。D -和V-可以通过使用配置文件优化计划来获得具有/不具有成本约束的最佳测试计划。研究敏感性分析以阐明最佳规划如何受模型参数的实验成本和规划值的影响。通过数值模拟和案例研究说明了理论结果。模拟、技术推导和辅助公式可作为补充材料在线获得。