In this paper, we consider a two-stage sequential estimation procedure to estimate the parameters of a cumulative exposure model under an accelerated testing scenario. In particular, we focus on a step-stress model where the stress level changes after a pre-specified number of failures occur, which is also random. This is termed as a ‘random stress change time’ in the literature. We further aim to estimate these parameters using maximum precision and hence use a certain variance optimality criteria. Our proposed two-stage estimation procedures follow interesting efficiency properties and their applicability is seen through extensive simulation analyses and a pseudo-real data example from reliability studies.

在本文中，我们考虑了一个两阶段顺序估计程序来估计加速测试场景下累积暴露模型的参数。特别是，我们关注一个阶跃应力模型，其中应力水平在发生预先指定的故障次数后发生变化，这也是随机的。这在文献中被称为“随机应力变化时间”。我们进一步的目标是使用最大精度来估计这些参数，因此使用一定的方差最优性标准。我们提出的两阶段估计程序遵循有趣的效率特性，并且通过广泛的模拟分析和可靠性研究的伪真实数据示例可以看出它们的适用性。