We propose a Bayesian framework for planning simple step-stress accelerated life tests when items are subject to two independent competing failure modes We assume that the competing risks are independent, with lifetimes following Weibull distributions, and adopt the cumulative exposure model with a log-linear stress-life relationship to connect failure time distributions across stress levels. The optimality criterion is the preposterior variance of the $p$-th quantile of the lifetime distribution at use stress, evaluated without reliance on asymptotic approximations, making the methodology valid regardless of sample size. Building on the idea of quantile-based reparametrisation used in single-mode ALT \citep{zhang2006bayesian}, we extend this approach to the competing risks setting by reparametrising the model parameters for each failure mode to physically interpretable and approximately independent quantities, making it possible to elicit priors directly from engineering knowledge of device behaviour. Posterior inference is carried out using the No-U-Turn Sampler implemented in Stan, and the optimal design is located via Monte Carlo simulation over a grid of candidate designs. The methodology is illustrated on a real step-stress dataset for a solar lighting device subject to capacitor and controller failure modes. A comprehensive sensitivity analysis with respect to the quantile probability, the lower stress level, the prior hyperparameter specification, and the sample size shows that the optimal stress-change time is moderately sensitive to these inputs while the optimal lower stress level consistently favours operation close to use conditions, a finding that holds across all prior specifications considered.

翻译：我们提出了一种贝叶斯框架，用于规划当产品面临两个独立竞争失效模式时的简单步进应力加速寿命试验。假设竞争风险相互独立，寿命服从威布尔分布，并采用累积暴露模型与对数线性应力-寿命关系来连接不同应力水平下的失效时间分布。优化准则为使用应力下寿命分布第$p$分位数的先验方差，该方差不依赖渐近近似进行估计，使得该方法适用于任意样本量。基于单模式加速寿命试验中分位数重参数化的思想，我们将其扩展到竞争风险场景，通过为每个失效模式重参数化模型参数，使其具有物理可解释性且近似独立，从而能够直接从工程知识中获取先验信息。后验推断使用Stan中的No-U-Turn采样器实现，最优设计通过蒙特卡洛模拟在候选设计网格上定位。该方法应用于实际步进应力数据集——太阳能照明设备中电容器和控制器失效模式案例。针对分位数概率、低应力水平、先验超参数设定及样本量的全面敏感性分析表明，最优应力改变时间对这些输入参数具有中等敏感性，而最优低应力水平始终倾向于接近使用条件的操作，这一发现适用于所有考虑的先验设定。