Researchers have widely used accelerated life tests to determine an optimal inspection plan for lot acceptance. All such plans are proposed by assuming a known relationship between the lifetime characteristic(s) and the accelerating stress factor(s) under a parametric framework of the product lifetime distribution. As the true relationship is rarely known in practical scenarios, the assumption itself may produce biased estimates that may lead to an inefficient sampling plan. To this endeavor, an optimal accelerating life test plan is designed under a Type-I censoring scheme with a generalized link structure similar to a spline regression, to capture the nonlinear relationship between the lifetime characteristics and the stress levels. Product lifetime is assumed to follow Weibull distribution with non-identical scale and shape parameters linked with the stress factor through a piecewise linear function. The elements of the Fisher information matrix are computed in detail to formulate the acceptability criterion for the conforming lots. The decision variables of the sampling plan including sample size, stress factors, and others are determined using a constrained aggregated cost minimization approach and variance minimization approach. A simulated case study demonstrates that the nonlinear link-based piecewise linear approximation model outperforms the linear link-based model.

翻译：研究人员广泛采用加速寿命试验来确定批次验收的最优检验方案。现有方案均基于产品寿命分布的参数化框架，假设寿命特性与加速应力因子之间存在已知关系。由于实际场景中真实关系鲜为人知，该假设本身可能产生有偏估计，从而导致抽样方案效率低下。为此，本研究在Ⅰ型截尾方案下设计了一种最优加速寿命试验方案，采用类似样条回归的广义链接结构来捕捉寿命特性与应力水平之间的非线性关系。假设产品寿命服从威布尔分布，其尺度参数和形状参数通过分段线性函数与应力因子关联。详细计算了费希尔信息矩阵的各元素，以构建合格批次的验收准则。抽样方案的决策变量（包括样本量、应力因子等）通过约束聚合成本最小化方法和方差最小化方法确定。模拟案例研究表明，基于非线性链接的分段线性近似模型优于基于线性链接的模型。