Linear Interpolation with a Nonparametric Accelerated Failure-Time Model
非参数加速失效时间模型中的线性插值AI 解读 ↓
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非参数加速失效时间模型中的线性插值
- 研究问题
- 在非参数加速失效时间模型下，如何沿应力与失效时间平面的负斜率线段，同时向更长时间和更低应力外推失效概率？
- 方法与思路
- 作者使用带曲率约束的尺度族模型，提出线性插值式外推，并在两应力水平下用拟合检验及两种检验考察附加有效性条件。
- 材料陈述的贡献
- 摘要称提出同时跨时间与应力的外推方法及配套条件检验，并用删失寿命数据说明，以模拟考察功效和稳健性。
- 阅读关注点
- 应核对模型曲率约束、时间分位数的凸性及外推所需两个附加条件，并判断有限样本检验如何支持这些条件。
- 阅读边界
- 依据 OpenAlex 索引摘要，稿件版本未注明，不能推断刊本变化；外推依赖模型与附加条件，摘要未给出误差保证或模拟数值。
原文摘要
Assuming a nonparametric accelerated failure-time model, a method is proposed for extrapolating low stress-response probabilities on negative-sloping line segments in the stress-failure-time plane. The method (analogous to linear interpolation in dose-response studies) results in simultaneous extrapolation ahead in time and down in stress. In the two-sample (two stress level) setting, a goodness-of-fit test of the nonparametric model is considered and two hypothesis tests are proposed, each pertaining to a condition that (in addition to the assumed model) must be met for the method to be valid. The method is illustrated with censored strand-life data, and some simulated examples are used to consider power and robustness. The failure-time model is a scale family with curvature constraints. The failure probability is assumed to be a sigmoid function of the product of time and a sigmoid scaling function of stress. Time percentiles as functions of stress are assumed to be convex. The goodness-of-fit test is of the Kolmogorov-Smirnov type. Given data at stresses x 1 and x 2, the linear interpolation procedure requires a negative-sloping line such that (a) the failure probability increases along the line as the stress increases from x 1 to x 2, and (b) at the point on the line at x 1 the ratio of the failure probability to time increases in time. A Kolmogorov-Smirnov hypothesis test is used to support (a), and a binomial probability test is used for (b).