分位数回归在竞争失效加速寿命试验统计分析中的应用

Quantile Regression Based Accelerated Life Test Analysis for Problem with Competing Risks of Failure

利用加速寿命试验的失效数据对产品的分位数寿命进行统计推断时,需要对统计模型做具体的假设。但是在工程实际中,错误的模型设定会严重影响估计精度。针对这个问题,提出了一种基于分位数回归的竞争失效产品分位数寿命的统计分析方法。分位数回归模型不受寿命分布假设的约束,且描述产品寿命与加速应力的关系时更加灵活。考虑到由于逐步II型截尾和竞争失效模式而产生的试验数据非完整性,采用基于cause-specific hazard(CSH)的鞅方法为待估的分位数回归模型构造无偏估计方程,并将方程的求解等价为凸函数的极小值的求解。同时采用扰动重抽样方法得到参数的区间估计值。最后应用实例验证了方法的有效性。

Based on accelerated life tests(ALT) data, inferences on quantiles of the lifetime distribution at the use condition are obtained via an assumption of a specific working model. But in engineering practice, model misspecification can result in significant estimation bias. In order to solve this problem, a statistical analysis approach based on quantile regression is proposed to estimate quantiles of the lifetime distribution with competing causes of failure. Quantile regression is distribution-free and more flexible in modeling life-stress relations. Full consideration is given to the incompleteness of test data, which is due to Type-II progressive censoring as well as competing risks. The martingales based on cause specific hazards are used to construct unbiased estimating equations for the quantile regression model, and the solution of equations is equivalent to search for minimizations of convex functions. By using perturbation resampling approach, the interval estimations are presented. Finally, the Monte Carlo method is used to evaluate the performance of the proposed method.