加速寿命数据的贝叶斯建模与分析

Bayesian modeling and analysis of accelerated life data

在加速寿命试验的可靠性设计中,随机化设计的限制以及删失数据不可避免地导致低分位数估计出现较大的偏差。针对上述的问题,结合贝叶斯抽样技术以及非线性混合模型(nonlinear mixed model,NLMM)提出了一种可靠性改进的分析方法。首先,需要检验所收集的数据是否服从威布尔分布以及验证形状参数是否是恒定常数。其次,考虑随机效应对尺度参数和形状参数的影响,运用NLMM构建了尺度参数和形状参数与试验因子之间的函数关系。然后,利用贝叶斯方法估计低分位数的可靠性寿命。最后,实际案例研究表明,在考虑删失问题和未完全随机设计的影响时,所提方法能够获得更为稳健和可靠的估计结果。

In the reliability design of accelerated life tests,the limitations of randomized design and censored data inevitably lead to significant deviations in low percentile estimation.Given the above problems,a reliability-improved analysis method is proposed combining Bayesian sampling technology and nonlinear mixed model.Firstly,it is necessary to check whether the collected data follow the Weibull distribution and verify whether the shape parameters are constant.Secondly,considering the effects of random effects on scale parameters and shape parameters,a nonlinear mixed model is used to construct the functional relationship between scale parameters,shape parameters and test factors.Thirdly,a Bayesian method is used to estimate the reliability life of low percentiles.Finally,a practical example reveals that the proposed method can obtain more robust and reliable estimation results under considering the impact of censored data and non-randomization.