逆幂律模型下Frechet分布序进应力加速寿命试验的统计分析

Statistical Analysis of Frechet Progressive Stress Accelerated Life Test for Inverse Power Law Model with Linear Relation Between the Stress and Time

加速寿命试验是评估产品寿命的常用方法,被广泛用于工业产品寿命试验中以改善产品的性能,通过提高寿命试验的应力水平,以便更快地在正常条件下获得所需的产品信息。Frechet分布是极值分布理论中的重要分布之一,在更新理论及分支过程、经济学、水文气象学中均有重要的应用。针对逆幂律模型下寿命服从Frechet分布的产品,在应力为时间的一般线性关系下的序进应力加速寿命试验下进行统计分析。分别利用极大似然估计、MPS估计以及最小距离估计给出分布参数的点估计,并通过大量Monte-Carlo模拟试验对比3种估计方法的优劣,给出实际应用中对于不同的分布参数应选择的估计方法的建议。

Accelerated life testing is a common method for assessing product life and is widely used in industrial product life testing to improve product performance by increasing the stress level of life testing to obtain the desired product information faster under normal conditions.Frechet distribution is one of the important distributions in the theory of extreme value distribution.It has important applications in updating theory and branching process,economics and hydrometeorology.Based on the frechet distribution under inverse power law model,statistical analysis is performed on the progressive stress accelerated life tests with linear relation between the stress and time.Maximum likelihood estimate,method of maximum product of spacings and minimum distances estimate were used to give the point estimates of the distributed parameters.The advantages and disadvantages of different estimation methods were compared by a large number of Monte-Carlo simulations,and several suggestions in practical applications were proposed.