Gamma恒定应力加速寿命试验的统计分析  

Statistical analysis for the gamma constant-stress accelerated life test

作　　者：王炳兴[1] 覃水丹 潘鑫 周君兴 WANG Bing-xing;QIN Shui-dan;PAN Xin;ZHOU Jun-xing(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China;School of Data Sciences,Zhejiang University of Finance and Economics,Hangzhou 310018,China)

机构地区：[1]浙江工商大学统计与数学学院,浙江杭州310018 [2]浙江财经大学数据科学学院,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2019年第4期389-401,共13页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11671303);浙江省一流学科A类(浙江工商大学统计学;浙江财经大学统计学);浙江工商大学研究生科研创新基金

摘　　要：证明了基于恒定应力加速寿命试验数据Gamma模型参数的最大似然估计在一定条件下存在,进而导出了Gamma模型参数的备择估计.利用Cornish-Fisher展开导出了Gamma形状参数的近似置信区间,另外也给了Gamma模型的其它参数和正常应力水平下产品寿命的一些重要可靠性指标的广义置信区间.利用模拟方法研究了所给点估计和区间估计的精度,模拟结果显示所给点估计和区间估计的精度是相当好的.In this paper, it is verified that there exist the maximum likelihood estimations for the gamma constant stress accelerated life model under some conditions. Furthermore, the alternative estimations have been derived. Using the Cornish-Fisher expansion, the approximate confidence interval for the shape parameter has been obtained. The generalized confidence intervals for other model parameters and some important reliability metrics such as the mean life and the reliability at the normal stress level are proposed. The performances of the proposed procedures are evaluated by Monte Carlo simulation. The simulation results show that the coverage percentages of the proposed confidence intervals are quite close to the nominal coverage probabilities.

关 键 词：加速寿命试验 GAMMA分布 最大似然估计 Cornish-Fisher展开 广义置信区间 

分 类 号：O213.2[理学—概率论与数理统计]