逐步Ⅱ型截尾样本下恒定应力部分加速寿命试验的统计分析

Statistical Analysis of Constant Stress Partial Accelerated Life Tests Under Progressive Type II Censored Samples

在逐步Ⅱ型截尾样本下,研究广义逆Weibull分布恒定应力部分加速寿命试验(PALTs)的参数估计问题。利用极大似然法得到未知参数和加速因子的极大似然估计(MLE),并根据其渐近正态性计算渐近方差—协方差矩阵,以得到未知参数和加速因子的近似置信区间。取未知参数的先验分布为伽马分布,取加速因子的先验分布为均匀分布,使用Lindley近似算法和Metropolis-Hastings(MH)算法,在平方误差损失(SEL)函数下给出未知参数和加速因子的贝叶斯(Bayes)估计和最大后验密度(HPD)置信区间。通过蒙特卡洛模拟,对MLE和Bayes估计进行了比较。结果表明,在所有考虑的情况下,Bayes估计效果较好,其中MH算法相比Lindley估计更有优势。

The parametric estimation issues on constant stress partial accelerated life tests(PALTs)with generalized inverse Weibull distribution was studied under the progressive type II censored samples.Maximum likelihood estimation(MLE)of unknown parameters and acceleration factors was obtained by maximum likelihood method,and the asymptotic variance-covariance matrix was calculated according to its asymptotic normality,so as to obtain approximate confidence intervals of unknown parameters and acceleration factors.Taking the prior distribution of unknown parameters as gamma distribution,and the prior distribution of acceleration factors as uniform distribution,the Lindley approximation algorithm and Metropolis-Hastings(MH)algorithm were used,and Bayes estimation and highest posterior density(HPD)confidence interval of unknown parameters and acceleration factors were given under the squared error loss(SEL)function.Through Monte Carlo simulation,MLE and Bayes estimation were compared.The results show that the Bayes estimation is effective in all cases,in which the MH algorithm has more advantages than Lindley estimation.