Shi Weihua, Gui Wenhao
School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, People's Republic of China.
J Appl Stat. 2023 May 3;51(8):1470-1496. doi: 10.1080/02664763.2023.2207787. eCollection 2024.
Comparative lifetime experiments are remarkable when the study is to ascertain the relative merits of two competing products regarding the duration of their service life. This paper considers the comparative lifetime experiments of two Gompertz populations under a balanced joint progressive Type-II censoring scheme. The lifetime distributions of the units are assumed to follow the Gompertz distribution with a common shape but different scale parameters. The maximum likelihood estimates of the unknown parameters are derived. The existence of the maximum likelihood estimates is proved. Expectation-maximization and stochastic expectation-maximization algorithms are provided to calculate the estimates. The bootstrap-p, bootstrap-t, and approximate confidence intervals are established. To obtain the Bayesian estimates, it is assumed that the prior of scale parameters is a Beta-Gamma distribution and the prior of the common shape parameter is an independent Gamma distribution. Under squared error loss and LINEX loss functions, the Metropolis-Hastings algorithm is provided to compute the Bayes estimates and the credible intervals. Further, the statistical inferences with order restriction are studied when it is known a priori that the expectation of the lifespan of one population is shorter than that of the other population. A wide range of simulation experiments is conducted to evaluate the performance of the proposed methods. Finally, the lifetimes of white organic light-emitting diodes and the breaking strengths of jute fiber of gauge lengths are analyzed to illustrate the practical application of the proposed model and methods.
当研究目的是确定两种竞争产品在使用寿命时长方面的相对优势时，比较寿命实验就显得尤为重要。本文考虑了在平衡联合渐进II型截尾方案下两个冈珀茨总体的比较寿命实验。假设各单元的寿命分布服从形状相同但尺度参数不同的冈珀茨分布。推导了未知参数的最大似然估计。证明了最大似然估计的存在性。提供了期望最大化和随机期望最大化算法来计算估计值。建立了自助p值法、自助t值法和近似置信区间。为了获得贝叶斯估计，假设尺度参数的先验分布为贝塔-伽马分布，共同形状参数的先验分布为独立伽马分布。在平方误差损失函数和LINEX损失函数下，提供了Metropolis-Hastings算法来计算贝叶斯估计和可信区间。此外，当预先知道一个总体的寿命期望短于另一个总体时，研究了带有序约束的统计推断。进行了广泛的模拟实验来评估所提方法的性能。最后，分析了白色有机发光二极管的寿命和标准长度黄麻纤维的断裂强度，以说明所提模型和方法的实际应用。
