Abstract

In lifetime experiments, sometimes censoring is inevitable to save experimental cost and to accelerate execution of the test. For conducting a comparative lifetime experiment of the products, which are from different production lines under the same environmental conditions, the joint type-II censoring scheme is practically much significant. The present article deals with inferences, when jointly type-II censored sample is taken from k$k$$k$ Lindley populations. The maximum likelihood estimators of the model parameters are derived with their asymptotic confidence intervals and log-transformed asymptotic confidence intervals. The boot-p and boot-t confidence intervals are also calculated. In order to evaluate the impact of prior information, the parameters are estimated in Bayesian framework based on balanced loss function assuming the informative and non-informative priors. Since the expressions for Bayes estimates cannot be obtained in closed form so the importance sampling and the Gibbs sampling techniques are used. Finally, a Monte Carlo simulation study and a real dataset are given to exemplify all the methods of estimation developed here.

摘要

在寿命实验中，有时为了节省实验成本并加速测试的执行，审查是不可避免的。对于在相同环境条件下对来自不同生产线的产品进行比较寿命实验，联合II型审查方案具有实际意义。本文涉及的推论是，当联合 II 类审查样本取自k$k$$k$林德利人口。模型参数的最大似然估计量是通过其渐近置信区间和对数变换渐近置信区间得出的。还计算 boot-p 和 boot-t 置信区间。为了评估先验信息的影响，在假设信息性和非信息性先验的情况下，基于平衡损失函数的贝叶斯框架中估计参数。由于贝叶斯估计的表达式无法以封闭形式获得，因此使用重要性采样和吉布斯采样技术。最后，给出了蒙特卡罗模拟研究和真实数据集来举例说明这里开发的所有估计方法。