In this article, the estimation of the unknown parameters and the survival and hazard functions of Weibull distribution is studied with the adaptive Type-II progressively censored competing risks data, where the lifetime random variables of the individual failure causes are independent and follow Weibull distribution with different scale and shape parameters. For frequentist estimation, the maximum likelihood estimators are obtained utilizing Newton-Raphson method, whose existence and uniqueness are also proved. Making use of the asymptotic normality of maximum likelihood estimators and delta method, we construct the respective confidence intervals of the parameters and the survival and hazard functions. For Bayesian estimation, we take advantage of Monte Carlo Markov Chain technique and importance sampling method to derive the Bayesian estimators and the credible intervals. Extensive Monte Carlo simulation experiments and a real-life mortality dataset analysis are implemented to evaluate the performance of the developed methods. And then, we discuss the issue of expected experimentation time. In the end, the model is extended to the case of dependent failure modes. Marshall-Olkin bivariate Weibull distribution is considered and the theoretical derivations are presented.

本文利用自适应Type-II逐步删失竞争风险数据研究了未知参数的估计以及Weibull分布的生存和风险函数，其中单个故障原因的寿命随机变量是独立的并遵循Weibull分布不同的尺度和形状参数。对于频率估计，利用Newton-Raphson方法得到最大似然估计，并证明了其存在性和唯一性。利用最大似然估计量的渐近正态性和delta方法，我们构建了参数和生存和风险函数的各自置信区间。对于贝叶斯估计，我们利用蒙特卡洛马尔可夫链技术和重要性采样方法来推导贝叶斯估计量和可信区间。实施了广泛的蒙特卡罗模拟实验和现实生活中的死亡率数据集分析，以评估所开发方法的性能。然后，我们讨论预期实验时间的问题。最后，将模型扩展到相关故障模式的情况。考虑了 Marshall-Olkin 双变量 Weibull 分布并给出了理论推导。该模型扩展到相关故障模式的情况。考虑了 Marshall-Olkin 双变量 Weibull 分布并给出了理论推导。该模型扩展到相关故障模式的情况。考虑了 Marshall-Olkin 双变量 Weibull 分布并给出了理论推导。