In this article, we consider statistical inference based on dependent competing risks data from Marshall-Olkin bivariate Weibull distribution. The maximum likelihood estimates of the unknown model parameters have been computed by using the Newton-Raphson method under adaptive Type II progressive hybrid censoring with partially observed failure causes. The existence and uniqueness of maximum likelihood estimates are derived. Approximate confidence intervals have been constructed via the observed Fisher information matrix using the asymptotic normality property of the maximum likelihood estimates. Bayes estimates and highest posterior density credible intervals have been calculated under gamma-Dirichlet prior distribution by using the Markov chain Monte Carlo technique. Convergence of Markov chain Monte Carlo samples is tested. In addition, a Monte Carlo simulation is carried out to compare the effectiveness of the proposed methods. Further, three different optimality criteria have been taken into account to obtain the most effective censoring plans. Finally, a real-life data set has been analyzed to illustrate the operability and applicability of the proposed methods.

翻译：本文研究基于Marshall-Olkin双变量威布尔分布的相依竞争风险数据的统计推断问题。在部分观测失效原因的自适应Ⅱ型逐步混合删失方案下，采用牛顿-拉夫森方法计算未知模型参数的最大似然估计，并推导了最大似然估计的存在性与唯一性。利用最大似然估计的渐近正态性，通过观测Fisher信息矩阵构建了近似置信区间。在伽马-狄利克雷先验分布下，采用马尔可夫链蒙特卡洛技术计算了贝叶斯估计及最高后验密度可信区间，并对马尔可夫链蒙特卡洛样本的收敛性进行了检验。此外，通过蒙特卡洛模拟比较了所提方法的有效性，并基于三种不同优化准则筛选出最优删失方案。最后，通过实际数据分析验证了所提方法的可操作性与适用性。