The model of adaptive progressive Type-II censoring introduced by Ng et al. (2009) (referred to as Ng–Kundu–Chan model) is extended to allow switching from a given initial censoring plan to any arbitrary given plan of the same length. In this generalized model, the joint distribution of the failure times and the corresponding likelihood function is derived. It is illustrated that the computation of maximum likelihood and Bayesian estimates are along the same lines as for standard progressive Type-II censoring. However, the distributional properties of the estimators will usually be different since the censoring plan actually applied in the (generalized) Ng–Kundu–Chan model is random. As already mentioned in Cramer and Iliopoulos (2010), we directly show that the normalized spacings are independent and identically exponentially distributed. However, it turns out that the spacings themselves are generally dependent with mixtures of exponential distributions as marginals. These results are used to study linear estimators. Finally, we propose an algorithm for generating random numbers in the generalized Ng–Kundu–Chan model and present some simulation results. The results obtained also provide new findings in the original Ng–Kundu–Chan model; the corresponding implications are highlighted.

中文翻译：

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自适应渐进型 II 型审查的广义 Ng-Kundu-Chan 模型及相关推理

Ng 等人提出的自适应渐进式 II 型审查模型。(2009)（称为 Ng-Kundu-Chan 模型）经过扩展，允许从给定的初始审查计划进行切换任意给定的计划相同长度的。在这个广义模型中，导出了故障时间的联合分布和相应的似然函数。图中表明，最大似然和贝叶斯估计的计算与标准渐进式 II 型审查的思路相同。然而，估计量的分布特性通常会有所不同，因为（广义）Ng-Kundu-Chan 模型中实际应用的审查计划是随机的。正如 Cramer 和 Iliopoulos (2010) 中已经提到的，我们直接证明归一化间距是独立的且呈相同指数分布。然而，事实证明，间距本身通常依赖于作为边际的指数分布的混合。这些结果用于研究线性估计器。最后，我们提出了一种在广义 Ng-Kundu-Chan 模型中生成随机数的算法，并给出了一些仿真结果。获得的结果也为原始 Ng-Kundu-Chan 模型提供了新的发现；突出显示了相应的影响。