We treat optimal equidistant and optimal non-equidistant inspection times for interval censoring of exponential distributions. We provide in particular a new approach for determining the optimal non-equidistant inspection times. The resulting recursive formula is related to a formula for optimal spacing of quantiles for asymptotically best linear estimates based on order statistics and to a formula for optimal cutpoints by the discretisation of continuous random variables. Moreover, we show that by the censoring with the optimal non-equidistant inspection times as well as with optimal equidistant inspection times, there is no loss of information if the number of inspections is converging to infinity. Since optimal equidistant inspection times are easier to calculate and easier to handle in practice, we study the efficiency of optimal equidistant inspection times with respect to optimal non-equidistant inspection times. Moreover, since the optimal inspection times are only locally optimal, we also provide some results concerning maximin efficient designs.

中文翻译：

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区间删失检验次数的优化设计

我们对待指数分布的区间删失的最佳等距和最佳非等距检查时间。我们特别提供了一种确定最佳非等距检查时间的新方法。得到的递归公式与基于阶统计的渐近最佳线性估计的最佳分位数间距公式和通过连续随机变量离散化的最佳截点公式相关。此外，我们表明，通过使用最佳非等距检查时间和最佳等距检查时间进行审查，如果检查次数收敛到无穷大，则不会丢失信息。由于最佳等距检查时间更容易计算并且在实践中更容易处理，我们研究了最佳等距检查时间相对于最佳非等距检查时间的效率。此外，由于最优检查时间只是局部最优，我们还提供了一些关于最大化效率设计的结果。