This paper deals with parametric inference about the independent and identically distributed discrete lifetimes of components of a k-out-of-n system. We consider the maximum likelihood estimation assuming that the available data consists of component failure times observed up to and including the moment of the breakdown of the system. First, we provide general conditions for the almost sure existence of a strongly consistent sequence of maximum likelihood estimators (MLE’s). Then, we focus on three typical discrete failure distributions—the Poisson, binomial and negative binomial distributions—and prove that in these cases the MLE’s are unique, provided they exist, and that they are strongly consistent. Finally, we complete our results by Monte Carlo simulation study. Interestingly, the inference considered in the paper can be viewed as equivalent to one based on Type-II right censored discrete data. Therefore, our results can as well be applied to the case when Type-II right censored sample from a discrete distribution is observed.

本文讨论了关于k的n个分量的独立且均匀分布的离散寿命的参数推断系统。我们考虑最大似然估计，假设可用数据由直至系统崩溃时刻为止的组件故障时间组成。首先，我们为几乎肯定存在的最大似然估计序列（MLE）的强一致序列提供了一般条件。然后，我们关注三种典型的离散故障分布（泊松分布，二项式分布和负二项式分布），并证明在这些情况下，MLE（如果存在）是唯一的，并且它们是强一致的。最后，我们通过蒙特卡洛模拟研究来完成我们的结果。有趣的是，本文中考虑的推论可以视为等同于基于II类右删失离散数据的推论。因此，