This paper introduces discrete production systems where units are produced one at a time. These systems exist in industry but to the best of our knowledge, they have not been addressed in the open literature. Manufacturing of large iron castings and special precast panels are examples of such production systems. We consider the case where the production process is imperfect resulting in non-conforming units that would be reworked. We assume that the rework process is imperfect and repeated as many times as needed until a conforming unit is produced or the production run ends. The outcomes of this process can be presented by a tree where each branch represents a sequence of production and rework attempts. We call each branch a scenario. The possible number of branches/scenarios is enormously huge, even for reasonable production periods. We employ novel ideas to characterize all branches/scenarios in order to develop the probability mass function for the number of conforming units produced in a given length of the production period. We also, find the expected number of production attempts and rework attempts and the net cost of producing a conforming unit.

本文介绍了一次生产一个单元的离散生产系统。这些系统存在于工业中，但据我们所知，它们尚未在公开文献中提及。大型铸铁件和特殊预制板的制造就是这种生产系统的例子。我们考虑生产过程不完善导致不合格单元需要返工的情况。我们假设返工过程是不完美的，并根据需要重复多次，直到生产出合格的单元或生产运行结束。这个过程的结果可以用一棵树来表示，其中每个分支代表一系列的生产和返工尝试。我们称每个分支为一个场景。即使在合理的生产周期内，可能的分支/场景数量也非常庞大。我们采用新颖的想法来表征所有分支/场景，以便为在给定的生产周期长度内生产的合格单元的数量开发概率质量函数。我们还找到了生产尝试和返工尝试的预期数量以及生产合格单元的净成本。