Coinage production of ancient powers such as Athens and Rome is usually inferred from die statistics of monetary issues. The present work applies a Kaplan-Meier analysis of resistance to failure to 29 sets of well-documented monetary issues. The failure rate function assumes a U-shaped form known in reliability engineering literature as the ‘bathtub curve’. With the geometric distribution of die failure being demonstrably violated for a large fraction of the data sets, the die distribution of each data set was instead fitted by a mixture of two Weibull distributions corresponding to two failure regimes. Dies can be divided into bad dies, failing early for various reasons, and good dies, failing late by fatigue. The dual populations reflect the efforts of the smiths at the time to produce bronze dies that would meet two conflicting needs: the reduction of premature die failure (= infant mortality) and the limitation of ductile deformation during minting. The variable proportions of the two populations suggest that not all workshops had fully mastered die technology. Because of the dichotomy induced by contrasting mechanical properties, corrections for missing dies based on singletons and causes of die failure must be carefully assessed for each data set.

通常从货币问题的统计数据中推断出古代强国如雅典和罗马的造币生产。本工作对29套有据可查的货币问题进行了对失败抵抗力的Kaplan-Meier分析。故障率函数采用可靠性工程文献中称为“浴盆曲线”的U形形式。由于在大部分数据集中明显违反了模具失效的几何分布，因此每个数据集的模具分布都由对应于两种失效模式的两种威布尔分布的混合拟合。模具可分为坏模具（由于各种原因而导致早期失效）和好的模具（因疲劳而导致晚期失效）。双重人口反映了当时的铁匠们为生产能够满足两个相互矛盾的需求的青铜模具而做出的努力：减少过早的模具衰竭（=婴儿死亡率）和限制铸造期间的延性变形。两种人群的比例各不相同，这表明并非所有的工作室都完全掌握了模具技术。由于机械性能的差异导致了二分法，因此必须针对每个数据集仔细评估基于单件和模具失效原因的模具缺失校正。