Model for ancient Greek and Roman coinage production

Abstract

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.