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• Reliability analysis on flood defences designed without probabilistic criteria. • Characterizing precipitation and evaporation time series • Generation of water level data using copulas, Markov chains, and hydrological data. • The resulting probability of failure is consistent with historical sources. In some cases, hydraulic infrastructures of different sizes and importance are built without formal design criteria and it may be desired to infer the reliability level for which it was originally designed. In this paper, we present a method to perform the reliability analysis of a dike that was, in all likelihood, designed without probabilistic criteria. This is the Nezahualcoyotl dike, an ancient structure built by the Aztec empire around 1445 in modern-day Mexico City. The method consists of 1. Characterizing time-series of relevant environmental variables. We use precipitation and evaporation by combining a discrete time-state Markov chain with a copula-based stochastic process. 2. Simulating from the time series model a large number of observations to "load" the structure of interest and finally, 3. Compute the probability of failure of the structure with respect to a failure mechanism. In this case, we focus on overflow. The proposed model is able to reproduce to a good extent the hydrology of the system. The return period for overflow obtained in our research is consistent with historical accounts. This work can be used as a reference to assess the reliability of other (ancient or present-day) structures whose design is based on informal criteria. [ABSTRACT FROM AUTHOR]