The level of CO_2, H_2O, or O_2 aboard the International Space Station (ISS) at a given time during a flight increment is a function of the mean time between failure (MTBF) and mean time to repair (MTTR) for several pieces of machinery, as well as the number of crewmembers aboard. The non-linear interaction between these elements requires a simulation approach to probability calculations in lieu of a static fault or event tree model. We chose to implement our models as a particular type of finite state machine called a Petri Net, an architecture that permits both stochastic (random) and deterministic events. To run the Petri Net, we combined an existing freeware Petri Net graphical user interface (GUI) with our own Excel/Visual Basic for Applications (VBA) simulation code in a platform that permits easy design, analysis, and verification of model logic. A single run through the model in our analysis represents a single possible timeline aboard the ISS, with random failures of equipment and repair times distributed according to the best available probability data. By running the model with the same input parameters a large number of times in a Monte Carlo analysis, we derive with high confidence the probability of occurrence of a particular event of interest (in this case, exceedance of a critical consumable threshold) up to a particular time, at much higher fidelity than would be possible without simulation. This analytical tool will be useful for estimating probabilities in a wide variety of systems.
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