Use of Semi-Markov Models for Quantitative ECLSS Reliability Analysis: Spares and Buffer Sizing

As the duration of human spaceflight missions increases, it becomes less feasible to attempt to design Environmental Control and Life Support Systems (ECLSS) with components of such high reliability that they will never fail. Instead, systems must be designed to be resilient – to maintain functionality in the face of component failure. A major question for system designers then becomes: how resilient? Additional redundancy, spares, or consumable margin increase a system’s resilience, but they also increase cost and mass. Also, buffers within the system have a significant impact on system reliability, especially when external spares are utilized; however, this also comes at a cost. In order to properly consider resilience in system trade studies, a quantitative and objective means to measure the benefits of resilience-related system elements must be utilized. This paper presents the use of semi-Markov models to model the reliability and resilience of ECLSS for long- duration spacecraft and habitats, with states defined by the status of each component (functional/failed) and transition probability distributions defined by failure rates, repair rates, and the time that the system can survive after component failure. This technique enables calculation of the probability of system failure before the end of the mission, as well as several other metrics of interest. A simple example is given, and benefits and limitations of the technique are discussed.