Radical new electrically propelled aircraft are being considered to meet strict future performance goals. One concept design proposed is a Turboelectric Distributed Propulsion (TeDP) aircraft that utilises a number of electrically driven propulsors. Such concepts place a new and significant reliance on an aircraft's electrical system for safe and efficient flight. Accordingly, in addition to providing certainty that supply reliability targets are being met, a contingency analysis, evaluating the probability of component failure within the electrical network and the impact of that failure upon the available thrust must also be undertaken for architecture designs. Solutions that meet specified thrust requirements at a minimum associated weight are desired as these will likely achieve the greatest performance against the proposed emissions targets. This paper presents a Fault Tree Analysis (FTA) based design approach for the electrical system and thrust reliability analysis of TeDP aircraft architectures. This approach extends beyond the single failure rate provided by traditional FTA methods by profiling the reliability and thrust provision of each possible system configuration (i.e. following the failure of one or more components), which combined with a measure of total system weight and volume provides an effective design capability. The paper presents a case study for a TeDP design configuration showing how Thrust - Reliability (TR) dispatch targets may be achieved using a contingency analysis method utilising k-out-of-n probability and concludes by discussing plans to build upon the described work and utilise the method for more complex studies.