Reliability and Cost Modeling of Reusable Launch Vehicles

Abstract

The renaissance of reusable space launch vehicles that is being witnessed in the current space industry demands a new cost estimating approach, which takes into account not only the time dependency in the lifecycle brought upon by reusability, but also the complementary considerations of minimizing cost and reliability. To achieve this end, a methodology was developed which allows to estimate both cost and reliability, and in a trade-space test various configurations at the development and operating phases, in order to achieve an optimum configuration which minimizes cost, maximizes reliability, and fulfills the design requirements. The development, manufacturing and operations costs of reusable launch vehicles were obtained using the Theoretical First Unit equivalence method. This includes the particular cost features of reusability, including the recovery hardware, the retrieval of the reusable equipment and its refurbishment. Furthermore, a model for the failure cost was developed, including: Flight replacement, Insurance Penalties, Failure Investigation, Modifications and Downtime. A reliability model is implemented in parallel to the cost model, which allows to obtain a flight-dependent reliability estimate, taking into account the possible reliability increase methods, such as redundancy, derating, engine-out capability, and extensive testing. This is achieved using publicly available test and operational data and using non-parametric (Kaplan-Meier) as well as parametric (Exponential and Weibull Maximum Likelihood Estimates) techniques in order to obtain life-cycle reliability. These two models coalesce into a trade-space where it is possible to tune the launcher configuration in order to meet its requirements, while minimizing cost and/or maximizing reliability. At the design level, the features of different configurations and testing programs can be compared, in order to achieve the lowest cost possible while attaining the necessary reliability targets. On the other hand, at the operation level, the reliability figures can be used in conjunction with the cost per flight in order to obtain the expected cost of failure and value throughout the life-cycle of the launch vehicle. This allows the designer to forecast the potential financial losses throughout the operating life of the vehicle, and look to minimize these losses while securing proper funding to cover them, which is especially critical in the first years of operations. Two use-cases are presented. Firstly, the model is applied to the Falcon 9 vehicle. Verification of the cost figures shows that the error of the methodology is under 30%. A projection of the life-cycle costs is obtained, as well as the expected cost of failure and expected value. Recommendations are given in order to mitigate losses and advise the planning of the life-cycle of the fleet and its reuses. It was found that at an initial stage, where cost reduction from learning and reliability growth haven’t yet taken hold, flights have a negative expected value, meaning that the launch provider can expect to lose money with these flights. Insurance options are investigated in order to mitigate these losses. Secondly, a study is done based on the Ariane 6 publicly available data, in order to study the impact of varying the number of engines in its first stage as well as engine commonality with the upper stage. It was found that for an expendable vehicle such as the Ariane 6, a single-engine configuration provides the most value, as the manufacturing costs of producing several engines per flight does not compensate eventual lower development costs. On the other hand, it was found that for a reusable vehicle, the stricter the reliability requirements, the more a multi-engine configuration is advantageous. This is due to the lower development costs combined with the replacement of the high cost of manufacturing engines with refurbishment costs, with an optimum for a configuration of 4-5 engines.