Reliability for relativistic spacecraft

Abstract

In this paper for the first time it is merged the relativistic interstellar flight theory with the reliability theory. If a spacecraft flies to a far stellar system with velocities not negligible in comparison with the speed of light it has to be taken into account special relativistic effects, in particular for the time depending quantities. But probability density function, reliability, hazard rate, and other linked quantities, in general are time depending then they can be studied under this point of view. In particular the most used distributions in space engineering have been considered, i.e. Weibull, exponential, normal, lognormal, gamma, Gumbel, and they have been studied for three different kinds of space flights: non-relativistic, relativistic uniform linear motion and relativistic hyperbolic motion. In the first kind of flight the coordinate time t coincides with the proper time τ (in relativistic sense) then the proper functions coincide with the coordinate functions. For the other two cases the proper functions are again the classical quantities, instead the main result of this work gives the collection of the corresponding coordinate functions that are the quantities calculated on the Earth, necessary to design and follow the mission at a distance.