In the current paper we study the reliability of the functioning of a flight module of a tethered high-altitude telecommunication platform, utilizing the k-out-of-n: F model. Several variants of such a model are considered, including the one taking into account the diverse failure logic, i.e. the dependence of system failures on the configuration of failed components. An algorithm has been developed and implemented in software that allows calculating the reliability function of such a system, its mean time to failure and variance of its uptime, as well as the quantiles of the distribution function. In order to verify the practicality of the approach, numerical and graphical reliability analysis for two most common special cases was performed.