This paper is a review and some development of previous authors works. On the base of p-set function definition the solution of two airframe reliability problems are considered: the choice of both the specified maximum permitted life and inspection program for fatigue-prone airframe. The problems should be solved by processing of the lifetime test data. Instead of the use of confidence intervals for lifetime distribution parameters new approach based on the p-set function is offered. Then we do not need to solve the problem how to choose two values: confidence probability in conjunction with the required reliability. In fact we only need to know permissible probability of failure in service. For the case of approval test the minimax approach is offered. Some numerical examples are given.