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The article is devoted to the relevant issue of prolongation of operating lifetimes for expensive objects. The methods of prolongation of operating lifetimes for complex technical systems have been described. In particular, the mathematical model of prolongation of operating lifetimes by the calculation and analytical method, which is based on normal distribution law of actual load and durability, has been represented. The experimental method, which is based on analysis of actual technical state of element base and material, has been described. The probabilistic method of calculation of reliability function during prolonged operating lifetime taking into account actual technical state of element base has been represented.

Mathematical models and methods of prolongation of operating lifetimes for expensive objects