Abstract
Ensuring survivability, defined as the ability of the technical system in a damaged state, to carry out (in full or in part) their
 duties and avoid catastrophic damage, is an important element of the complex security problems technosphere objects.
 In this paper are considered the basic approaches to quantitative assessment of complex technical systems’ survivability
 taking into account that damage accumulation and fracture processes are developed along a broad range of the system’s
 scales: starting from the nano-scale level and up to the global structural level of the system. Three basic scales were
 single out from the entire spectrum of the system’s scales. These scales allow describe the system failure process. A set of
 indexes describing systems’ survivability at the specified above scale levels has been presented. The next basic approaches
 to quantitative assessment of complex systems’ survivability have been developed: approaches based on deterministic
 and probabilistic assessments of system’s residual strength after macro-defects initiation, as well as integral approaches
 based on risk assessment and on estimation of reducing of system’s key strength characteristics when its damage level has
 increased.
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