A measure of vulnerability and damage tolerance

The purpose of the paper is to present probabilistic definitions of ‘vulnerability’ and ‘damage tolerance’. A new measure of damage is also proposed. Disastrous failures, such as of the Titanic or the Chernobyl reactor, have revealed that some systems can be highly vulnerable. A seemingly insignificant damage can reduce such a systemʹs resistance severely. Attempts to write design code requirements for damage tolerance or structural integrity have not been successful so far. One reason is that these ideas have not been defined with the necessary precision. ggested definitions aim to be general, applicable to all engineered systems, and readily specializable to particular system types. Vulnerability is defined as the ratio of the failure probability of the damaged system to the failure probability of the undamaged system. It is argued that ‘vulnerability’ and ‘damage tolerance’ are complementary concepts. Damage tolerance is defined as the reciprocal of vulnerability. Vulnerability and damage tolerance both concern hypothetical future damage. A damage factor, applicable for the analysis of an existing structure in an assessed state of damage, is defined analogous to vulnerability. Application is illustrated by examples.