Robustness is the quality of being able to withstand stresses, pressures, or changes in procedure or circumstance. A system, organism or design may be said to be "robust" if it is capable of coping well with variations (sometimes unpredictable variations) in its operating environment with minimal damage, alteration or loss of functionality.
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In biology 'Robust" is used to describe species with a Morphology based on strength and heavy build, the alternative morphology is the 'gracile' body type. For example comparing similar species, rats have robust body types whilst mice are gracile, other such pairs include the leopard and cheetah. Male and females of the same species, may display sexual dimorphism and have robust and gracile morphologies.
An algorithm in computer science is robust if it continues to operate despite abnormalities in input, calculations, etc.
A robust statistical technique is one that performs well even if its assumptions are somewhat violated by the true model from which the data were generated.
A robust decision is a decision that is as immune to uncertainty as is possible and looks good to all constituents long after it is made.