The life extension achieved by a safety scheme that reduces or eliminates a prolonged radiation exposure is a necessary parameter for calculating the Judgment-or J-value, which enables the scheme's worth to be measured on a common, objective scale against which health and safety spend across all economic sectors can be assessed. The life-expectancy calculation for radiation exposure is necessarily complex because of the long and stochastic incubation periods associated with radiation-induced cancers. Analytical methods are presented to reduce the size of this calculation approximately a hundredfold. This renders the J-value assessment much quicker and easier for new safety systems that may be considered for nuclear plant.