A recurrence relation for calculating a reliability increment in a series-parallel system

A recurrence relation is given for the easy calculation of an increment in the reliability of a series-parallel system if the number of redundant elements is increased by one. This relation is used for cold or standby redundancy when the number of failures obeys the Poisson distribution. The formulas have been implemented in various computer programs for system reliability calculation and optimization. The experience with many real and hypothetical examples has shown no computational problems. There is no need to care either about the magnitude of the number of redundancies or about the accuracy of computation. This shows the advantage of this algorithm over the approximation proposed by M. Messinger and M. Shooman (1970).