TSG Reliability Practice Exam

The expression models a parallel arrangement where a series path of two components is in parallel with a third component. A series pair has reliability R1 × R2 because both components must work for that path to succeed. The whole system then works if either that series path works or the individual third component works (or both), which is the essence of parallel redundancy. For parallel paths, the system fails only if every path fails. The series path fails with probability 1 − (R1 × R2), and the third component fails with probability 1 − R3. Assuming independence, the probability that both paths fail is (1 − R1×R2) × (1 − R3). Therefore, the overall reliability is 1 minus that failure probability: R_sys = 1 − (1 − R1×R2)(1 − R3). This aligns exactly with the given formula, confirming the configuration is a series path of R1 and R2 in parallel with R3. If all three were in series, reliability would be R1 × R2 × R3. If all three were in parallel, reliability would be 1 − (1 − R1)(1 − R2)(1 − R3). A single component with no redundancy would just be one R value.