A new reliability metric called belief reliability takes both aleatory and epistemic uncertainty into consideration. Conventional system belief reliability theory depends on a complicated formula for belief reliability that is challenging to understand and apply in practical systems having random and uncertain components. To resolve these issues, an efficient method, i.e. disjoint method, is proposed that generates a very smaller number of terms in comparison with conventional decomposition method for belief reliability evaluation of a practical system. Benchmark problem, i.e. F-18 LLF system, helps to quantify the findings and validate the outcomes.