For over 20 years, U. S. Army management has used quantitative risk analysis results to make informed technical decisions. These decisions are difficult because competing risk and operational factors must be weighed and considered simultaneously before the correct choice can be determined. The calculation of complex system risk at a known confidence level can suffer from compounding conservatism. Compounding conservatism arises when two or more system variables are involved in calculating system risk and are computed as upper bounds at the known/specified system confidence level. When these upper bound values are combined to compute the system risk, the resulting system risk is overestimated while the system confidence level is underestimated. This paper describes a numerical method to compute complex system risk while avoiding compounding conservatism. This paper also discusses alternative analytical and simulation techniques to address compounding conservatism, presents several examples using this numerical method, highlights important findings and benefits, and suggests potential improvements for future development.