A calculation method is analytical when results are computed using formulas derived from some type of mathematical analysis. For example, if λ is the failure rate of a component, then the reliability of the component for mission time t is R(t) = exp[-λt]. The numeric result for R(t) can be obtained by computing exp{-λt} with the specified numeric values of λ and t. In general, analytical methods are quick and accurate. However, analytical methods are feasible only if no complex dependencies exist.

Simulation is when results are computed by mimicking the dynamic behavior of a system. In its broader sense, simulation is the process of observing the dynamic behavior of a system with varying sets of inputs. In reliability engineering, randomness almost always exists in the system behavior. Thus, to mimic this behavior, simulation requires random numbers as inputs. Simulation that involves random numbers is known as Monte Carlo simulation.

Simulation can be used for analyzing any system. However, the accuracy of the results depends on the number of iterations and the complexity of the system. Analytical methods that are based on advanced algorithms are generally quicker and produce more accurate results than simulation. Therefore, when possible, using analytical methods is better. However, if analytical results are infeasible, or if algorithms are so complex that results are prone to numeric round-off errors, then simulation should be used.