Variance of system-reliability estimates with arbitrarily repeated components

A model is developed to determine the variance of system reliability estimates and to estimate confidence intervals for series-parallel systems with arbitrarily repeated components. For these systems, different copies of the same component-type are used several or many times within the system, but only a single reliability estimate is available for each distinct component-type. The single estimate is used everywhere the component appears in the system design, and component estimation-error is then magnified at the system-level. The "system-reliability estimate" variance and confidence intervals are derived when the number of component failures follow the binomial distribution with an unknown, yet estimable, probability of failure. The "system-reliability estimate" variance and confidence intervals are obtained by expressing system reliability as a linear sum of products of higher order moments for component unreliability. The generating function is used to determine the moments of the component-unreliability estimates. This model is preferable for many system reliability estimation problems because it does not require independent component and subsystem reliability estimates; it is demonstrated with an example.