System-reliability confidence-intervals for complex-systems with estimated component-reliability

A flexible procedure is described and demonstrated to determine approximate confidence intervals for system reliability when there is uncertainty regarding component reliability information. The approach is robust, and applies to many system-design configurations and component time-to-failure distributions, resulting in few restrictions for the use of these confidence intervals. The methods do not require any parametric assumptions for component reliability or time-to-failure, and allows type-I or -II censored data records. The confidence intervals are based on the variance of the component and system reliability estimates and a lognormal distribution assumption for the system reliability estimate. This approach applies to any system design which can be decomposed into series and/or parallel connections between the components. To evaluate the validity of the confidence limits, numerous simulations were performed for two hypothetical systems with different data sample-sizes and confidence levels. The test cases and empirical results demonstrate that this new method for estimating confidence intervals provides good coverage, can be readily applied, requires only minimal computational effort, and applies for a much greater range of design configurations and data types compared to other methods. For many design problems, these confidence intervals are preferable because there is no requirement for an exponential time-to-failure distribution nor are component data limited to binomial data.