The reliability of a non series-parallel system of five components is computed by providing different flow of information through a single component. The logic diagram technique is used to develop simple parallel paths (called duplication paths) between IN and OUT terminals according to the flow of information. Each path contains components whose successful operation can lead to the success of the system. The paths which dominate over the other paths in the logic diagram are ignored as these paths have no effect on reliability of the system. The failure rates of the components follow Weibull distribution. The expressions for reliability and mean time to system failure (MTSF) are derived to highlight the effect of operating time, failure rate and shape parameter for their arbitrary values on these measures.