Reliability　performance,　especially　the　lower　confidence　limit　of　reliability,　plays　an　important　role　in　reliability　assessment,　and　it　is　also　of　concern　to　researchers　and　engineers.　In　this　article,　a　novel　estimate　of　the　lower　confidence　limit　of　the　reliability　for　two-parameter　Weibull　distribution　is　proposed　based　on　the　generalized　fiducial　inference.　The　corresponding　adaptive　Metropolis-Hastings　within　Gibbs　algorithm　is　provided　to　analyze　the　generalized　fiducial　lower　confidence　limit.　The　proposed　lower　confidence　limit　of　the　reliability　is　compared　with　that　from　frequentist　method.　In　addition,　this　novel　procedure　is　generalized　to　the　series　system　and　the　parallel　system　which　consists　of　identical　Weibull　components.　Simulation　results　show　that　the　proposed　generalized　fiducial　lower　confidence　limit　is　more　applicable　than　the　frequentist　method,　especially　for　the　case　of　small　sample　size.　Finally,　the　MOS　transistor　lifetime　data　is　used　to　illustrate　the　new　procedure.