Abstract: This study considers the reliability of a multicomponent stress-strength model involving one stress and multiple strengths from a series system. We derive the Jeffreys prior when the stress and strength variables follow Weibull distribution with a common shape parameter. The necessary and sufficient conditions of the propriety of the posterior distribution based on the Jeffreys prior are obtained. Lindley's approximation and Markov chain Monte Carlo method are presented to obtain the estimates of the system reliability. The performance of the proposed methods is evaluated by Monte Carlo simulation. The simulation results show the Bayesian method outperforms maximum likelihood method, especially in the case of a small sample size. Finally, a real dataset is analyzed for illustration.