Bayesian approach is commonly used in the reliability assessment of repairable systems with small samples in fields such as aerospace. The knowledge about the informative prior and/or failure data from repairable systems may not be collected as precisely as possible due to uncertain factors, but can be obtained in terms of lower and upper bounds. For the case of such interval uncertainty information, this paper studies the Bayesian reliability analysis approach of multiple repairable systems whose failure process follow the power law process (PLP). Under the informative priors, the interval-based Bayesian posterior analysis of the PLP is essentially transformed into solving the constrained optimization problem in which the objective function is just the traditional Bayesian posterior analysis result of the PLP under the informative priors. Considering that the objective function in the constrained optimizations is complicated multiple integrals with no closed-form expressions and is highly nonlinear, the covariance matrix adaptation evolution strategy is employed to find the optimal solution of the optimization problem. Specific engineering examples verify the feasibility and effectiveness of the proposed approach. The proposed interval-based Bayesian approach of the PLP can provide a reference method for the reliability assessment of repairable systems with small samples in consideration of the influence of uncertain factors.