The present paper addresses the problem of interval estimation of model parameters under a common scale setup for two Weibull populations having different and unknown shapes. The maximum likelihood estimators (MLEs) of the model parameters have been obtained numerically as the closed forms do not exist. Using the information matrix of the model, the asymptotic confidence intervals have been constructed. The parametric bootstrap intervals, namely, the bootstrap-p and bootstrap-t, are derived. The highest posterior density intervals using the Markov chain Monte Carlo procedure have been derived. Numerical simulation is performed to see the performance of these proposed methods. A real-life example is considered for the purpose of illustration.