Product weights can be statistically related to controllable and uncontrollable factors of the production processes. Uncontrollable factors may be correlated with controllable factors. We fitted a response surface approximator of product weights and found sub-optimal controllable factors’ values that minimize product weight. Furthermore, we found that the uncertainty of uncontrollable variables and the correlation among them may affect the result of product weight minimization. The company may implement these findings to reduce the cost of production. Also, we formulated a fully Bayesian experimental design problem to minimize product weight tolerance limits and built hierarchical models. Posterior distributions of the hierarchical models’ parameters can be simulated by a Gibbs sampler. However, we conclude that the effectiveness and convergence of the Gibbs sampler may not be robust to candidate design settings while searching over the design space to solve the experimental design problem.