Optimal centering and tolerance design for correlated variables

This paper proposes a procedure for the concurrent optimization of design centering and tolerances. The novelty of the proposal is that it takes into account the covariance structure of the variables, which is estimated from the manufacturing process. The procedure can be interpreted as a process of recentering of the design factors such that the tolerances can be maximized without incurring in quality losses. The optimal parameters and tolerances are found by solving an optimization problem where the sum of the tolerances is maximized and where the covariance matrix of the variables is used in the optimization process. By taking the covariance matrix into account, the solution is more compatible with the manufacturing process, allowing larger tolerances with the same cost. The added complexity due to the use of the dependence structure of the process is solved by applying a singular value decomposition to the covariance matrix. This decomposition transforms the original dependent variables into uncorrelated factors, making the optimization problem more tractable. Some examples are provided illustrating the benefits of the proposal.