Estimation of process parameter variations in a pre-defined process window using a Latin hypercube method

The aim of this paper is to present a methodology that provides an analytical tool for estimation of robustness and response variation within a pre-defined process window. To exemplify the developed methodology, the stochastic simulation technique is used for a sheet-metal forming application. A sampling plan based on the Latin hypercube sampling method for variation of design parameters is utilized, and the thickness reduction is specified as the response. Moreover, the response surface methodology is applied for understanding the quantitative relationship between design parameters and response value. The conclusions of this study are that the applied method gives a possibility to illustrate and interpret the variation of the response versus a design parameter variation. Consequently, it gives significant insights into the usefulness of individual design parameters. It has been shown that the method enables us to estimate the admissible design parameter variations and to predict the actual safe margin for given process parameters. Furthermore, the dominating design parameters can be predicated using sensitivity analysis, and this in its turn clarifies how the reliability criteria are met. Finally, the developed software can be used as an additional module for set-up of stochastic finite element simulations and to collect the numerical results from different solvers within different applications.