A nonparametric approach to modeling dependence among production parameters for energy cost estimation

Dependence existing among production parameters can significantly affect energy costs. For material removal processes, processing times and material amounts to be cut have positive dependence, and the dependence can affect energy costs by varying a peak electricity load. Existing methods to model the dependence of production parameters are based on parametric approaches that cannot accurately represent the dependence due to the rigid nature of parametric models. To address this issue, this study proposes a method to quantify dependence among manufacturing parameters through the application of the empirical copula to the dependence between the milling processing time and the amount of volume to be cut. The proposed method is illustrated by a case study of a manufacturing facility consisting of milling machines; a total of 27 scenarios are simulated for energy cost estimations. The case study clearly shows that the proposed method can capture the dependence between the milling parameters more accurately than a conventional dependence measure from parametric correlation models. The findings from this study would be useful to estimate energy costs in that the proposed method provides a better fit to real production data than conventional parametric approaches can.