Regular Article

Robust design optimization of dynamic and static manufacturing processes using the stochastic frontier model

¹ Laboratory of Mechanics, Production and Energetics (LR18ES01), University of Tunis, Higher National Engineering School of Tunis, 5 Av. Taha Hussein, BP. 56. Bâb Manara, 1008 Tunis, Tunisia
² ICube Laboratory, UMR 7357 CNRS, Mechanics Department, University of Strasbourg, 67000 Strasbourg, France

* e-mail: jmal@unistra.fr

Received: 15 October 2023
Accepted: 8 November 2024

Abstract

The paper discusses a novel method, which addresses robust design optimization of dynamic and static multi-objective processes. For a dynamic process, the optimal setting of the graded signal and input parameters are sought so that it is least sensitive to internal and external noises. In addition to addressing planned and unplanned experiments (cross-sectional and panel data), the method estimates the random and nonrandom variance components variably (i.e., returns a non-constant uncertainty at each combination level or treatment). The stochastic frontier model is utilized to ensure this purpose. For dynamic processes, the method operates in three main steps, (i) data preparation by transforming the outputs to maximization functions, (ii) estimate of the composed variation (random and non-random error components), (iii) and, composition of the process uncertainty array for each output across the signal levels. The robust design optimization solution corresponds to the levels combination of the signal and the input factors, which adds up to the lowest global uncertainty score. The applicability of the approach is then illustrated with a case study that uses one signal factor at two levels and four input factors (x1, x2, x3, and x4) at three levels each. The process responses, Y1, Y2, and Y3 are of types Dynamic Larger the Best (DLB), Dynamic Nominal the Best (DNB), and Dynamic Smaller the Best (DSB), respectively.