A Study of Stopping Rules in the Steepest Ascent Methodology for the Optimization of a Simulated Process

Abstract

first_pagesettingsOrder Article Reprints Open AccessArticle A Study of Stopping Rules in the Steepest Ascent Methodology for the Optimization of a Simulated Process by Paulo Eduardo García-Nava *,†ORCID,Luis Alberto Rodríguez-Picón †ORCID,Luis Carlos Méndez-GonzálezORCID andIván Juan Carlos Pérez-OlguínORCID Department of Industrial Engineering and Manufacturing, Autonomous University of Ciudad Juárez, Av. del Charro no. 450 Nte. Col. Partido Romero, Ciudad Juárez 32310, Chihuahua, Mexico * Author to whom correspondence should be addressed. † These authors contributed equally to this work. Axioms 2022, 11(10), 514; https://doi.org/10.3390/axioms11100514 Received: 5 September 2022 / Revised: 23 September 2022 / Accepted: 24 September 2022 / Published: 29 September 2022 (This article belongs to the Special Issue Applied Optimization and Decision Analysis on Interdisciplinary Areas) Download Browse Figures Review Reports Versions Notes Abstract Competitiveness motivates organizations to implement statistical approaches for improvement purposes. The literature offers a variety of quantitative methods intended to analyze and improve processes such as the design of experiments, steepest paths and stopping rules that search optimum responses. The objective of this paper is to run a first-order experiment to develop a steepest ascent path to subsequently apply three stopping rules (Myers and Khuri stopping rule, recursive parabolic rule and recursive parabolic rule enhanced) to identify the optimum experimentation stop from two different simulated cases. The method includes the consideration of the case study, the fitting of a linear model, the development of the steepest path and the application of stopping rules. Results suggest that procedures’ performances are similar when the response obeys a parametric function and differ when the response exhibits stochastic behavior. The discussion section shows a structured analysis to visualize these results and the output of each of the stopping rules in the two analyzed cases.