Multi-objective economic-statistical design of simple linear profiles using a combination of NSGA-II, RSM, and TOPSIS

Abstract

A multi-objective economic-statistical design is aimed in this article for simple linear profiles. In this design, the interval between two successive sampling intervals, the sample size and the number of adjustment points alongside, the parameters of the monitoring scheme are determined such that not only the implementation cost is minimized, but also the profile exhibits desired statistical performances. To this aim, three objective functions are considered in the multi-objective optimization model of the problem. The Lorenzen–Vance cost function is used to model the implementation cost as the first objective function to be minimized. The second objective function maximizes the in-control average run length of the monitoring scheme (ARL0 ), while the third objective function minimizes the out-of-control average run length (ARL1 ). In addition, a lower bound is defined in a constraint for ARL0 and an upper bound is determined in another constraint for ARL1. The complex multi-objective optimization problem is solved by an NSGA-II algorithm, whose parameters are tuned using response surface methodology (RSM). A numerical illustration is solved, for which the Pareto optimal solutions are ranked by a multi-criteria decision-making method called Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Finally, sensitivity analyses are conducted on the parameters of the cost function, based on which the time required to sample and create a profile is the most important factor.