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Mathematical Problems in Engineering
Volume 2014, Article ID 879456, 20 pages
Research Article

Building Cost Function 3D Benchmarks to Improve the Economic Statistical Design of Control Charts

Technological University of the Mixteca, Road to Acatlima K.m. 2.5, 69000 Huajuapan de León, OAX, Mexico

Received 8 May 2014; Revised 12 September 2014; Accepted 14 September 2014; Published 9 November 2014

Academic Editor: Pandian Vasant

Copyright © 2014 Santiago-Omar Caballero-Morales. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Shewhart or control charts are important Statistical Process Control (SPC) techniques used for prompt detection of failures in a manufacturing process and minimization of production costs which are modelled with nonlinear functions (cost functions). Heuristic methods have been used to find the chart’s parameters integrated within the cost function that best comply with economic and statistical restrictions. However heuristic estimation is highly dependent on the size of the search space, the set of initial solutions, and the exploration operators. In this paper the 3D analysis of the cost function is presented to more accurately identify the search space associated with each parameter of control charts and to improve estimation. The parameters estimated with this approach were more accurate than those estimated with Hooke and Jeeves (HJ) and Genetic Algorithms (GAs) under different failure distributions. The results presented in this work can be used as a benchmark to evaluate and improve the performance of other heuristic methods.