Visualization of the patterns or behaviors of complex functions is an important approach to identifying their solution spaces. This approach can lead to improving the design of search algorithms for optimization purposes. This paper presents a 2D visualization method based on minimum cost scores (MCS) to identify the most likely regions to find optimal values for the economic statistical design of X-bar control charts. Uniform sampling was considered for the analysis of the cost function of Rahim and Banerjee (1993). Elliptical regions were found to model the minimum regions defined by MCS values estimated for this cost function through different values of sample size (n), length of the sampling interval (h) and coefficient of the control chart’s limits (L). This method was assessed by finding the optimal set of n and h values within these elliptical regions. Optimal values reported in the literature with Genetic Algorithms (GA) were considered for this case. It was observed that the optimal values were located within the boundaries of the elliptical regions and were associated with sub-regions with the highest MCS values. This confirms the suitability of this approach to obtain the a-priori estimation of the solution space.
References
[1]
Caballero-Morales, S. (2014). Building Cost Function 3D Benchmarks to Improve the Economic Statistical Design of Control Charts. Mathematical Problems in Engineering, 2014, 1-20. https://doi.org/10.1155/2014/879456
[2]
Caballero-Morales, S., & Rahim, A. (2015). Analyzing the Effect of Non-Normality on the Solution Space for the Economic Statistical Design of X-Bar Control Charts. In 2015 International Conference on Industrial Engineering and Operations Management (IEOM) (pp. 1-6). IEEE. https://doi.org/10.1109/ieom.2015.7093766
[3]
Chih, M., Yeh, L., & Li, F. (2011). Particle Swarm Optimization for the Economic and Economic Statistical Designs of the Control Chart. Applied Soft Computing, 11, 5053-5067. https://doi.org/10.1016/j.asoc.2011.05.053
[4]
Goel, A., Baker, C. A., Shaffer, C. A., Grossman, B., Mason, W. H., Watson, L. T. et al. (2001). Vizcraft: A Problem-Solving Environment for Aircraft Configuration Design. Computing in Science & Engineering, 3, 56-66. https://doi.org/10.1109/5992.895188
[5]
Halim, S., & Yap, R. H. C. (2007). Designing and Tuning SLS through Animation and Graphics: An Extended Walk-Through. In T. Stützle, M. Birattari, & H. Hoos (Eds.), Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics (pp. 16-30). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-74446-7_2
[6]
Halim, S., Yap, R., & Lau, H. (2006). Visualization for Analysing Trajectory-Based Meta-heuristic Search Algorithms. In Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006) (pp. 703-704). IOS Press.
[7]
Pérez, J., Almanza, N., Hidalgo, M., Vela, G., Alvarado, L., García, M., Mexicano, A., & Zavala, C. (2013). A Graphical Visualization Tool for Analyzing the Behavior of Metaheuristic Algorithms. International Journal of Emerging Technology and Advanced Engineering, 3, 32-36.
[8]
Rahim, M. A., & Banerjee, P. K. (1993). A Generalized Economic Model for the Economic Design of Control Charts for Production Systems with Increasing Failure Rate and Early Replacement. Naval Research Logistics, 40, 787-809. https://doi.org/10.1002/1520-6750(199310)40:6<787::aid-nav3220400605>3.0.co;2-4
[9]
Wang, Q., & Saunders, B. (1999). Interactive 3D Visualization of Mathematical Functions Using VRML (pp. 1-7). U.S. Dept. of Commerce Technology Administration, National Institute of Standards and Technology, U.S. Dept. of Energy.
[10]
Wang, S., Interrante, V., & Longmire, E. (2010). Multivariate Visualization of 3D Turbulent Flow Data. In SPIE Proceedings. SPIE. https://doi.org/10.1117/12.839093
