Contour Approach for Analysis of Minimum Regions for the Economic Statistical Design of X-Bar Control Charts
- 1 Department of Logistics and Supply Chain Management, Universidad Popular Autonoma del Estado de Puebla, UPAEP, Puebla, Mexico
- 2 Faculty of Business Administration, University of New Brunswick, Fredericton, Canada
Abstract
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.
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