Maryam Fazelimoghadam - Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Mohammad Javad Ershadi - Department of Information Technology, Iranian Research Institute for Information Science and Technology (IRANDOC), Tehran, Iran
Seyed Taghi Akhavan Niaki - Department of Industrial Engineering , Sharif University of Technology, Tehran, Iran

Statistically constrained economic design for profiles usually refers to the selection of some parameters such as the sample size, sampling interval, smoothing constant, and control limit for minimizing the total implementation cost while the designed profiles demonstrate a proper statistical performance. In this paper, the Lorenzen-Vance function is first used to model the implementation costs. Then, this function is extended by the Taguchi loss function to involve intangible costs. Next, a multi-objective particle swarm optimization (MOPSO) method is employed to optimize the extended model. The parameters of the MOPSO are tuned using response surface methodology (RSM). In addition, data envelopment analysis (DEA) is employed to find efficient solutions among all near-optimum solutions found by MOPSO. Finally, a sensitivity analysis based on the principal parameters of the cost function is applied to evaluate the impacts of changes on the main parameters. The results show that the proposed model is robust on some parameters such as the cost of detecting and repairing an assignable cause, variable cost of sampling, and fixed cost of sampling.

Economic-statistical design, Linear profiles, Quadratic loss function, Data Envelopment Analysis (DEA), MOPSO, Response Surface Methodology (RSM)