An economic-statistical design of simple linear profiles with multiple assignable causes using a combination of MOPSO and RSM

Ershadi, M. J ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1007/s00500-021-05854-7
  3. Publisher: Springer Science and Business Media Deutschland GmbH , 2021
  4. Abstract:
  5. An economic-statistical design with multiple assignable causes following exponential distribution is presented in this paper for linear profiles. For this purpose, a tri-objective optimization model is proposed to minimize the cost with desired statistical performances. Average Run Length (ARL) as the primary statistical measure is employed for the appraisal of the designed linear profiles. The first objective to be minimized is a cost function that models the implementation cost in different states. The second objective is to maximize ARL or the in-control average run-length of the monitoring scheme. The third objective to be minimized is ARL 1 or the out-of-control average run-length of the control chart. Besides, there are two constraints defined as the lower and the upper bounds on ARL and ARL 1, respectively. This model optimizes the sample size, the sampling intervals, and related parameters for assignable causes concerning exponential distribution. As the problem is hard to solve analytically, a parameter-tuned meta-heuristic solution algorithm involving a multiple objective particle swarm optimization (MOPSO) alongside the response surface methodology (RSM) is employed to find a near-optimum solution. In this meta-heuristic, the response surface methodology is utilized to tune the parameters of the optimization problem. A numerical example is presented to illustrate the application of the proposed approach and assess its performance. Finally, sensitivity analyses of some parameters on the effects of the design parameters are performed. The results show the parameter profiling cost per set-points of a sample has the most effective implementation costs of linear profiles. Also, the proposed model is robust on some parameters such as the cost of identifying and modifying an assignable cause, fixed cost of sampling, and variable cost of the sampling process. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature
  6. Keywords:
  7. Cost accounting ; Cost functions ; Heuristic algorithms ; Heuristic methods ; Particle size analysis ; Particle swarm optimization (PSO) ; Robustness (control systems) ; Sensitivity analysis ; Surface properties ; Economic statistical design ; Exponential distributions ; Identifying and modifying ; Multiple objective particle swarm optimizations ; Objective optimization ; Optimization problems ; Response surface methodology ; Statistical performance ; Multiobjective optimization
  8. Source: Soft Computing ; Volume 25, Issue 16 , 2021 , Pages 11087-11100 ; 14327643 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s00500-021-05854-7