Abstract: ARMA control chart is an effective quality monitoring tool for autocorrelated process. In order to optimize the efficiency and cost of the monitoring scheme of ARMA control chartsimultaneously, calculating methods of average run length and quality cost of the ARMA control chart are analyzed respectively, and a multi-objective optimization design model of the ARMA control chart is established in this paper. Using NSGA-Ш intelligent optimization algorithm, the calculating method of this model is illustrated by a numerical sample, and the noninferior solution sets of multi-objective optimization design are given for different degree of process shifts. Then the sensitivity analysis method is used to study the influence of six main design parameters on the efficiency and cost of the monitoring schemeseparately. Finally, the advantages of the multi-objective design method proposed in this paper are illustrated by comparing and analyzing other optimal design schemes of ARMA control chart.

Key words: ARMA control chart, multi-objective optimization, autocorrelated process, average run length

摘要： ARMA控制图是一种有效的自相关过程质量监控方法,为了能够同时对ARMA控制图监控方案的效率和成本进行优化,本文分别研究了ARMA控制图的平均运行长度和质量成本的计算方法,并由此建立了ARMA控制图的多目标优化设计模型。采用NSGA-Ш智能优化算法,通过一个具体的算例对该模型的计算方法进行了说明,针对不同程度的过程偏移给出了多目标优化设计的非劣解解集。然后通过灵敏度分析的方法研究了模型中的主要设计参数对监控方案的效率和成本的影响程度。最后,通过与其它几种ARMA控制图优化设计方案的比较分析,说明了本文提出的设计方法的优势。

关键词: ARMA控制图, 多目标优化, 自相关过程, 平均运行长度