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A Genetic Algorithm Approach To Determine The Sample Size For Control Charts With Variables And Attributes

机译：确定带有变量和属性的控制图样本量的遗传算法

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摘要

Generally today's production systems consist of multistage processes. Control of these processes is a very important to meet customer's and engineering's specifications. Generally control charts which are used to monitor the process and process capability analysis (PCA) which is a summary statistic to show the process performance are used to determine whether or not the process is in statistical control and meet specifications. Although control charts have been applied in very large area of process control, determining the sample size for control charts is generally a problem. In the literature many techniques to solve this problem have been executed. Kaya and Engin [Kaya, I. & Engin, O. 2007. A new approach to define sample size at attributes control chart in multistage processes: An application in engine piston manufacturing process. Journal of Materials Processing Technology, 183,38-48] also proposed a model based on minimum cost and maximum acceptance probability to determine the sample size in AttributernControl Charts (ACCs). In this paper, this model is solved by Genetic Algorithms (GAs) with linear real-valued representation and a new chromosome structure is suggested to increase the efficiency of GAs. The performance of GAs is affected by mutation and crossover operators and their ratios. To determine the most appropriate operators, five different mutation and crossover operators are used and they are compared with each other. For this purpose a computer program is coded by MS Visual Basic and it has been run to determine the suitable operators and ratios, respectively. One of the results of the model is sample size, n, and it is suggested to set up ACCs and Variable Control Charts (VCCs). Also the sample size, n, is used to PCA. To show the usage of the proposed model an application from a motor engine factory is illustrated. For quality characteristics cannot be easily represented in numerical form, "u-control charts" and for characteristics measurable on numerical scales, "x - R control charts" are constructed for every stage by taking into account the sample size, n, determined by GAs from the proposed model. These control charts are used to determine whether or not the every stage is in statistical control. Then PCA has been executed for every stage and capability ratios are determined.
机译：通常，当今的生产系统由多阶段过程组成。这些过程的控制对于满足客户和工程规范非常重要。通常，用于监视过程和过程能力分析（PCA）的控制图是用来显示过程性能的摘要统计信息，用于确定过程是否处于统计控制中并符合规格。尽管控制图已应用于非常大的过程控制领域，但是确定控制图的样本大小通常是一个问题。在文献中已经执行了许多解决该问题的技术。 Kaya and Engin [Kaya，I.＆Engin，O.2007。一种在多阶段过程中的属性控制图中定义样本大小的新方法：在发动机活塞制造过程中的应用。材料加工技术杂志，183,38-48]还提出了一种基于最小成本和最大接受概率的模型，用于确定Attributern控制图（ACC）中的样本量。在本文中，该模型通过具有线性实值表示的遗传算法（GA）进行了求解，并提出了一种新的染色体结构以提高GA的效率。遗传算法的性能受变异和交叉算子及其比率的影响。为了确定最合适的运算符，使用了五个不同的变异和交叉运算符，并将它们相互比较。为此，计算机程序由MS Visual Basic编码，并且已运行该计算机程序来分别确定合适的运算符和比率。该模型的结果之一是样本量n，建议设置ACC和变量控制图（VCC）。样本大小n也用于PCA。为了显示所提出模型的用法，举例说明了一家汽车发动机厂的应用程序。对于无法通过数字形式轻松表示的质量特征，“ u控制图”；对于可在数字刻度上测量的特征，通过考虑由GA确定的样本量n，为每个阶段构建“ x-R控制图”从提出的模型中这些控制图用于确定每个阶段是否处于统计控制中。然后，已经针对每个阶段执行了PCA，并确定了能力比率。

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