基于贝叶斯方法小批量生产的统计过程控制研究

发布时间：2018-11-02 15:21

【摘要】：小批量生产过程主要特点是信息缺乏,而传统的SPC统计技术适用于大批量的连续生产,因此无法对其进行质量控制。本文基于贝叶斯理论对小批量生产环境下的统计过程控制进行研究,提出了贝叶斯控制图和贝叶斯过程能力指数,能有效解决小批量生产环境下因样本量少无法建立有效质量控制模型的难题。一般情况下,当生产过程稳定受控时,同一条生产线上或相同生产条件下生产的相同规格产品质量特性的先验信息与后验信息均服从同一正态分布。基于此,本文根据贝叶斯理论推导出均值、极差和标准差的迭代计算公式,并将其运用于统计过程控制,进而得到控制图控制线以及过程能力指数和不合格品率的计算公式。在实证部分,一方面利用Matlab仿真技术比较休哈特方法和贝叶斯方法应用于均值-极差(RX?)控制图和均值—标准差(SX?)控制图的差异性,结果显示随着批次的增加,基于贝叶斯方法的统计控制图控制线比休哈特方法更接近控制线的实际值;另一方面,选用实际案例,分别用贝叶斯方法和常规方法计算某电子企业小批量制造过程的过程能力指数和不合格品率,通过与过程能力指标和不合格品率指标的比较来验证贝叶斯方法的可靠性,结果表明随着批次的增加,常规方法计算的过程能力指数Cpk在1.33和1.67之间,过程能力处于理想状态,而贝叶斯方法计算的Cpk却小于1.33,生产线需发出警告;同时贝叶斯方法计算的不合格品率相较于常规方法大大提高,因此将贝叶斯方法运用于过程能力分析,更能准确预警生产线不合格品的产生,比传统SPC技术更加可靠、有效。
[Abstract]:The main feature of the small batch production process is the lack of information, but the traditional SPC statistical technology is suitable for the continuous production of large quantities, so it is impossible to control the quality of the small batch production process. In this paper, based on Bayesian theory, the statistical process control in small batch production environment is studied, and the Bayesian control chart and Bayesian process capability index are proposed. It can effectively solve the problem of establishing an effective quality control model because of the small sample size in small batch production environment. In general, when the production process is stable and controlled, the prior information and the posterior information of the same specification products produced on the same production line or under the same production conditions are subject to the same normal distribution. Based on this, the iterative formulas of mean value, range deviation and standard deviation are derived according to Bayesian theory, and applied to statistical process control, and then the control line of control chart and the calculation formulas of process capability index and unqualified product rate are obtained. In the empirical part, on the one hand, the Matlab simulation technology is used to compare the Heinhart method and Bayesian method in the mean range (RX?). Control Chart and Mean-Standard deviation (SX?) The difference of control chart shows that with the increase of batches, the control line of statistical control chart based on Bayesian method is closer to the actual value of control line than that of Shewhart method. On the other hand, the Bayesian method and the conventional method are used to calculate the process capability index and unqualified product rate of a small batch manufacturing process in an electronic enterprise. The reliability of Bayesian method is verified by comparing with process capability index and nonconforming product rate index. The results show that the process capability index (Cpk) calculated by conventional method is between 1. 33 and 1. 67 with the increase of batches. The process capability is in ideal condition, but the Cpk calculated by Bayesian method is less than 1.33, so the production line should be warned. At the same time, the rate of unqualified products calculated by Bayesian method is much higher than that of conventional method. Therefore, applying Bayesian method to process capability analysis is more reliable and effective than traditional SPC technology.
【学位授予单位】：中国计量学院
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F224;F407.63;F273

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