多源异构灰数据背景下的贝叶斯迭代优化控制图模型
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摘要
在统计过程控制中,为了利用专家信息减少不确定性,并在控制图模型中将不同属性的专家先验信息结合起来综合利用,提出一种新的广义标准灰数概念,将不同属性的专家信息结合在同一个空间上,用统一架构进行表征,并提出新的运算法则来计算这些多源异构的专家灰信息.结合经典贝叶斯理论,在灰数据背景下对统计质量控制图模型进行参数估计,并利用累积样本信息对参数进行迭代优化,使灰色区域不断收敛,降低不确定性.实例分析结果表明,这种灰贝叶斯迭代优化模型可以在小样本贫信息的情况下减少监测数据的异常波动,更准确地利用专家信息进行预警,并在样本累积过程中逐步偏重于实际数据,得到符合新样本信息的参数.
In the statistical process control, in order to make use of expert information to reduce uncertainty, and to make comprehensive use of the prior information of different attributes in the control charts model, a new concept of general standard grey number is proposed to combine all these expert information and transform them into one space. Besides,a mathematical framework is established to characterize the information, and new rules of operation are proposed to calculate the multi-source heterogeneous grey information. Then, based on the classic Bayesian theory, parameters of the statistical quality control chart are estimated under the background of grey information, and cumulative sample data is used to optimize the parameters in an iterative approach, while expert grey information degenerating with data accumulation. The result shows that this model is able to reduce abnormal fluctuation and false alert, and gradually relies more on actual data.
In the statistical process control, in order to make use of expert information to reduce uncertainty, and to make comprehensive use of the prior information of different attributes in the control charts model, a new concept of general standard grey number is proposed to combine all these expert information and transform them into one space. Besides,a mathematical framework is established to characterize the information, and new rules of operation are proposed to calculate the multi-source heterogeneous grey information. Then, based on the classic Bayesian theory, parameters of the statistical quality control chart are estimated under the background of grey information, and cumulative sample data is used to optimize the parameters in an iterative approach, while expert grey information degenerating with data accumulation. The result shows that this model is able to reduce abnormal fluctuation and false alert, and gradually relies more on actual data.
引文
[1]仲建兰,马义中.面向小批量生产过程的两阶段串联可修系统SPC与维修策略整合优化[J].计算机集成制造系统,2014,20(8):1959-1968.(Zhong J L,Ma Y Z.Integrated optimization for SPC and maintenance strategy of two-stage series repairable systems oriented to short-run production[J].Computer Integrated Manufacturing Systems,2014,20(8):1959-1968.)
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[5]张根保,冉琰.基于模糊物元的小批量生产典型工序能力分析[J].机械工程学报,2015,51(23):116-122.(Zhang G B,Ran Y.Typical process capability analysis of small-batch production based on fuzzy matter-element[J].J of Mechanical Engineering,2015,51(23):116-122.)
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[10]Wu X,Miao R,Zhang X,et al.A conjugate Bayesian approach to control chart for multi-batch and low volume production[J].Int J of Production Research,2015,53(7):2179-2185.
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[13]刘思峰,方志耕,谢乃明.基于核和灰度的区间灰数运算法则[J].系统工程与电子技术,2010,32(2):313-316.(Liu S F,Fang Z G,Xie N M.Algorithm rules of interval grey numbers based on the“Kernel”and the degree of greyness of grey numbers[J].Systems Engineering and Electronics,2010,32(2):313-316.)
[14]刘解放,刘思峰,方志耕.基于核与灰半径的连续区间灰数预测模型[J].系统工程,2013,31(2):61-64.(Liu J F,Liu S F,Fang Z G.Prediction model of continuous interval grey number based on the kernel and gray radius[J].Systems Engineering,2013,31(2):61-64.)
[15]郭晓君,刘思峰,方志耕.基于合成灰数灰度的区间灰数自忆性预测模型[J].系统工程与电子技术,2014,36(6):1124-1129.(Guo X J,Liu S F,Fang Z G.Self-memory prediction model of interval grey number based on grey degree of compound grey number[J].Systems Engineering and Electronics,2014,36(6):1124-1129.)
[16]Yang Y,John R.Grey sets and greyness[J].Information Sciences,2012,185(1):249-264.
[17]徐美萍,熊令纯.Levy分布参数估计的损失函数和风险函数的Bayes推断[J].数学的实践与认识,2009,39(20):221-226.(Xu M P,Xiong L C.Bayes inference for the loss and risk function in Levy distribution parameter estimation[J].Mathematics in Practice and Theory,2009,39(20):221-226.)
[18]周建,李子奈.Granger因果关系检验的适用性[J].清华大学学报:自然科学版,2004,44(3):358-361.(Zhou J,Li Z N.Applicability of the Granger causality test[J].J of Tsinghua University:Science and Technology,2004,44(3):358-361.)
[19]Miao R,Zhang X Y,Jiang Z B,et al.The Bayesian estimation of process capability indices for multi-batch and low volume manufacturing[J].Chinese High Technology Letters,2011,21(7):770-774.
[20]Wang Z J,Zou C L,Li Z H.Theory and method of statistical quality control chart[M].Beijing:Science Press,2013:54-59.
[2]姜兴宇,王世杰,赵凯,等.面向网络化制造的智能工序质量控制系统[J].机械工程学报,2010,46(4):186-194.(Jiang X Y,Wang S J,Zhao K,et al.Intelligent process quality control system for networked manufacturing[J].J of Mechanical Engineering,2010,46(4):186-194.)
[3]单龙艳,吉卫喜,余杰,等.高性能零件制造过程质量控制方法研究[J].现代制造工程,2013,35(12):60-64.(Shan L Y,Ji W X,Yu J,et al.Process quality control methods for the manufacture of high-performance parts[J].Modern Manufacturing Engineering,2013,35(12):60-64.)
[4]章欣已.基于贝叶斯估计多品种小批量生产的统计过程控制研究[D].上海:上海交通大学机械与动力工程学院,2013:22-23.(Zhang X Y.Statistical process control for job shop manufacturing with bayesian approach[D].Shanghai:School of Mechanical Engineering,Shanghai Jiaotong University,2013:22-23.)
[5]张根保,冉琰.基于模糊物元的小批量生产典型工序能力分析[J].机械工程学报,2015,51(23):116-122.(Zhang G B,Ran Y.Typical process capability analysis of small-batch production based on fuzzy matter-element[J].J of Mechanical Engineering,2015,51(23):116-122.)
[6]Xiang Y.Joint optimization of X-control chart and preventive maintenance policies:A discrete-time Markov chain approach[J].European J of Operational Research,2013,229(2):382-390.
[7]张鹏伟,苏秦,王甜甜.小批量生产过程VSI控制图经济设计[J].系统工程理论与实践,2013,33(5):1185-1191.(Zhang P W,Su Q,Wang T T.Economic design of VSI control chart for short-run production[J].Systems Engineering—Theory&Practice,2013,33(5):1185-1191.)
[8]Tagaras G.Dynamic control charts for finite production runs[J].European J of Operational Research,1996,91(1):38-55.
[9]Nenes G,Tagaras G.The economically designed two-sided Bayesian,X-bar math container loading mathjax,control chart[J].European J of Operational Research,2007,183(1):263-277.
[10]Wu X,Miao R,Zhang X,et al.A conjugate Bayesian approach to control chart for multi-batch and low volume production[J].Int J of Production Research,2015,53(7):2179-2185.
[11]Naderkhani F,Makis V.Economic design of multivariate Bayesian control chart with two sampling intervals[J].Int J of Production Economics,2016,174(4):29-42.
[12]方志耕,刘思峰,陆芳,等.区间灰数表征与算法改进及其GM(1,1)模型应用研究[J].中国工程科学,2005,7(2):57-61.(Fang Z G,Liu S F,Lu F,et al.Study on improvement of token and arithmetic of interval grey numbers and its GM(1,1)model[J].Engineering Sciences,2005,7(2):57-61.)
[13]刘思峰,方志耕,谢乃明.基于核和灰度的区间灰数运算法则[J].系统工程与电子技术,2010,32(2):313-316.(Liu S F,Fang Z G,Xie N M.Algorithm rules of interval grey numbers based on the“Kernel”and the degree of greyness of grey numbers[J].Systems Engineering and Electronics,2010,32(2):313-316.)
[14]刘解放,刘思峰,方志耕.基于核与灰半径的连续区间灰数预测模型[J].系统工程,2013,31(2):61-64.(Liu J F,Liu S F,Fang Z G.Prediction model of continuous interval grey number based on the kernel and gray radius[J].Systems Engineering,2013,31(2):61-64.)
[15]郭晓君,刘思峰,方志耕.基于合成灰数灰度的区间灰数自忆性预测模型[J].系统工程与电子技术,2014,36(6):1124-1129.(Guo X J,Liu S F,Fang Z G.Self-memory prediction model of interval grey number based on grey degree of compound grey number[J].Systems Engineering and Electronics,2014,36(6):1124-1129.)
[16]Yang Y,John R.Grey sets and greyness[J].Information Sciences,2012,185(1):249-264.
[17]徐美萍,熊令纯.Levy分布参数估计的损失函数和风险函数的Bayes推断[J].数学的实践与认识,2009,39(20):221-226.(Xu M P,Xiong L C.Bayes inference for the loss and risk function in Levy distribution parameter estimation[J].Mathematics in Practice and Theory,2009,39(20):221-226.)
[18]周建,李子奈.Granger因果关系检验的适用性[J].清华大学学报:自然科学版,2004,44(3):358-361.(Zhou J,Li Z N.Applicability of the Granger causality test[J].J of Tsinghua University:Science and Technology,2004,44(3):358-361.)
[19]Miao R,Zhang X Y,Jiang Z B,et al.The Bayesian estimation of process capability indices for multi-batch and low volume manufacturing[J].Chinese High Technology Letters,2011,21(7):770-774.
[20]Wang Z J,Zou C L,Li Z H.Theory and method of statistical quality control chart[M].Beijing:Science Press,2013:54-59.