多源异构灰数据背景下的贝叶斯迭代优化控制图模型

Bayesian iterative optimized control charts model based on multi-source heterogeneous grey information

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.