多元质量特性的贝叶斯均值向量控制图

Bayesian Mean Vector Control Chart for Multiple Quality Characteristics

贝叶斯控制图主要研究小样本情况或非稳定状态下的质量控制问题 ,是质量控制理论中的一个新的研究领域。通过建立多元质量特性控制的数学模型 ,利用多重线性模型的贝叶斯推断理论 ,证明了正态 -Wishart先验分布下多元质量特性模型的预报分布为多元t分布 ,并根据多元t分布与F分布之间的关系 ,构造了F统计量和相应的贝叶斯均值向量控制图。

Bayesian control chart mainly deals with the quality control problems when the sample size is small or the production condition is unstable, and it's a new area in quality control theory. The mathematical model for the multivariate quality control characteristics is established.The corresponding predictive distribution is proved to be the multivariate t distribution under the condition that the parameter's prior is the normal-Wishart distribution. According to the relationship between the multivariate t and F statistical distribution, the F variable and corresponding Bayesian F process control chart are established.