报告题目：Optimal Design of the Multivariate Bayesian Generalised Likelihood Ratio Schemes for Monitoring the Mean Vector

报告时间：2026年1月9日下午15:30

报告地点：北湖东校区数统新楼201室

主办单位：欧洲杯

报告人：张久军

报告人简介：张久军，辽宁大学欧洲杯 教授，博士研究生导师，统计与数据科学系主任。辽宁大学“双带头人”教师党支部书记，美国明尼苏达大学访问者。辽宁省第13批“百千万人才工程”百人层次人选，“沈阳市高级人才-领军人才”，辽宁省普通本科教学名师，辽宁省高校“校园先锋示范岗”（个人）。曾被评为辽宁大学本科优秀主讲教师、辽宁大学师德师风模范标兵等称号。兼任中国现场统计研究会多元统计分析分会理事，中国现场统计学会生存分析分会理事，辽宁省数学会理事。主持、参与国家自然科学基金，辽宁省自然科学基金十余项，发表论文50余篇。

摘要：Bayesian approaches have gained popularity in dealing with operational research and management problems, including process monitoring or product quality assessments.In particular,Bayesian approaches are often used to deal with multivariable complex processes. This paper analyses and evaluates a multivariate Bayesian generalised likelihood ratio, abbreviated as MBGLR, scheme to monitor the mean vector of a multivariate Gaussian process distribution. The Monte Carlo simulation is employed to evaluate the detection performance of the MBGLR scheme, and the optimal window size is provided in terms of the simulation results. The optimal design of the MBGLR scheme is presented based on the relative mean index (RMI).

Furthermore, the MBGLR scheme is compared with the multivariate Bayesian cumulative sum, referred to as MBCUSUM, and a combination of two MBCUSUM,denoted as 2MBCUSUM, schemes according to the steady-state average time to signal(SSATS). The simulation results demonstrate that the MBGLR scheme exhibits superior competitiveness in overall detection performance. We consider a case study involving the lumber manufacturing process to illustrate the implementation of the MBGLR scheme. Some concluding remarks are offered.