Research On The Statistical And Economic Design Of Bayesian Control Chart

The topic of this article comes from the National Natural Science Foundation ofChina (71271078). To address the deficiency in statistical study of traditionalBayesian control chart, this research is carried out to improve the statistical properties.Meanwhile, multivariate Bayesian control chart is more complex and more realistic, itis still in the research frontier. On one hand, the statistical and economic properties ofthe multivariate Bayesian control chart are verified through an integrated case; and onthe other hand, by constructing a multivariate Bayesian VSI control chart, thisresearch provides new ideas of multivariate Bayesian control chart with variableparameters.The main content of this research includes:(1) A Bayesian fast initial response control chart, with a better sensitivity in theprocess migration situation, is proposed. Compared with ordinary Bayesian controlchart, it can discover more quickly whether the process is out of control. After takingrapid initial response method into consideration, an improved Bayesian control chartis proposed through setting limits and transfer rules. Through Monte Carlo stochasticsimulation, comparisons are made between the average running length when processis out-of-control and the original Bayesian control. Results show that the improvedBayesian control chart can discover the process offset quickly and has betterapplicability when the process is under strict control.(2) Multivariate Bayesian control chart is applied to case study, thus puttingforward cost function and determining relevant parameters. And the reduction ofenterprise’s quality cost is achieved through simulation and actual verification. Fromthe perspective of quality cost and false alarm rate, the advantages of multivariateBayesian control chart are analyzed. Therefore, it can be concluded that, reducing thefalse alarm rate is an important factor in cost improvement of multivariate Bayesiancontrol chart.(3) Multivariate Bayesian control chart is constructed and VSI （VariableSampling Interval） control strategy is proposed. Cost function model is designed andrelevant parameters are determined. Through the contrastive analysis with the fixedsampling interval multivariate Bayesian control chart, a multivariate Bayesian VSIcontrol chart is proposed in this thesis. And the proposed multivariate Bayesian VSI control chart, with the advantages of reducing costs effectively and obtaining greateconomic benefit, and at the same time showing some statistical advantage, is ofpractical use and worth exploring.