The Performance Of Multivariate Control Charts With Estimated Parameters

With the development of science and technology, increasing complexity of products and improvement of consumers demand, the evaluation criterion of products quality should not be restricted to one quality characteristic. To this question, multivariate control chart should be used. In the past study, most scholars set process parameters to be known. However, the process parameters should be estimated in order to show the real performance of control charts in practice.The topic of this thesis comes from the National Natural Science Foundation of China(71271078). Based on Monte Carlo method, this thesis carried out research on the multivariate control charts with estimated parameters. On the one side, this thesis investigated the statistical performance of traditional multivariate control charts with estimated parameters when process is in control or out of control; on the other side, this thesis investigated the economic performance of multivariate Bayesian control chart with estimated parameters.The main content of this thesis includes:(1) Firstly, when process is in-control, the Full Multivariate Exponentially Weighted Moving Average(FEWMA) control chart with estimated parameters was investigated, then a recommendation on the overall sample size was given. On the base of binary search, the control limit of FEWMA control chart with unknown parameters was designed. Then using the least square estimation, the control limit was fitting. Secondly, when the process is out-of-control, the T2 control chart, Multivariate Exponentially Weighted Moving Average(MEWMA) control chart and Multivariate Cumulative Sum(MUSUM) control chart with estimated were analyzed and compared.(2) Firstly, when parameters are known, the statistical performance of GEWMA based on PSO was investigated. The results showed the GEWMA is better than FEWMA control chart. Secondly, when parameters are unknown, the performance of GEWMA control chart was analyzed. Based on PSO, the stability of GEWMA and FEWMA control chart were compared, the results showed the stability is changed with offset direction. Consequently, the influence of parameters estimation cannot be ignored.(3) When parameters are estimated, the economic performance of multivariate Bayesian control chart was analyzed. The influence of offset direction and number of quality characteristics were investigated, then the influence of sampling strategies in Phase II were investigated. An overall sample size recommendation in phase I was provided.