Research On The Statistical And Economic Design Of Modified MEWMA Control Chart Base On PSO

The control chart has a wide range of applications in constructing andmaintaining the statistical process control (SPC).The standard multivariateexponentially weighted moving average (MEWMA) control chart is pr eferred to usein order to monitor the tiny and moderate shift in multivariate quality-control (orprocess-monitoring) problems. In this article, a new modified general MEWMA(GEWMA) control chart is proposed, which is applied to monitor the correlativityamong quality characteristics. Furthermore, an economic and economic-statisticalmodel of GEWMA is developed and then based on the Particle Swarm Optimization(PSO) approach, an example is used to solve the model and the results are comparedwith other models. In the end, a sensitivity analysis is made for the model ofGEWMA.In this paper, the main researches are as follows:(1) This paper introduces the economic model of the control chart and fourdominating calculation methods for it. A more appropriate solving method for thisarticle’s model is proposed by using a modified PSO approach, and the resultsdemonstrate this method is more suitable for this article’s model.(2) Based on the Lorenzen&Vance model, A preferable economic model ofGEWMA is designed. Then, the economic model of GEWMA and MEWMA isemployed to an example, which is solved respectively. What is more, the sensitivity ofGEWM’s main parameters is analyzed. We find, hen the shift is tiny, the economicperformance of GEWMA is better than that of MEWMA and vice versa. Besides,miss-specification of has the greatest impact on the cost. The results of changingcost of each false alarm，cost of locating and repairing an assignable cause and thetime between two consecutive samples show that those parameter deviation does notincrease the cost very much. Therefore, a rough estimate could be obtained.(3) Based on the economic model, an economic-statistical model of GEWMA isconstructed. After that, an economic-statistical model of GEWMA and MEWMA isadopted to research an example respectively, and then a sensitivity analysis of theirmain parameters is made. At last, compared with the economic performance ofGEWMA with its economic-statistical performance, the results show that theeconomic-statistical performance of GEWMA is better when the shift is small and vice versa. The cost function is the most sensitive on. The results of changing costof each false alarm，cost of locating and repairing an assignable cause and the timebetween two consecutive samples show that those parameter deviation does notincrease the cost very much. Therefore, a rough estimate could be obtained.In addition, the economic-statistical cost of GEWMA is always higher than itseconomic cost in different shift.