Statistical Control Of High Quality Process Based On Weibull Distribution

With the application of statiscal process control in high quality process statistical control,Time Between Events control chart is widely used because it overcomes the shortcoming of traditional attribute control chart in high quality process statistical control.Based on the existing research theories and methods at home and abroad,and under the assumption that the time between events following weibull distribution for statistical control problems of some high quality process,the problem of detecting the shift of the weibull scale and shape parameters along with the problem of parameter estimation are systematically studied,and the control chart is designed and whose performance is evaluated by simulation.The detailed contents of this paper are as follows:(1)Median control chart based on the special weibull distribution(exponential distribution).For the monitoring of weibull distributed time between events with known shape parameter,the weibull distribution is simplified to exponential distribution,and the median control chart is designed to detect the large shift of the weibull scale parameter.First,the design procedure of the control chart is proposed.Then,the effects of parameter estimation on the chart performance are evaluated in terms of the CFAR,the AARL and the SDARL.Next,the Bootstrap method is proposed to adjust the control limits for the small sample problem.At last,an illustrative example is given.(2)WMedian-EWMA control chart based on the weibull distribution.Firstly,the WMedian-EWMA control chart is designed based on the sample median to detect the small shift of weibull scale parameters,and the calculation method of control limit parameters is given.Secondly,the effect of parameter estimation on the performance of the designed control chart is evaluated by AARL and SDARL for both the in control and out of control state,which provides reference for its practical application.Finally,an example is used to illustrate the practical use of the designed control chart.(3)Bayesian-Beta control chart based on the weibull distribution.In order to detect the shift of weibull shape parameter,firstly,an approximate normal statistic is constructed by using the pivotal quantity of shape parameter,control chart is designed and the monitoring procedure of control chart is given.Then,the Bayesian estimation method of shape parameters and the choice of prior distribution parameters are given.Next,the effect of parameter estimation and the error of prior information on the performance of the designed control chart are evaluated.Finally,an illustrative example is given for practical use.At last,the further research problems are elaborated after summarizing the research results.