Control Chart For Monitoring The Weibull Scale:Parameter With Type ? Censored Data

Statistical process control is widely used in aerospace manufacturing,semiconductor circuit packaging,optical fiber manufacturing,medical and pharmaceutical,as well as electronic component manufacturing.Control charts are important tool for analyzing and controlling process quality.With the development of science and technology and the improvement of people's living standards,prolonging product lifetime and improving product quality have received widespread attention from all walks of life.Therefore,designing more efficient control charts is essential to strengthen product lifetime management and improve product stability.The Weibull distribution is a special type of distribution that can reflect an increase or decrease in product lifetime,and is often used to describe the time interval between two consecutive failures.At the same time,the Weibull distribution is also used as the distribution of product properties,such as strength(electrical or mechanical),elongation and resistance,etc.Because of its full flexibility,the Weibull distribution can simulate various failure models,thus becoming an important tool for characterizing lifetime data.In the actual production process,due to various limitations of the experiment,the collected product lifetime data are not always complete,and censoring is likely to occur.Therefore,effective analysis and monitoring of censored lifetime data is crucial.To this end,in order to improve the detection ability of lifetime data with type I right-censored lifetime,this paper proposes a double exponentially weighted moving average(DEWMA)chart with the conditional expected value(CEV)based on transformed data to monitor the scale parameter of Weibull distribution,so as to realize online monitoring of lifetime data.Firstly,based on different monitoring purposes,two one-sided DEWMA CEV charts are given to monitor the increase and decrease of scale parameter.Under different parameters combination,the Monte Carlo simulation method is used to measure the detection ability of the control chart by the average run length(ARL)of the control chart,as well as the relative mean index(RMI).And the design scheme of the control chart is given.Secondly,the performance of the control chart proposed in this paper is compared with the existing two control charts.The simulation results show that the control chart proposed has better detection ability for these from small to medium shifts,which further verifies the superiority of the new control chart proposed.For example,when n=5,?=0.5,Pc=0.7,?=0.05,the shift d=0.1,DEWMA-ARL1=169.40,EWMA-ARL1=197.66.Finally,an example in production is used to illustrate the practical application of the new control chart proposed in this paper.