Mixed GWMA-CUSUM Control Chart For Monitoring Scale Parameter Of Weibull-distributed Time Between Events

With the development of internet technology and intelligent manufacturing,it have led to significant improvements in the production quality of products,and product life is an important characteristic to describe product quality.The monitoring of false alarms can be even higher when the high quality processes with lower failure rates.Generally,these events are modeled by a homogeneous Poisson process,where the time between events(TBE)follows as exponential random variables.The Weibull distribution is the theoretical basis for reliability analysis and life testing and is often used as a distribution of product characteristics,such as strength(electrical or mechanical),elongation and resistance,etc.The Weibull distribution is also often used to describe the time between two consecutive failures.It is an important tool for portraying lifetime data because of its flexibility in describing different failure models.In the statistical process control(SPC),online monitoring of the product quality is usually implemented by monitoring the TBE.In practice,the greater concern is usually the reduction in product quality,i.e.the reduction in the TBE mean.Thus,it would be practical importance to design a control chart that efficiently monitors the reduction of the TBE mean which obey the Weibull distribution.Based on the relationship between the TBE mean and the parameters of the Weibull distribution,this paper proposes a mixed control chart combining the generally weighted moving average(GWMA)method with the cumulative sum(CUSUM)method for online detection of TBE mean by monitoring the scale parameters of the Weibull distribution.Firstly,this paper introduces some existing control charts based on data transformations for monitoring the Weibull distribution scale parameters,and then propose the new control chart.A Monte Carlo simulation procedure is used to evaluate the average of run length(ARL)and the standard deviation of the run length(SDRL),and then analyse the performance of the proposed control chart for different parameter cases,while giving the optimal combination of parameters for different shift intervalsis and comparing with existing methods through several indicators.Simulation results show that the proposed control chart consistently outperforms existing control charts in monitoring small to moderate shifts with fixed shape parameters.Finally,the practical application of the proposed method is illustrated by analysing real examples of reliability data from hard disk drives of computer products.