Control Chart For Monitoring The Weibull Scale Parameter By Double CUSUM Procedure

In statistical process control,control chart is an important method for real-time monitoring of product quality.Traditional control charts include Shewhart control chart,Cumulative Sum(CUSUM)control chart,and Exponential Weighted Moving Average(EWMA)control chart.Weibull distribution has important applications in reliability analysis and life testing theory,and is often used as a distribution of product characteristics,such as strength,elongation,and resistance.Due to its flexibility in describing various failure models,it has become an important distribution for characterizing life data.Although traditional EWMA control charts and CUSUM control charts can effectively monitor small and medium-sized drifts in the process and have some optimality,this optimality has limitations.Specifically,when the actual changes in the process are not the target parameters designed in the control chart,the ability to monitor such real drifts will be greatly reduced.In addition,the monitoring ability of these two charts for process large drift is not as superior as the Shewhart control chart.Therefore,it is necessary to construct a control chart that can simultaneously monitor the interval drift of process parameters.In the field of SPC,traditional control charts for monitoring Weibull distributions mostly focus on small or large drift of a certain parameter,and cannot effectively monitor the drift of the parameter within a certain range.In the field of SPC,traditional control charts for monitoring Weibull distribution mostly focus on small or large drifts of a certain parameter,while a single control chart can’t effectively monitor the drift of parameter(s)within a certain range simultaneously.To this end,in this paper,we propose a dual CUSUM(DCUSUM)control chart for monitoring the scale parameter of Weibull distribution within a range shift.The new chart can be easily designed.The performance of the new chart is evaluated by average run length(ARL)through Monte Carlo simulation.In addition,the comparison between other existing charts,including the traditional CUSUM chart and the CUSUM chart based on conditional expectation(CEV)is given.The simulation results indicate that the new chart has better performance in monitoring interval drift of Weibull distribution scale parameter.Finally,the actual application of the new chart is illustrated through a real data on the fracture strength of carbon fibers.