The Design Of Time Between Events Control Charts

With the improvement of the level of science and technology,the defect rate in many processes has been decreased to such an extent sometimes to zero that the conventional attribute charts are found to be inefficient,so monitoring the observed times interval between consecu-tive events(TBE)instead of the observed number of events has been recommended.For high quality process,it is traditionally assumed that the occurrence of events follows a homogeneous Possion process and thus the TBE follows an exponential distribution.In order to improve the performance,this paper designs and studies the performance of tr control chart based on continuous r time intervals.When the in-control parameters are known,the performance of Shewhart-tr control chart,Synthetic-tr control chart and EWMA-tr control chart are compared based on equal-tailed and ARL-unbiased concept.Then,in practice,however,the in-control parameters are often unknown and have to be estimated from an in-control Phase I data set.Therefore,it is very important and necessary to study the influence of parameter estimation on the proposed control charts.The current literature on the impact of parameter estimation generally assumes that an infinite number of Phase I data sets can be obtained for estimating process parameters.In practice,for an operator,there may be only one Phase I data set.In this case,it is more meaningful to study the performance of the control chart based on one given Phase I data set(conditional performance).Based on the distribution of average run length,especially the standard deviation of average run length,we use the exact method to study the conditional performance of Shewhart-tr control chart,Synthetic-tr control chart and EWMA-tr control chart with parameter estimation.The results show that parameter estimation seriously affects the performance of control charts and may cause excessive false alarms and excessive unnecessary adjustments in the process.In order to monitor the process as early as possible,based on the available Phase I sample data,this paper uses the exact method to design Shewhart-tr control chart with desired conditional performance.In order to improve the performance of Shewhart-tr control chart,then this paper proposes Synthetic-tr control chart and EWMA-tr control chart with desired conditional performance.The main conclusions are as follows:Comparison results indicate that the ARL-unbiased control chart is better than the corresponding equal-tailed control chart,regardless of known parameter case or estimated parameter case;When the parameters are unknown,for Shewhart-tr control chart,Synthetic-tr control chart and EWMA-tr control chart,it is better to select a smaller value of r;When studying the perfo-rmance of Synthetic-tr control chart with estimated parameter,Synthetic-tr control chart should select a smaller value of H;When the parameter is estimated,the conditional performance of Synthetic-tr control chart and EWMA-tr control chart is better than Shewhart-tr control chart.Operators can select the most appropriate control charts and parameters for monitoring actual production situation.