Optimal Design Of One-sided Exponential Chart Based On Median Run Length

Statistical Process Monitoring(SPM)can monitor the product quality characteristic values in the production process,which can detect the existence of abnormal factors and issue alarm signals in time to prevent the production of a large number of unqualified products in advance.Control chart,as one of the important tools of SPM,mainly applies the method and technique of mathematical statistics to monitor each stage of the production process online and determine whether the process is in-control and improve the quality of products.In some modern manufacturing processes,such as integrated circuits,automotive engines,etc.,the failure rate of products is very low,and such processes are usually referred to as low failure rate process.In the low failure rate process,the direct monitoring of the number or the rate of non-conforming products will issue too many false alarms.Exponential control chart can be used to monitor Time Between Events(TBE)data to achieve the monitoring of the low failure rate process.Besides,the statistical characteristics of the run length(RL)distribution of the exponential chart are highly-skewed.This results in some confusion in the interpretation of control charts based on Average Run Length(ARL)for practitioners.Median Run Length(MRL),which is more intuitive for users,could be employed as a good alternative measure.Therefore,theoretical research on the exponential chart based on MRL is meaningful,which will also provide guidelines for some industrial applications.Based on the existing research of SPM,we investigate the optimal design of the exponential charts based on MRL.The main research results of this thesis are summarized as follows:(1)Optimal design of one-sided exponential Exponentially Weighted Moving Average(EWMA)chart based on MRL.Considering the low product failure rate in the low failure rate process,the one-sided exponential EWMA chart is employed to monitor the mean shift.The RL properties of the chart are studied using the Markov chain method.It is noted that the shape of the RL distribution of the chart is highly-skewed,and is affected by the mean shift size.To better characterize the characteristics of the RL distribution of the chart,MRL is recommended as an alternative measure to evaluate the performance of the chart.Moreover,the optimal design procedures are developed for the one-sided exponential EWMA chart based on MRL and Expected MRL(EMRL),respectively.From the simulation results,it is more reasonable to use MRL and EMRL as the criterion for the situation where the RL distribution is highly-skewed.(2)Optimal design of one-sided exponential EWMA chart with estimated parameters based on MRL.In real industrial applications,the in-control process mean of the low failure rate process is rarely known in advance,and need to be estimated from historical data of the production process.Then the one-sided exponential EWMA chart with estimated parameters is applied to monitor the TBE data.The RL properties of the chart are studied using the Markov chain method.Due to the bias of the RL distribution,the optimal design procedures based on MRL of the one-sided exponential EWMA chart with estimated parameters are discussed.From the simulation results,the one-sided exponential EWMA chart with estimated parameters can overcome the effect of parameter estimation to achieve the expected statistical performance.(3)Optimal design of one-sided exponential Cumulative Sum(CUSUM)chart based on MRL.Considering both known-and estimated-parameter cases,the one-sided exponential CUSUM charts are studied through a Markov chain approach.The effect of the estimated parameters on the statistical performance of the chart is investigated.Since the shape of the RL distribution of the chart is highly-skewed,MRL is employed as a good alternative performance measure for the chart.The optimal design procedures based on MRL of the one-sided exponential CUSUM charts with known and estimated parameters are developed.From the simulation results,it is more reasonable to employ MRL as the criterion.Also,the one-sided exponential CUSUM chart with estimated parameters can overcome the effect of parameter estimation to achieve the expected statistical performance.(4)Optimal design of one-sided exponential synthetic chart based on MRL.Considering both known-and estimated-parameter cases,we derive the RL distribution and the performance measures of the one-sided exponential synthetic chart by using the Markov chain method.Then we study the effect of the estimated parameters on the statistical performance of the chart.For the biased RL distribution,MRL is a more reasonable performance measure to design the optimal one-sided exponential synthetic chart.From the simulation results,using the proposed optimal design procedures,the performance of the one-sided exponential synthetic chart with estimated parameters is close to the optimal chart with known parameters.(5)Optimal design of one-sided exponential Adaptive EWMA(AEWMA)chart based on MRL.The one-sided exponential AEWMA chart is used to take into account the simultaneous monitoring of different shift sizes in the process.Then the RL properties of the chart are studied using the Markov chain method.For the biased RL distribution,MRL is a good alternative measure to design the optimal one-sided exponential AEWMA chart.From the simulation results,it is more reasonable to employ MRL as the criterion,and the optimal chart offers a more balanced detection against different shifts.