Control Chart For Monitoring Two Parameter Exponential Distribution

The conventional control are based on the assumption that the distribution of the pro-cess to be monitored follows the normal distribution.And the research based on normal distribution is abundant.However,there are little work of control chart for two-parameter exponential distribution which is widely applied in many areas such as reliability mod-eling and the time to failure.Therefore,it is very important to design a control chart for two-parameter exponential distribution.As we know,the memory chart,such as,exponentially weighted moving average(EWMA)and cumulative sum(CUSUM)control charts can improve the ability of detecting small and moderate shifts comparing to the Shewart chart.The control chart which integrated EWMA procedure into likelihood ratio statistic is an useful scheme.Comparing to the EWMA and CUSUM chart,these type of charts are more efficient.Researchers will always consider to design a chart using this method,because it it not only simple in design,but also widely used.In actual production and manufacture,the process parameters are usially unknown and needed to be estimat?ed from phase I.But we know that it will inevitably affect on the performance of the control chart when the parameters are estimated from phase I.Therefore,in this paper,we will consider to analyze the performance of control cha.rt with estimated parameter.The two-parameter exponential distribltion exist the phenomenon of censored data when describing the survival analysis and life distribution,thus,two EWMA type schemes are designed to detect location and scale parameters of the two-parameter exponential distri-bution under the type ? censored data.The main content and innovation of this research includes:(1)Control chart for two-parameter exponential distribution based on likelihood ratio test which integrate EWMA is proposed.Simulation results show that this method can improve the detection efficiency compared with other control charts.The performance with estimated parameter from phase ? is analyzed and the appropriate number of sample is given in order to have the same i)erfonnance with known parameters.(2)Two EWMA type control charts for monitoring two-parameter exponential distri-bution under traditional type ? censored data are desiged,denoted Max-EWA4A and LR-EWMA control chart,respectively.When the location paraleter shifted and the scale parameter is larger than one,we recommend using the LR-EWS control chart.It is better to use the LR-EWS control chart when scale parameter is smaller than one.In addition,the ohserved sampler when the test stopped can affect the effieiency of control chart,the smaller the number of samples that are censored,the better the detection efficiency.