A Control Chart Based On Gini Index

Quality control chart has become an indispensable management tool in industrial production quality management.It is a kind of chart with upper and lower control limits to distinguish whether the causes of quality fluctuations are accidental or systematic,so as to determine whether the production process is in a controlled state.The traditional Shewhart control chart requires a high distribution of the observed data,which is usually assumed to be approximately normally distributed,while in real life,the observed data often obeys a non-normal distribution,and the sampling distribution of the parameter estimates is difficult to obtain.The monitoring efficiency of the control chart is low when the observed data obey multi-parameter distribution.It is well known that the Gini index can be used to measure the inequality of income in a country or region,and the integral expression of the Gini index can be converted into the form of an order statistic using an empirical distribution function when the distribution function of income distribution is unknown,and the asymptotic distribution form of this statistic was proved by Alizadeh in 2014,and Hadi in 2017 used this statistic to test the logistic distribution of The goodness of fit,in this thesis,we will combine the Gini statistic and the Bootstrap method to design control charts,thus improving the shortcomings of the traditional Shewhart control chart and making it available for arbitrary continuous distribution data and for monitoring multiple parameters at once.In this thesis,the monitoring performance of control charts will be compared around Shewhart control charts,Bootstrap quantile control charts,and Gini control charts,assuming that the data obey Weibull and logistic distributions.First,the distribution theory and parameter estimation methods will be briefly introduced,and simulated data obeying the two distributions will be randomly generated;second,the principles and construction methods of the three different control charts will be introduced in detail,and the monitoring performance of the three control charts under two different production states will be compared and analyzed using the randomly simulated data;finally,the effect of the control charts will be tested by citing the actual case data from two foreign literatures.Finally,this thesis concludes that the Shewhart control chart is severely ineffective for monitoring non-normally distributed data in the controlled state,and the control chart has a high probability of false alarms,while the performance of the Gini control chart and the Bootstrap quantile control chart are roughly the same.Comparing the monitoring of runaway data,the difference between the performance of Gini control chart and Bootstrap quantile control chart is small when the drift of a parameter is small,and the performance of Gini control chart improves as the drift increases,and the performance of Gini control chart is significantly better than Bootstrap quantile control chart when both parameters drift at the same time.