A Control Chart Based On Pivot Statistic

Control chart is one of the most commonly used tools in quality control.The Pivot statistic was proposed by A.R.Soltani in 2019 and it has been proved that under certain conditions,the limit distribution of the Pivot statistic is the standard normal distribution.The purpose of this thesis is to use Pivot statistics and Bootstrap method to construct a control chart that is suitable for many kinds of distributions and can monitor all parameters of the population at once.This thesis first introduces the method of constructing control a Pivot control chart.This paper calculated the average run length（ARL）of the Pivot control chart.For Weibull distribution,it is found that the!of the Pivot control chart is the closest to the theoretical value,but"-charts are not.When only the scale parameters are shifted,the Pivot control chart performs better than Bootstrap Percentile control chart.But the Pivot control chart is not suitable for monitoring the situation where only the shape parameter shifts.When the shape parameter and the scale parameter are shifted at the same time,the Pivot control chart performs better than the Bootstrap quantile control chart.For Logistic distribution,the APL₀ of the Pivot control chart is close to the theoretical value.Although the Bootstrap quantile control chart is better than the Pivot control chart when only the scale parameter is shifted or only the position parameter is shifted,the Pivot control chart is better than the Bootstrap quantile control chart when the scale parameter and the position parameter are shifted at the same time.Finally,this thesis applies the Pivot control chart to the real data that obey the Weibull distribution and the Logistic distribution respectively.The Pivot control chart successfully monitored the process changes,but the"-chart and the Bootstrap quantile control chart were not monitored,indicating that the Pivot control chart is more effective.