Research On Quality Index Based On Control Charts And Confidence Interval

Confidence interval is a commonly used interval estimation method.The control charts are mainly used to monitor whether the production process is stable.In statistical process control,we often use the confidence interval to determine the upper and lower limits of the control chart.In the thesis,the following two aspects of work has been done for control charts and confidence intervals:Firstly,in previous VSI studies,the sampling interval function d(·) realized only two distinct values.Limiting the selection of the sampling interval to two fixed values may not be reasonable,especially when the monitoring statistic value is at the edge or near the middle of these two intervals so that the advantages of VSI methods cannot be fully reflected.Therefore,we propose a nonparametric exponentially weighed moving average control chart with a dynamic sampling interval in the thesis,in which the dynamic sampling interval is an extension of two fixed sampling intervals.The dynamic sampling interval can be continuous valued and is determined by an indicator of the magnitude of the unknown shift.This chart can efficiently detect various magnitudes of shifts and performs robustly for different distributions according to simulation studies.The small computational cost indicates that the method is applicable for monitoring large data streams.Data from an aluminum electrolytic capacitor manufacturing process are used to illustrate the implementation of this chart.Secondly,hospital standardized mortality ratio(HSMR)is hospital observed mortality-toexpected mortality ratio(O/E ratio).In confidence interval studies for the O/E ratios,the O/E ratios are assumed to be normally distributed in existing methods.This is not a reasonable assumption,because the value of O/E is always greater than 0 and fluctuates around 1.In the thesis,we propose a new method to calculate the HSMR confidence intervals.We derive the confidence intervals for the O/E ratios by calculating the confidence intervals of log(O/E).Then,we use the coverage probability of confidence intervals to compare the performance of our method and existing methods.In scenarios with different true relative risks,when the mortality rate is less than or equal to 1%,the bias of our method is substantially smaller than that of existing methods.The simulation results shows that for low mortality rates,our method is more accurate than existing methods in estimating confidence intervals of O/E ratios.