Effects Of Measurement Error On Control Charts For Monitoring Process Variability

In the application of control charts,most works in statistical process monitoring assume that the measurements are accurate.However,exact measurements are rare and the measurement error does exist.The existence of measurement error will lead to the increase of process fluctuation and affect the performance of control charts.However,most documents ignore the effects of measurement error,the theoretical research on measurement error still needs to be further studied.Most literatures investigated the effects of measurement error on mean control charts,and most of them based on one error model.Therefore,this paper studies the effects of measurement error on variance control charts.In this paper,we design four control charts with measurement error.Theoretical derivation and random simulation are combined to analyze the effects of measurement error.In simulation,we study the performance of control charts under two assumptions.One assumption is that we know the measurement error exists before the control chart is used,so the control limit needs to be adjusted for varying model parameters.The other assumption is that the existence of measurement error is uncertain,and the control limit is fixed.Control charts are evaluated by their ARL performance.We analyze the effects of the model parameters and find appropriate parameters to minimize the effects of measurement error.Provide theoretical basis for practical application.We also consider multiple measurements to reduce the effects of measurement error.Simulation results show that this method can effectively reduce the influence of measurement error.The creative ideas are represented as follows: Based on likelihood ratio test,we use two error models to develop control charts with measurement error,and study the performance of those charts.With a new perspective,the performance of four control charts under different assumptions is investigated,and the influence of measurement errors on the control charts is analyzed comprehensively and systematically.