Research And Application Of The Variance Control Charts Based On Conditional Performance

The process variance has a large impact on the stability of product quality,so it is necessary to monitor the change of process variance in the actual production process.Shewhart-S² control chart is a common control chart for monitoring process variance,but it is not sensitive enough when the process variance changes slightly.Based on the research of previous scholars,the run sum S² control chart is designed to monitor the process variance.Based on the known parameters,this paper compares the performance of the 2-of-3,3-of-4,M:2-of-3,M:3-of-4 run rules S² control charts and the GR 2-of-2 S² chart based on the equal-tailed and ARL-unbiased concept design.The main research content of this paper is as follows:(1)Based on the known parameters,this paper compares the performance of run sum S²chart,the 2-of-3,3-of-4,M:2-of-3,M:3-of-4 run rules S² control charts and the GR 2-of-2 S² chart based on the equal-tailed and ARL-unbiased concept design.(2)Based on the conditional perspective,the Markov chain method was used to calculate the percentile,the mathematical expectation and the standard deviation of the conditional ARL distribution to evaluate the influence of parameter estimation on the performance of the control chart.(3)The results show that parameter estimation has a great impact on the control chart performance,resulting in excessive false alarms,which will affect the production process.This paper corrects schemes by using an accurate method based on a set of Phase I samples available.Make the control chart have the desired conditional performance.The main conclusions are as follows:For four run sum S² control charts with different score vectors,the C1:RSS₄(0,1,2,4)scheme is most suitable for monitoring the upward shift of the process variance,and the C3:RSS₈(0,2,3,8) scheme performs better in detecting the downward drift of process variance.For the 2-of-3,3-of-4,M:2-of-3 and M:3-of-4 run rules schemes and the GR 2-of-2 new run rule S² chart,compared to the equal-tailed control chart,the ARL-unbiased control chart performs better when detecting the decrease in process variance,and the equal-tailed chart is more suitable in detecting the increase of the process variance.Comprehensive comparison of run sum charts and the charts with run rules,the results show that when the process variance drifts upward,it is recommended to select the equal-tailed GR 2-of-2 run rule chart,while the ARL-unbiased GR 2-of-2 run rule S² control chart is best when the process variance drifts downward.