The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outsid...The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outside the control limit is calculated. The above-mentioned results are substituted into the infinite definition expression of the average run length （ARL）, and then the final finite ARL expression is obtained. An example is used to demonstrate the procedures of the proposed method. In the comparative study, eight autocorrelated processes and four different mean shifts are performed, and the ARL values of the proposed method are compared with those obtained by simulation method with 50 000 replications. The accuracy of the proposed method can be illustrated through the comparative results.展开更多
It is not uncommon that two or more related process quality characteristics are needed to be monitored simultaneously in production process for most of time.Meanwhile,the observations obtained online are often seriall...It is not uncommon that two or more related process quality characteristics are needed to be monitored simultaneously in production process for most of time.Meanwhile,the observations obtained online are often serially autocorrelated due to high sampling frequency and process dynamics.This goes against the statistical I.I.D assumption in using the multivariate control charts,which may lead to the performance of multivariate control charts collapse soon.Meanwhile,the process control method based on pattern recognition as a non-statistical approach is not confined by this limitation,and further provide more useful information for quality practitioners to locate the assignable causes led to process abnormalities.This study proposed a pattern recognition model using Random Forest(RF)as pattern model to detect and identify the abnormalities in bivariate autocorrelated process.The simulation experiment results demonstrate that the model is superior on recognition accuracy(RA)(97.96%)to back propagation neural networks(BPNN)(95.69%),probability neural networks(PNN)(94.31%),and support vector machine(SVM)(97.16%).When experimenting with simulated dynamic process data flow,the model also achieved better average running length(ARL)and standard deviation of ARL(SRL)than those of the four comparative approaches in most cases of mean shift magnitude.Therefore,we get the conclusion that the RF model is a promising approach for detecting abnormalities in the bivariate autocorrelated process.Although bivariate autocorrelated process is focused in this study,the proposed model can be extended to multivariate autocorrelated process control.展开更多
基金Supported by National Natural Science Foundation of China (No.70931004 and No. 70802043)
文摘The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outside the control limit is calculated. The above-mentioned results are substituted into the infinite definition expression of the average run length （ARL）, and then the final finite ARL expression is obtained. An example is used to demonstrate the procedures of the proposed method. In the comparative study, eight autocorrelated processes and four different mean shifts are performed, and the ARL values of the proposed method are compared with those obtained by simulation method with 50 000 replications. The accuracy of the proposed method can be illustrated through the comparative results.
基金This research was financially supported by the National Natural Science Foundation of China(52065033).
文摘It is not uncommon that two or more related process quality characteristics are needed to be monitored simultaneously in production process for most of time.Meanwhile,the observations obtained online are often serially autocorrelated due to high sampling frequency and process dynamics.This goes against the statistical I.I.D assumption in using the multivariate control charts,which may lead to the performance of multivariate control charts collapse soon.Meanwhile,the process control method based on pattern recognition as a non-statistical approach is not confined by this limitation,and further provide more useful information for quality practitioners to locate the assignable causes led to process abnormalities.This study proposed a pattern recognition model using Random Forest(RF)as pattern model to detect and identify the abnormalities in bivariate autocorrelated process.The simulation experiment results demonstrate that the model is superior on recognition accuracy(RA)(97.96%)to back propagation neural networks(BPNN)(95.69%),probability neural networks(PNN)(94.31%),and support vector machine(SVM)(97.16%).When experimenting with simulated dynamic process data flow,the model also achieved better average running length(ARL)and standard deviation of ARL(SRL)than those of the four comparative approaches in most cases of mean shift magnitude.Therefore,we get the conclusion that the RF model is a promising approach for detecting abnormalities in the bivariate autocorrelated process.Although bivariate autocorrelated process is focused in this study,the proposed model can be extended to multivariate autocorrelated process control.
