On the statistical performance of quality control charts with estimated parameters /
Nesma Ali Mahmoud Saleh
On the statistical performance of quality control charts with estimated parameters / حول الأداء الإحصائي لخرائط التحكم في حالة المعلمات المقدرة Nesma Ali Mahmoud Saleh ; Supervised Mahmoud Alsaid Mahmoud - Cairo : Nesma Ali Mahmoud Saleh , 2016 - 133 P. : facsimiles ; 25cm
Thesis (Ph.D.) - Cairo University - Faculty of Economics and Political Science - Department of Statistics
Under estimated in-control parameters, the Phase II control chart performance is expected to vary among practitioners due to the use of different Phase I data sets. Accordingly, the typical measure of Phase II control chart performance, the average run length (ARL), becomes a random variable. In the literature, control charts with estimated parameters were assessed and the appropriate amounts of Phase I data were recommended based on the in-control performance averaged across the practitioner-to-practitioner variability. In this study, aspects of the ARL distribution, such as the standard deviation of the average run length (SDARL) and some quantiles are used to quantify the between-practitioner variability in control charts performance when the process parameters are estimated. It is shown that no realistic amount of Phase I data is sufficient to have confidence that the attained in-control ARL is close to the desired value. Moreover, it is shown that even with the use of larger amounts of historical data, there is still a problem with the excessive false alarm rates. Due to the extreme difficulty of lowering the variation in the in-control ARLs, an alternative design criterion based on the bootstrap approach is recommended for adjusting the control limits. The technique is quite effective in controlling the percentage of short in-control ARLs resulting from the estimation error. Three of the most well-known univariate control charts (Shewhart, EWMA, and CUSUM), and two multivariate charts (T2, and MEWMA) are studied
Bootstrap Control Charts Estimation Effect
On the statistical performance of quality control charts with estimated parameters / حول الأداء الإحصائي لخرائط التحكم في حالة المعلمات المقدرة Nesma Ali Mahmoud Saleh ; Supervised Mahmoud Alsaid Mahmoud - Cairo : Nesma Ali Mahmoud Saleh , 2016 - 133 P. : facsimiles ; 25cm
Thesis (Ph.D.) - Cairo University - Faculty of Economics and Political Science - Department of Statistics
Under estimated in-control parameters, the Phase II control chart performance is expected to vary among practitioners due to the use of different Phase I data sets. Accordingly, the typical measure of Phase II control chart performance, the average run length (ARL), becomes a random variable. In the literature, control charts with estimated parameters were assessed and the appropriate amounts of Phase I data were recommended based on the in-control performance averaged across the practitioner-to-practitioner variability. In this study, aspects of the ARL distribution, such as the standard deviation of the average run length (SDARL) and some quantiles are used to quantify the between-practitioner variability in control charts performance when the process parameters are estimated. It is shown that no realistic amount of Phase I data is sufficient to have confidence that the attained in-control ARL is close to the desired value. Moreover, it is shown that even with the use of larger amounts of historical data, there is still a problem with the excessive false alarm rates. Due to the extreme difficulty of lowering the variation in the in-control ARLs, an alternative design criterion based on the bootstrap approach is recommended for adjusting the control limits. The technique is quite effective in controlling the percentage of short in-control ARLs resulting from the estimation error. Three of the most well-known univariate control charts (Shewhart, EWMA, and CUSUM), and two multivariate charts (T2, and MEWMA) are studied
Bootstrap Control Charts Estimation Effect