Abstract
Traditional/Asymptotic confidence estimation has limited applicability since it needs statistical theories to estimate the confidences, which are not available for all indicators/parameters. Furthermore, in case the theories are available for a specific indicator/parameter, the theories are based on assumptions that do not always hold in practice. The aim of this thesis was to illustrate the concept of bootstrap-based confidence estimation in PCA and MSPC. It particularly shows how to build bootstrapbased confidence limits in these areas to be used as alternative to the traditional/asymptotic limits. The goal was to improve process monitoring by improving the quality of MSPC charts and contribution plots.
Bootstrapping algorithm to build confidence limits was illustrated in a case study format (Paper I). The main steps in the algorithm were discussed where a set of sensible choices (plus the recommended decisions) to build rational confidence limits were given. Two NIR datasets were used to study the effect of outliers and bimodal distributions on the bootstrap-based limits. The results showed that bootstrapping can give reasonable estimate of distributions for scores and loadings. It can also be used to detect outliers in the data since the outliers can distort the bootstrap estimates.
Bootstrap-based confidence limits were suggested as alternative to the asymptotic limits for control charts and contribution plots in MSPC (Paper II). The results showed that in case of the Q-statistic the bootstrap limits were as good as the most accurate asymptotic limits (based on the normal distribution), while they were better than the other asymptotic limits (based on the chi-squared distribution). The results also showed that reasonable bootstrap-based confidence limits for D-statistic were estimated. The bootstrap could also offer confidence limits for contribution plots with acceptable fault diagnostic power.
The performance of bootstrap-based and asymptotic confidence limits was compared in batch MSPC (Paper III). Real and simulated batch process datasets were used to build the limits for five PCA-based MSPC strategies. The performance of the limits was assessed through Overall Type I and II errors. The results showed that the bootstrapbased limits perform as good as the asymptotic limits for the SPE-chart, while they outperform the asymptotic limits for the D-chart.
This thesis has shown that the bootstrap can offer reliable confidence limits for multivariate statistical methods (like PCA) and MSPC which can replace traditional/asymptotic confidence limits.
Bootstrapping algorithm to build confidence limits was illustrated in a case study format (Paper I). The main steps in the algorithm were discussed where a set of sensible choices (plus the recommended decisions) to build rational confidence limits were given. Two NIR datasets were used to study the effect of outliers and bimodal distributions on the bootstrap-based limits. The results showed that bootstrapping can give reasonable estimate of distributions for scores and loadings. It can also be used to detect outliers in the data since the outliers can distort the bootstrap estimates.
Bootstrap-based confidence limits were suggested as alternative to the asymptotic limits for control charts and contribution plots in MSPC (Paper II). The results showed that in case of the Q-statistic the bootstrap limits were as good as the most accurate asymptotic limits (based on the normal distribution), while they were better than the other asymptotic limits (based on the chi-squared distribution). The results also showed that reasonable bootstrap-based confidence limits for D-statistic were estimated. The bootstrap could also offer confidence limits for contribution plots with acceptable fault diagnostic power.
The performance of bootstrap-based and asymptotic confidence limits was compared in batch MSPC (Paper III). Real and simulated batch process datasets were used to build the limits for five PCA-based MSPC strategies. The performance of the limits was assessed through Overall Type I and II errors. The results showed that the bootstrapbased limits perform as good as the asymptotic limits for the SPE-chart, while they outperform the asymptotic limits for the D-chart.
This thesis has shown that the bootstrap can offer reliable confidence limits for multivariate statistical methods (like PCA) and MSPC which can replace traditional/asymptotic confidence limits.
| Original language | English |
|---|
| Publisher | Department of Food Science, University of Copenhagen |
|---|---|
| Number of pages | 204 |
| Publication status | Published - 2012 |