Πολυδιάστατα διαγράμματα ελέγχου διεργασιών και εφαρμογές

Σοφικίτου, Ελισάβετ

Multivariate Process Control Charts and Applications

Doctoral Thesis

Author

Σοφικίτου, Ελισάβετ

Date

2017-12

Abstract

The present PhD dissertation deals with topics related to the Theory of Order Statistics and Statistical Quality Control. Some important notions on basic concepts concerning the Theory of Order Statistics and their Concomitants, as well as the Theory of Copulas are first presented. Subsequently, new distributions for bivariate order statistics and enumarating variables for them, which have a practical application in quality control, are introduced. The new results are used to construct four new bivariate semi-parametric control charts and are applied to establish expressions for their characteristics, such as the operating characteristic function and the (false) alarm rate. It is worth noting that two of the proposed schemes are capable of detecting mean shifts of the underlying process, while the rest are effective in track- ing possible deviations from the null values of both the mean and the variability of the features under study. One of the two charts proposed for the monitoring of process mean, is affected by the de- pendence structure of the quality characteristics, as reflected on the copula associated with the bivariate distribution that describes the monitored characteristics; it is not influenced by the (univariate) marginals. On the contrary, for the rest three charts the values of the false alarm rate and the in-control average run length do not change crucially when different copulas are used. Consequently, their key advantage is the fact that they can be exploited as fully non parametric schemes. Finally, it should be stressed that the contruction of the above bivariate control charts is quite simple. As a result, the new schemes can be easily extended to higher dimensions, so that the monitoring of more than two quality characteristics is maintenaid, at the cost of more complicated expressions for the determination of their characteristics.

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

244

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/11244

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Show full item record

Except where otherwise noted, this item's license is described as
Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές