Συμβολή στη μελέτη ιδιοτήτων γήρανσης συστημάτων αξιοπιστίας και μη περαμετρικών διαγραμμάτων ελέγχου με χρήση της θεωρίας διατεταγμένων παρατηρήσεων

Abstract

Τhe present PhD Thesis deals with the theory and applications of Order Statistics in the fields of Reliability Theory and Statistical Quality Control. More specifically, in the first chapter it presents important notions and properties of the order statistics that will be proved useful in the sequel. In the second chapter, it introduces an important feature of a reliability system, which is called signature and is defined in terms of the ordered lifetimes of its components. In addition, it provides a formula that facilitates the evaluation of the signature of a reliability structure by a generating function approach. A simple sufficient condition is also derived for proving the nonpreservation of the IFR property by exploiting the signature of the system. Finally it studies applications of the signature in the stochastic comparison of reliability systems’ lifetimes. In the third chapter, it presents an overview of the literature on parametric and non-parametric control charts, while in the fourth chapter it introduces two new distribution-free control charts that take into account the location of a single order statistic of test samples. Finally, in the fifth chapter it introduces three new nonparametric Shewhart-type control charts that exploit run and Wilcoxon-type rank sum statistics to detect possible shifts of a monitored process.