| Waiting time distributions of runs and patterns have been successfully used in various areas of statistics and applied probability—for example, in reliability, sampling inspection, quality control, DNA sequencing and hypothesis testing. The main goal of this thesis is to give a comprehensive study of waiting time distributions of runs and patterns using the finite Markov Chain imbedding technique. We provide a simple and general method to obtain the exact distributions, means and probability generating functions for waiting time distributions of compound and later patterns. Computational algorithms based on the finite Markov chain imbedding technique are developed for automatically computing the exact distributions, means and probability generating functions of waiting times for compound and later patterns.;To see the applications of waiting time distributions, we introduce a general theoretical framework that leads to the run-length distribution for a multitude of control charts that are based either on a simple rule (e.g., Shewhart, Cusum, EWMA charts) or on a compound set of rules (e.g., Shewhart with runs rules, robust Cusum and robust EWMA charts). It handles both discrete and continuous cases and can incorporate process properties, such as different types of shifts, directly. The framework is simple to apply and is fully automated. |
