Table of Contents
Journal of Quality and Reliability Engineering
Volume 2013, Article ID 494976, 9 pages
http://dx.doi.org/10.1155/2013/494976
Research Article

Distributions of Patterns of Pair of Successes Separated by Failure Runs of Length at Least and at Most Involving Markov Dependent Trials: GERT Approach

1Department of Statistics, University of Delhi, Delhi 7, India
2RMS India, A-7, Sector 16, Noida 201 301, India
3The Institute for Innovation and Inventions with Mathematics and IT (IIIMIT), Shiv Nadar University, Greater Noida 203207, India

Received 25 June 2012; Revised 10 December 2012; Accepted 11 December 2012

Academic Editor: Tadashi Dohi

Copyright © 2013 Kanwar Sen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use the Graphical Evaluation and Review Technique (GERT) to obtain probability generating functions of the waiting time distributions of 1st, and th nonoverlapping and overlapping occurrences of the pattern , involving homogenous Markov dependent trials. GERT besides providing visual picture of the system helps to analyze the system in a less inductive manner. Mean and variance of the waiting times of the occurrence of the patterns have also been obtained. Some earlier results existing in literature have been shown to be particular cases of these results.