Distributions of Patterns of Pair of Successes Separated by Failure Runs of Length at Least k1 and at Most k2 Involving Markov Dependent Trials: GERT Approach. (5th June 2013)

• Record Type: Journal Article
• Authors: Sen, Kanwar; Mohan, Pooja; Agarwal, Manju Lata
• Other Names: Dohi Tadashi Academic Editor.
• Is Part Of: Journal of quality and reliability engineering. Volume 2013(2013)
• Publication Date: 2013-06-05
• Subjects: Reliability (Engineering) -- Periodicals; Engineering -- Quality control -- Periodicals; Failure analysis (Engineering) -- Periodicals; Engineering -- Quality control; Failure analysis (Engineering); Reliability (Engineering); Electronic journals; Periodicals; 620.0045
• DOI: 10.1155/2013/494976
• Languages: English
• ISSNs: 2314-8055

Abstract

Abstract : We use the Graphical Evaluation and Review Technique (GERT) to obtain probability generating functions of the waiting time distributions of 1st, andm th nonoverlapping and overlapping occurrences of the patternΛ f k 1, k 2 = S F F ⋯ F ︸ k 1 ≤ k f ≤ k 2 S ( k 1 > 0 ), 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.