Dynamic analysis of a unified multivariate counting process and its asymptotic behavior
type: Item
instance of: scholarly article
title: Dynamic analysis of a unified multivariate counting process and its asymptotic behavior
zbMATH Open document ID: 1179.60029
DOI: 10.1155/2009/219532
author: Ushio Sumita
author: Jia-Ping Huang
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2009-11-10T00:00:00Z
full work available at URL: https://eudml.org/doc/45714
review text: Summary: The class of counting processes constitutes a significant part of applied probability. The classic counting processes include Poisson processes, nonhomogeneous Poisson processes, and renewal processes. More sophisticated counting processes, including Markov renewal processes, Markov modulated Poisson processes, age-dependent counting processes, and the like, have been developed for accommodating a wider range of applications. These counting processes seem to be quite different on the surface, forcing one to understand each of them separately. The purpose of this paper is to develop a unified multivariate counting process, enabling one to express all of the above examples using its components, and to introduce new counting processes. The dynamic behavior of the unified multivariate counting process is analyzed, and its asymptotic behavior as \(t\rightarrow \infty \) is established. As an application, a manufacturing system with certain maintenance policies is considered, where the optimal maintenance policy for minimizing the total cost is obtained numerically.
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60K15
zbMATH DE Number: 5627878
zbMATH Keywords: unified multivariate counting process
zbMATH Keywords: dynamic behavior
zbMATH Keywords: manufacturing system with certain maintenance policies
Wikidata QID: Q58648413
MaRDI profile type: Publication
OpenAlex ID: W2148426395
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description: scientific article; zbMATH DE number 5627878