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Theory of two-parameter Markov chain with an application in warranty study

Authors
  • Calvache, Álvaro
  • Arunachalam, Viswanathan
Type
Preprint
Publication Date
Apr 30, 2012
Submission Date
Apr 30, 2012
Identifiers
arXiv ID: 1204.6641
Source
arXiv
License
Yellow
External links

Abstract

In this paper we present the classical results of Kolmogorov's backward and forward equations to the case of a two-parameter Markov process. These equations relates the infinitesimal transition matrix of the two-parameter Markov process. However, solving these equations is not possible and we require a numerical procedure. In this paper, we give an alternative method by use of double Laplace transform of the transition probability matrix and of the infinitesimal transition matrix of the process. An illustrative example is presented for the method proposed. In this example, we consider a two-parameter warranty model, in which a system can be any of these states: working, failure. We calculate the transition density matrix of these states and also the cost of the warranty for the proposed model.

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