Viswanathan Arunachalam

arXiv2016

Generalized Shock Model Based On The Frequency of Shocks: A Simple Approach

In a $δ-$shock model, a system subject to randomly occurring shocks, the system fails when the time between two successive shocks lies below a threshold $δ$. In this note, we study the generalization of this model where such $δ-$shocks are accumulated and the system fails on the occurrence of $k^{th}$ such a $δ-$shock. The probability distribution of the system failure time and the statistical characteristics are explicitly obtained. Normal approximation to the failure time distribution is proposed.

stat.AP↗

arXiv2012

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

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.

math.ST↗