A Poisson limit theorem for reliability models based on Markov chains

Central Limit Theorem for Hitting times of Functionals of Markov Jump Processes

A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications. Mathem...

Central and Local Limit Theories in Markov Dependent Random Variables

Evaluation of First and Second Markov Chains Sensitivity and Specificity as Statistical Approach for Prediction of Sequences of Genes in Virus Double Strand DNA Genomes

Growing amount of information on biological sequences has made application of statistical approaches necessary for modeling and estimation of their functions. In this paper, sensitivity and specificity of the first and second Markov chains for prediction of genes was evaluated using the complete double stranded  DNA virus. There were two approaches for prediction of each Markov Model parameter,...

Bootstrap Central Limit Theorem for Chains of Infinite Order via Markov Approximations

We present a new approach to the bootstrap for chains of infinite order taking values on a finite alphabet. It is based on a sequential Bootstrap Central Limit Theorem for the sequence of canonical Markov approximations of the chain of infinite order. Combined with previous results on the rate of approximation this leads to a Central Limit Theorem for the bootstrapped estimator of the sample me...

A Bayesian Networks Approach to Reliability Analysis of a Launch Vehicle Liquid Propellant Engine

This paper presents an extension of Bayesian networks (BN) applied to reliability analysis of an open gas generator cycle Liquid propellant engine (OGLE) of launch vehicles. There are several methods for system reliability analysis such as RBD, FTA, FMEA, Markov Chains, and etc. But for complex systems such as LV, they are not all efficiently applicable due to failure dependencies between compo...