Strictly Increasing Markov Chains as Wear Processes
نویسنده
چکیده
To model the lifetime of a device, increasing Markov chains are used. The transition probabilities of the chain are as follows: pi, j = p if j = i+δ, and pi, j = 1− p if j = i+2δ. The mean time to failure of the device, namely the mean number of transitions required for the process, starting from x0, to take on a value greater than or equal to x0 + kδ is computed explicitly. A second version of this Markov chain, based on a standard Brownian motion that is discretized and conditioned to always move from its current state x to either x + δ or x + 2δ after time units, is also considered. Again the expected value of the time it takes the process to cross the boundary at x0 + kδ is computed explicitly.
منابع مشابه
On the stochastic evolution of finite populations.
This work is a systematic study of discrete Markov chains that are used to describe the evolution of a two-types population. Motivated by results valid for the well-known Moran (M) and Wright-Fisher (WF) processes, we define a general class of Markov chains models which we term the Kimura class. It comprises the majority of the models used in population genetics, and we show that many well-know...
متن کاملApproximation of Arbitrary Dirichlet Processes by Markov Chains 1);2)
We prove that any Hunt process on a Hausdorr topological space associated with a Dirichlet form can be approximated by a Markov chain in a canonical way. This also gives a new and \more explicit" proof for the existence of Hunt processes associated with strictly quasi-regular Dirichlet forms on general state spaces.
متن کاملEvaluation 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,...
متن کاملProbabilistic Sufficiency and Algorithmic Sufficiency from the point of view of Information Theory
Given the importance of Markov chains in information theory, the definition of conditional probability for these random processes can also be defined in terms of mutual information. In this paper, the relationship between the concept of sufficiency and Markov chains from the perspective of information theory and the relationship between probabilistic sufficiency and algorithmic sufficien...
متن کاملA Model For The Residence Time Distribution and Holdup Measurement in a Two Impinging Streams Cyclone Reactor/Contactor in Solid-Liquid Systems
In this paper a two impinging streams cyclone contacting system suitable for handling of solid-liquid systems has been studied. Certain pertinent parameters such as: solid holdup, mean residence time and Residence Time Distribution (RTD) of solid particles have been investigated. A stochastic model based on Markov chains processes has been applied which describe the behavior of solid partic...
متن کامل