This paper discusses the performance evaluation and availability analysis of ammonia synthesis unit of a fertilizer plant. The fertilizer plant is a complex and repairable engineering system comprises of various units viz. shell gasification and carbon recovery, desulphurization, co-shift conversion, decarbonation, nitrogen wash and ammonia synthesis etc. One of the most important functionaries...

A hard look in the mirror, as they say, is good for fitness and vitality. The time seems ripe, then, fifty years after the birth of modern linguistics, to reexamine its foundations. Or rather, the rubble, as the editors of Probabilistic linguistics suggest : corpus statistics, Markov chains, information theory, and the very notion of probability that were supposedly buried by the Chomskyan land...

In the context of Markov processes, we show a new scheme to derive a dual process and duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and annihilation operators. For some stochastic processes, duality relations have been known, which connect continuous time Markov processes with discrete state space and th...

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.

The purpose of this paper is to extend some results of Karlin and McGregor’s and Chihara’s concerning the three-terms recurrence relation for polynomials orthogonal with respect to a measure on the nonnegative real axis. Our findings are relevant for the analysis of a type of Markov chains known as birth-death processes with killing.

We study asymptotic properties of the continuous Glauber dynamics with unbounded death and constant birth rates. In particular, an information about the spectrum location for the symbol of the Markov generator is obtained. The latter fact is used for the proof of the ergodicity of this process. We show that the speed of convergence to the equilibrium is exponential.

It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions whose stationary distribution is the Ewens distribution, and some birth-death chains.

OBJECTIVES Previous studies indicate that nulliparous women (i.e., women having no previous births) are at higher risk for adverse birth outcomes than multiparous women (i.e., women having had at least one previous birth). We examined whether part of the difference in adverse outcome rates is attributable to nulliparous women with poor pregnancy outcomes being less likely (through choice or fec...

We analyze an interacting particle system with a Markov evolution of birth-anddeath type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population in course of the stochastic evolution.

This article defines and describes the level-dependent quasi-birth-and-death (LDQBD) process, a generalization of the homogeneous (or level-independent) quasi-birth-and-death (QBD) process. Like its level-independent counterpart, the LDQBD process is a bivariate Markov process whose transition probability matrix (or infinitesimal generator matrix) exhibits a block tri-diagonal structure. Howeve...