scholarly journals Semi-Markov reliability model of two different units cold standby system

2017 ◽  
pp. 1-1
Author(s):  
Franciszek Grabski
Keyword(s):  
Markov Processes ◽  
First Passage Time ◽  
Random Variable ◽  
Reliability Function ◽  
Passage Time ◽  
Time To Failure ◽  
Operation Process ◽  
Cold Standby ◽  
Standby System ◽  
Semi Markov Processes

A semi-Markov stochastic process is used for solving in a reliability problem in the paper. The problem concerns of two different component cold standby system and a switch. To obtain the reliability characteristic and parameters of the system we construct so called an embedded semi-Markov process in the process describing operation process of the system. In the model the conditional time to failure of the system is represented by a random variable denoting the first passage time from the given state to the specified subset of states. We apply theorems of the semi-Markov processes theory concerning the conditional reliability functions to calculate the reliability function and mean time to failure of the system. Often an exact reliability function of the system by using Laplace transform is difficult to calculate, frequently impossible. The semi-Markov processes perturbation theory, allows to obtain an approximate reliability function of the system in that case.

scholarly journals Reliability Electrical Power System of Hospital as Cold Standby System

2016 ◽  
Vol 37 (1) ◽  
pp. 153-168
Author(s):  
Franciszek Grabski
Keyword(s):  
Power System ◽  
Markov Processes ◽  
First Passage Time ◽  
Electrical Power ◽  
Random Variable ◽  
Time To Failure ◽  
Electrical Power System ◽  
Cold Standby ◽  
Standby System ◽  
Semi Markov Processes

Abstract The probabilistic model of a hospital electrical power system consisting of mains, an emergency power system and the automatic transfer switch with the generator starter are discussed in this paper. The reliability model is semi-Markov process describing two different units renewable cold standby system and switch. The embedded Semi-Markov processes concept is applied for description of the system evolution. Time to failure of the system is represented by a random variable denoting the first passage time of the process from the given state to the subset of states. The appropriate theorems of the Semi-Markov processes theory allow us to evaluate the reliability function and some reliability characteristics.

scholarly journals Stochastic Analysis of a Two-Unit Cold Standby System Wherein Both Units May Become Operative Depending upon the Demand

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Reetu Malhotra ◽  
Gulshan Taneja
Keyword(s):  
Markov Processes ◽  
Stochastic Analysis ◽  
The Other ◽  
Regenerative Processes ◽  
Cold Standby ◽  
Standby System ◽  
Semi Markov Processes ◽  
System Effectiveness

The present paper analyzes a two-unit cold standby system wherein both units may become operative depending upon the demand. Initially, one of the units is operative while the other is kept as cold standby. If the operative unit fails or the demand increases to the extent that one operative unit is not capable of meeting the demand, the standby unit becomes operative instantaneously. Thus, both units may become operative simultaneously to meet the increased demand. Availability in three types of upstates is as follows: (i) when the demand is less than or equal to production manufactured by one unit; (ii) when the demand is greater than whatever produced by one unit but less than or equal to production made by two units; and (iii) when the demand is greater than the produces by two units. Other measures of the system effectiveness have also been obtained in general case as well as for a particular case. Techniques of semi-Markov processes and regenerative processes have been used to obtain various measures of the system effectiveness.

Identifying Coefficients in the Spectral Representation for First Passage Time Distributions

1987 ◽  
Vol 1 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Mark Brown ◽  
Yi-Shi Shao
Keyword(s):  
Markov Processes ◽  
Time Distribution ◽  
Infinitesimal Generator ◽  
Spectral Representation ◽  
First Passage Time ◽  
Passage Time ◽  
Spectral Approach ◽  
Generator Matrix ◽  
Eigenvalues And Eigenvectors ◽  
First Passage

The spectral approach to first passage time distributions for Markov processes requires knowledge of the eigenvalues and eigenvectors of the infinitesimal generator matrix. We demonstrate that in many cases knowledge of the eigenvalues alone is sufficient to compute the first passage time distribution.

scholarly journals Non-radial functions, nonlocal operators and Markov processes over p-adic numbers

2019 ◽  
Vol 24 (2) ◽  
pp. 381-406 ◽  
Author(s):  
Leonardo Fabio Chacón-Cortés ◽  
Oscar Francisco Casas-Sánchez
Keyword(s):  
Markov Processes ◽  
First Passage Time ◽  
Parabolic Type ◽  
Passage Time ◽  
Fundamental Solutions ◽  
Nonlocal Operators ◽  
Transition Functions ◽  
Time Problem ◽  
The Cauchy Problem ◽  
First Passage Time Problem

The main goal of this article is to study a new class of nonlocal operators and the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated with them. The fundamental solutions of these equations are transition functions of Markov processes on an n-dimensional vector space over the p-adic numbers. We also study some properties of these Markov processes, including the first passage time problem.

scholarly journals A unified approach for drawdown (drawup) of time-homogeneous Markov processes

2017 ◽  
Vol 54 (2) ◽  
pp. 603-626 ◽  
Author(s):  
David Landriault ◽  
Bin Li ◽  
Hongzhong Zhang
Keyword(s):  
Markov Processes ◽  
Financial Risk ◽  
First Passage Time ◽  
Passage Time ◽  
Regularity Conditions ◽  
Unified Approach ◽  
First Passage ◽  
Underlying Process ◽  
Short Time ◽  
General Time

AbstractDrawdown (respectively, drawup) of a stochastic process, also referred as the reflected process at its supremum (respectively, infimum), has wide applications in many areas including financial risk management, actuarial mathematics, and statistics. In this paper, for general time-homogeneous Markov processes, we study the joint law of the first passage time of the drawdown (respectively, drawup) process, its overshoot, and the maximum of the underlying process at this first passage time. By using short-time pathwise analysis, under some mild regularity conditions, the joint law of the three drawdown quantities is shown to be the unique solution to an integral equation which is expressed in terms of fundamental two-sided exit quantities of the underlying process. Explicit forms for this joint law are found when the Markov process has only one-sided jumps or is a Lévy process (possibly with two-sided jumps). The proposed methodology provides a unified approach to study various drawdown quantities for the general class of time-homogeneous Markov processes.

A computational approach to first-passage-time problems for Gauss–Markov processes

2001 ◽  
Vol 33 (2) ◽  
pp. 453-482 ◽  
Author(s):  
E. Di Nardo ◽  
A. G. Nobile ◽  
E. Pirozzi ◽  
L. M. Ricciardi
Keyword(s):  
Markov Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Computational Approach ◽  
First Passage ◽  
First Passage Time Problems

scholarly journals Passage-time computation and aggregation strategies for large semi-Markov processes

2011 ◽  
Vol 68 (3) ◽  
pp. 221-236 ◽  
Author(s):  
Marcel C. Guenther ◽  
Nicholas J. Dingle ◽  
Jeremy T. Bradley ◽  
William J. Knottenbelt
Keyword(s):  
Markov Processes ◽  
Passage Time ◽  
Semi Markov Processes

scholarly journals Tools to Estimate the First Passage Time to a Convex Barrier

2005 ◽  
Vol 42 (1) ◽  
pp. 61-81
Author(s):  
Ola Hammarlid
Keyword(s):  
Limit Distribution ◽  
Sequential Analysis ◽  
Large Deviation ◽  
First Passage Time ◽  
Stopping Time ◽  
Random Variable ◽  
Passage Time ◽  
First Passage ◽  
Linear Barrier ◽  
Asymptotic Normal

The first passage time of a random walk to a barrier (constant or concave) is of great importance in many areas, such as insurance, finance, and sequential analysis. Here, we consider a sum of independent, identically distributed random variables and the convex barrier cb(n/c), where c is a scale parameter and n is time. It is shown, using large-deviation techniques, that the limit distribution of the first passage time decays exponentially in c. Under a tilt of measure, which changes the drift, four properties are proved: the limit distribution of the overshoot is distributed as an overshoot over a linear barrier; the stopping time is asymptotically normally distributed when it is properly normalized; the overshoot and the asymptotic normal part are asymptotically independent; and the overshoot over a linear barrier is bounded by an exponentially distributed random variable. The determination of the function that multiplies the exponential part is guided by consideration of these properties.

scholarly journals A New Analytic Method of Cold Standby System Reliability Model with Priority

2018 ◽  
Vol 175 ◽  
pp. 03060
Author(s):  
Di Peng ◽  
Ni Zichun ◽  
Hu Bin
Keyword(s):  
System Reliability ◽  
Reliability Function ◽  
Matrix Analysis ◽  
Reliability Model ◽  
Reliability Indicators ◽  
Reliability Modelling ◽  
Maintenance Time ◽  
Cold Standby ◽  
The Matrix ◽  
Standby System

For different importance of components in equipment system, a cold standby system with two different components is studied when important components enjoy the priority in use and maintenance. Considering the application of exponential distribution, Weibull distribution and other typical distributions in resolving the problems subject to complicated calculation and strict constraints in the past reliability modelling, the highly applicable phase-type (PH) distribution is utilized to describe the life and maintenance time of system components in a unified manner. A system reliability model is built for wider applicability. With the matrix analysis method, expressions are obtained for a number of reliability indicators such as system reliability function, steady-state availability, mean up time and mean down time of system. In the end, examples are presented to verify the correctness and applicability of the model.

scholarly journals A Symmetry-Based Approach for First-Passage-Times of Gauss-Markov Processes through Daniels-Type Boundaries

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 279
Author(s):  
Enrica Pirozzi
Keyword(s):  
Probability Density ◽  
Markov Processes ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Transition Probability ◽  
Passage Time ◽  
First Passage ◽  
Transition Probability Density ◽  
Symmetry Properties ◽  
Time Density

Symmetry properties of the Brownian motion and of some diffusion processes are useful to specify the probability density functions and the first passage time density through specific boundaries. Here, we consider the class of Gauss-Markov processes and their symmetry properties. In particular, we study probability densities of such processes in presence of a couple of Daniels-type boundaries, for which closed form results exit. The main results of this paper are the alternative proofs to characterize the transition probability density between the two boundaries and the first passage time density exploiting exclusively symmetry properties. Explicit expressions are provided for Wiener and Ornstein-Uhlenbeck processes.

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