scholarly journals Reliability Analysis of 6-Component Star Markov Repairable System with Spatial Dependence

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Liying Wang ◽  
Qing Yang ◽  
Yuran Tian
Keyword(s):  
Spatial Dependence ◽  
Repairable System ◽  
Analysis Method ◽  
Repairable Systems ◽  
Rate Matrix ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Reliability Indices ◽  
Transition Rate Matrix ◽  
Markov Repairable System

Star repairable systems with spatial dependence consist of a center component and several peripheral components. The peripheral components are arranged around the center component, and the performance of each component depends on its spatial “neighbors.” Vector-Markov process is adapted to describe the performance of the system. The state space and transition rate matrix corresponding to the 6-component star Markov repairable system with spatial dependence are presented via probability analysis method. Several reliability indices, such as the availability, the probabilities of visiting the safety, the degradation, the alert, and the failed state sets, are obtained by Laplace transform method and a numerical example is provided to illustrate the results.

AN IMPROVEMENT OF MARKOVIAN INTEGRATION BY PARTS FORMULA AND APPLICATION TO SENSITIVITY COMPUTATION

2021 ◽  
pp. 1-21
Author(s):  
Yue Liu ◽  
Zhiyan Shi ◽  
Ying Tang ◽  
Jingjing Yao ◽  
Xincheng Zhu
Keyword(s):  
Perturbation Analysis ◽  
Malliavin Calculus ◽  
Transition Rate ◽  
Infinitesimal Perturbation Analysis ◽  
Analysis Method ◽  
Rate Matrix ◽  
Integration By Parts ◽  
Transition Rate Matrix ◽  
Integration By Parts Formula ◽  
Infinitesimal Perturbation

This paper establishes a new version of integration by parts formula of Markov chains for sensitivity computation, under much lower restrictions than the existing researches. Our approach is more fundamental and applicable without using Girsanov theorem or Malliavin calculus as did by past papers. Numerically, we apply this formula to compute sensitivity regarding the transition rate matrix and compare with a recent research by an IPA (infinitesimal perturbation analysis) method and other approaches.

Q-homotopy analysis transform method applied to fractional Kundu–Eckhaus equation and fractional massive Thirring model arising in quantum field theory

2019 ◽  
Vol 12 (03) ◽  
pp. 1950045 ◽  
Author(s):  
Anas. A. M. Arafa ◽  
Ahmed. M. Sh. Hagag
Keyword(s):  
Field Theory ◽  
Power Efficiency ◽  
Approximate Solutions ◽  
Thirring Model ◽  
Quantum Field ◽  
Analysis Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Massive Thirring Model ◽  
Homotopy Analysis

In this paper, [Formula: see text]-homotopy analysis transform method ([Formula: see text]-HATM) is used to solve fractional Kundu–Eckhaus equation and fractional massive Thirring model. This method is a mixture of Homotopy analysis method (HAM) and Laplace transform method (LTM) when [Formula: see text]. The approximate solutions obtained by [Formula: see text]-HATM are compared with the exact solutions. Numerical results are known through different graphs and tables. The results light the power, efficiency, simplicity, and reliability of the proposed method.

Research on the model of a multistate aggregated Markov repairable system

2019 ◽  
pp. 1748006X1988765
Author(s):  
Quan Zhang ◽  
Shihang Yu ◽  
Yang Han ◽  
Yanjun Li
Keyword(s):  
System Performance ◽  
The State ◽  
Theory And Practice ◽  
Process Theory ◽  
Repairable System ◽  
Repairable Systems ◽  
Numerical Examples ◽  
Markov Repairable System ◽  
Special Case ◽  
Theoretical Results

In theory and practice, system performance is one of the most important issues. Therefore, a series of indexes has been proposed for evaluating the system performance, such as availability. However, these indexes still cannot meet the variant requirements in the reliability and other fields. The purpose of the article is to develop some theoretical results that may be used in modeling the evolution of system performance. So, based on the aggregated stochastic process theory, some new indexes are introduced and established in Markov repairable systems. In this model, the state space is partitioned into working subset W and failure subset F. The system is regarded as stable if the state of system enters one subset, either W or F, at any instance and sojourns within the subset exceeding a given non-negative threshold [Formula: see text]. Otherwise, the system is regarded as unstable. Under these assumptions, the concepts of point-wise and interval-wise are proposed, and the computation formulae of two types of indexes are derived in the theory. Finally, a special case and a few of numerical examples are given to illustrate the results obtained in the paper.

scholarly journals Stability Analysis of a Repairable System with Warning Device and Repairman Vacation

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Yangli Ren ◽  
Lina Guo ◽  
Lingling Zhang
Keyword(s):  
Existence And Uniqueness ◽  
Continuous Semigroup ◽  
Semigroup Theory ◽  
System Dynamic ◽  
Markov Renewal Process ◽  
Repairable System ◽  
Analysis Method ◽  
Reliability Indices ◽  
Dynamic Solution ◽  
Warning Device

This paper considers a simple repairable system with a warning device and a repairman who can have delayed-multiple vacations. By Markov renewal process theory and the probability analysis method, the system is first transformed into a group of integrodifferential equations. Then, the existence and uniqueness as well as regularity of the system dynamic solution are discussed with the functional analysis method. Further, the asymptotic stability, especially the exponential stability of the system dynamic solution, is studied by using the strongly continuous semigroup theory orC0semigroup theory. The reliability indices and some applications (such as the comparisons of indices and profit of systems with and without warning device), as well as numerical examples, are presented at the end of the paper.

Homotopy analysis transform algorithm to solve time-fractional foam drainage equation

2016 ◽  
Vol 5 (3) ◽  
Author(s):  
Mukesh Singh ◽  
Mohd Naseem ◽  
Amit Kumar ◽  
Sunil Kumar
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
Homotopy Analysis Method ◽  
Present Method ◽  
Analysis Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Analysis ◽  
Foam Drainage Equation ◽  
Foam Drainage

AbstractThis paper emphasizes on finding the solution for a foam drainageequation using the technique of modified homotopy analysis transform method (MHATM). MHATM is a new amalgamation of the homotopy analysis method and Laplace transform method with homotopy polynomial. Comparisons are made between the results of the proposed method for different values of fractional derivative α and exact solutions. Then, we analyze the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method.

scholarly journals A Simple Repairable System with Warning Device

2015 ◽  
Vol 2015 ◽  
pp. 1-18
Author(s):  
Xiao Zhang ◽  
Lina Guo
Keyword(s):  
Continuous Semigroup ◽  
Semigroup Theory ◽  
Good Condition ◽  
Markov Renewal Process ◽  
Repairable System ◽  
Analysis Method ◽  
Numerical Examples ◽  
Reliability Indices ◽  
Unique Existence ◽  
Warning Device

This paper considers a simple repairable system with a warning device which can signal an alarm when the system is not in good condition and a repairman who can have delayed-multiple vacations. By using Markov renewal process theory and the probability analysis method, the system is first described into a group of integrodifferential equations. Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution, are studied by using the strongly continuous semigroup theory orC0semigroup theory and the spectrum theory. The reliability indices and some applications (such as the comparisons of some indexes and profit of systems with and without warning device) as well as numerical examples are presented at the end of the paper.

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

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