L z -Transform for a Discrete-State Continuous-Time Markov Process and its Applications to Multi-State System Reliability

2011 ◽  
pp. 79-95 ◽  
Author(s):  
Anatoly Lisnianski
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
System Reliability ◽  
State System ◽  
Discrete State

scholarly journals Possibility of Application of the Theory of Semi-Markov Processes to Determine Reliability of Diagnosing Systems / MOŻLIWOŚĆ ZASTOSOWANIA TEORII PROCESÓW SEMI-MARKOWA DO OKREŚLENIA NIEZAWODNOŚCI SYSTEMÓW DIAGNOZUJĄCYCH

2012 ◽  
Vol 24 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Jerzy Girtler
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Continuous Time ◽  
Diagnostic Tests ◽  
The State ◽  
Actual State ◽  
Reliability Model ◽  
Discrete State ◽  
Semi Markov Process ◽  
Semi Markov Processes

Abstract The paper provides justification for the necessity to define reliability of diagnosing systems (SDG) in order to develop a diagnosis on state of any technical mechanism being a diagnosed system (SDN). It has been shown that the knowledge of SDG reliability enables defining diagnosis reliability. It has been assumed that the diagnosis reliability can be defined as a diagnosis property which specifies the degree of recognizing by a diagnosing system (SDG) the actual state of the diagnosed system (SDN) which may be any mechanism, and the conditional probability p(S*/K*) of occurrence (existence) of state S* of the mechanism (SDN) as a diagnosis measure provided that at a specified reliability of SDG, the vector K* of values of diagnostic parameters implied by the state, is observed. The probability that SDG is in the state of ability during diagnostic tests and the following diagnostic inferences leading to development of a diagnosis about the SDN state, has been accepted as a measure of SDG reliability. The theory of semi-Markov processes has been used for defining the SDG reliability, that enabled to develop a SDG reliability model in the form of a seven-state (continuous-time discrete-state) semi-Markov process of changes of SDG states.

Randomization of intensities in a Markov chain

1979 ◽  
Vol 11 (2) ◽  
pp. 397-421 ◽  
Author(s):  
M. Yadin ◽  
R. Syski
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
State Space ◽  
Continuous Time ◽  
Markovian Process ◽  
Time Parameter ◽  
Discrete State ◽  
Intensity Matrix ◽  
The Matrix ◽  
Discrete State Space

The matrix of intensities of a Markov process with discrete state space and continuous time parameter undergoes random changes in time in such a way that it stays constant between random instants. The resulting non-Markovian process is analyzed with the help of supplementary process defined in terms of variations of the intensity matrix. Several examples are presented.

Randomization of intensities in a Markov chain

1979 ◽  
Vol 11 (02) ◽  
pp. 397-421
Author(s):  
M. Yadin ◽  
R. Syski
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
State Space ◽  
Continuous Time ◽  
Markovian Process ◽  
Time Parameter ◽  
Discrete State ◽  
Intensity Matrix ◽  
The Matrix ◽  
Discrete State Space

The matrix of intensities of a Markov process with discrete state space and continuous time parameter undergoes random changes in time in such a way that it stays constant between random instants. The resulting non-Markovian process is analyzed with the help of supplementary process defined in terms of variations of the intensity matrix. Several examples are presented.

MANAGEMENT OF THE SUCCESS OF STUDENT’S LEARNING BASED ON THE MARKOV MODEL

2018 ◽  
pp. 4-11
Author(s):  
M. V. Noskov ◽  
M. V. Somova ◽  
I. M. Fedotova
Keyword(s):  
Information System ◽  
Markov Process ◽  
Continuous Time ◽  
Information Technologies ◽  
Educational Process ◽  
Automated Information System ◽  
The Subject ◽  
The University ◽  
Independent Work ◽  
Near Future

The article proposes a model for forecasting the success of student’s learning. The model is a Markov process with continuous time, such as the process of “death and reproduction”. As the parameters of the process, the intensities of the processes of obtaining and assimilating information are offered, and the intensity of the process of assimilating information takes into account the attitude of the student to the subject being studied. As a result of applying the model, it is possible for each student to determine the probability of a given formation of ownership of the material being studied in the near future. Thus, in the presence of an automated information system of the university, the implementation of the model is an element of the decision support system by all participants in the educational process. The examples given in the article are the results of an experiment conducted at the Institute of Space and Information Technologies of Siberian Federal University under conditions of blended learning, that is, under conditions when classroom work is accompanied by independent work with electronic resources.

scholarly journals Mapping TASEP back in time

2021 ◽  
Author(s):  
Leonid Petrov ◽  
Axel Saenz
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
Exclusion Process ◽  
Discrete Space ◽  
Baxter Equation ◽  
Simple Exclusion Process ◽  
Open Questions ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Hammersley Process

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

Bayesian Networks Application in Multi-State System Reliability Analysis

2013 ◽  
Vol 347-350 ◽  
pp. 2590-2595 ◽  
Author(s):  
Sheng Zhai ◽  
Shu Zhong Lin
Keyword(s):  
Bayesian Network ◽  
Reliability Analysis ◽  
System Reliability ◽  
Prior Probability ◽  
State System ◽  
Weak Links ◽  
Uncertain Reasoning ◽  
Reliability Modeling ◽  
Line System ◽  
Reliability Indices

Aiming at the limitations of traditional reliability analysis theory in multi-state system, a method for reliability modeling and assessment of a multi-state system based on Bayesian Network (BN) is proposed with the advantages of uncertain reasoning and describing multi-state of event. Through the case of cell production line system, in this paper we will discuss how to establish and construct a multi-state system model based on Bayesian network, and how to apply the prior probability and posterior probability to do the bidirectional inference analysis, and directly calculate the reliability indices of the system by means of prior probability and Conditional Probability Table (CPT) . Thereby we can do the qualitative and quantitative analysis of the multi-state system reliability, identify the weak links of the system, and achieve assessment of system reliability.

Dynamic performance evaluation of multi – state systems under non – homogeneous continuous time Markov process degradation using lifetimes in terms of order statistics

2017 ◽  
Vol 231 (3) ◽  
pp. 255-264 ◽  
Author(s):  
Funda Iscioglu
Keyword(s):  
Markov Process ◽  
Order Statistics ◽  
Continuous Time ◽  
Dynamic Performance ◽  
Real Life ◽  
State Change ◽  
Transition Rates ◽  
Lifetime Analysis ◽  
Complete Failure ◽  
Effect Of Age

In multi-state modelling a system and its components have a range of performance levels from perfect functioning to complete failure. Such a modelling is more flexible to understand the behaviour of mechanical systems. To evaluate a system’s dynamic performance, lifetime analysis of a multi-state system has been considered in many research articles. The order statistics related analysis for the lifetime properties of multi-state k-out-of-n systems have recently been studied in the literature in case of homogeneous continuous time Markov process assumption. In this paper, we develop the reliability measures for multi-state k-out-of-n systems by assuming a non-homogeneous continuous time Markov process for the components which provides time dependent transition rates between states of the components. Therefore, we capture the effect of age on the state change of the components in the analysis which is typical of many systems and more practical to use in real life applications.

Modeling multi-state system reliability analysis in a power station under fatal and nonfatal shocks: a simulation approach

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Reza Pourhassan ◽  
Sadigh Raissi ◽  
Arash Apornak
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
System Performance ◽  
Failure Process ◽  
State System ◽  
Failure Behavior ◽  
Simulation Approach ◽  
Critical System ◽  
Content Type ◽  
System Reliability Analysis

PurposeIn some environments, the failure rate of a system depends not only on time but also on the system condition, such as vibrational level, efficiency and the number of random shocks, each of which causes failure. In this situation, systems can keep working, though they fail gradually. So, the purpose of this paper is modeling multi-state system reliability analysis in capacitor bank under fatal and nonfatal shocks by a simulation approach.Design/methodology/approachIn some situations, there may be several levels of failure where the system performance diminishes gradually. However, if the level of failure is beyond a certain threshold, the system may stop working. Transition from one faulty stage to the next can lead the system to more rapid degradation. Thus, in failure analysis, the authors need to consider the transition rate from these stages in order to model the failure process.FindingsThis study aims to perform multi-state system reliability analysis in energy storage facilities of SAIPA Corporation. This is performed to extract a predictive model for failure behavior as well as to analyze the effect of shocks on deterioration. The results indicate that the reliability of the system improved by 6%.Originality/valueThe results of this study can provide more confidence for critical system designers who are engaged on the proper system performance beyond economic design.

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