Availability of periodically inspected systems subject to Markovian degradation

2002 ◽  
Vol 39 (4) ◽  
pp. 700-711 ◽  
Author(s):  
Peter C. Kiessler ◽  
Georgia-Ann Klutke ◽  
Yoonjung Yang
Keyword(s):  
Markov Chain ◽  
Lifetime Distribution ◽  
Periodic Inspection ◽  
Inspection Policy

This paper studies inspected systems with non-self-announcing failures where the rate of deterioration is governed by a Markov chain. We compute the lifetime distribution and availability when the system is inspected according to a periodic inspection policy. In doing so, we expose the role of certain transient distributions of the environment.

Availability of periodically inspected systems subject to Markovian degradation

2002 ◽  
Vol 39 (04) ◽  
pp. 700-711 ◽  
Author(s):  
Peter C. Kiessler ◽  
Georgia-Ann Klutke ◽  
Yoonjung Yang
Keyword(s):  
Markov Chain ◽  
Lifetime Distribution ◽  
Periodic Inspection ◽  
Inspection Policy

This paper studies inspected systems with non-self-announcing failures where the rate of deterioration is governed by a Markov chain. We compute the lifetime distribution and availability when the system is inspected according to a periodic inspection policy. In doing so, we expose the role of certain transient distributions of the environment.

Identifying Transition Rates of Ion Channels with One Loop

2011 ◽  
Vol 282-283 ◽  
pp. 395-398
Author(s):  
Xu Yan Xiang ◽  
Li Fang Liu ◽  
Ye Chen
Keyword(s):  
Markov Chain ◽  
Ion Channels ◽  
Lifetime Distribution ◽  
Transition Rates ◽  
Lifetime Distributions ◽  
Constrained Equations ◽  
Gating Scheme

The constrained equations between transition rates and the derivative of open lifetime and shut lifetime distribution for a given state set of Markov Chain are provided. For gating scheme of ion channels with one loop, it is derived by those underlying information that all transition rates can be identified by their open and shut lifetime distributions at state 0 and any other two adjacent states.

Availability of Systems Subject to Multiple Failure Modes Under Calendar-based Inspection

2020 ◽  
pp. 2150022
Author(s):  
Himani Pant ◽  
S. B. Singh ◽  
Neelam Chantola
Keyword(s):  
Wind Turbine ◽  
Failure Mode ◽  
Functional State ◽  
Failure Modes ◽  
Failure Time ◽  
Random Time ◽  
Multiple Failure Modes ◽  
Periodic Inspection ◽  
Wind Turbine System ◽  
Inspection Policy

The availability of a maintained system subject to multiple failure modes undergoing periodic inspection is studied in this paper. Calendar-based inspection policy is being incorporated. Explicitly, a system with a functional state and [Formula: see text] failure modes is taken into account. Failure time of each failure mode is random. As the [Formula: see text]th ([Formula: see text]) failure occurs, the respective corrective repair taking a random time [Formula: see text] [Formula: see text] is carried out. Some theorems on the point availability and limiting average availability are obtained in this study. The application of the derived result is explained through an example of wind turbine system.

scholarly journals A Stochastic Cobweb Dynamical Model

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
Serena Brianzoni ◽  
Cristiana Mammana ◽  
Elisabetta Michetti ◽  
Francesco Zirilli
Keyword(s):  
Dynamical System ◽  
Markov Chain ◽  
Random Variable ◽  
Asymptotically Stable ◽  
Stochastic Dynamical System ◽  
Cobweb Model ◽  
Linear Demand ◽  
Discrete Values ◽  
Analytical Tools

We consider the dynamics of a stochastic cobweb model with linear demand and a backward-bending supply curve. In our model, forward-looking expectations and backward-looking ones are assumed, in fact we assume that the representative agent chooses the backward predictor with probability , and the forward predictor with probability , so that the expected price at time is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.

scholarly journals Identifying the role of typhoons as drought busters in South Korea based on hidden Markov chain models

2015 ◽  
Vol 42 (8) ◽  
pp. 2797-2804 ◽  
Author(s):  
Jiyoung Yoo ◽  
Hyun-Han Kwon ◽  
Byung-Jin So ◽  
Balaji Rajagopalan ◽  
Tae-Woong Kim
Keyword(s):  
Markov Chain ◽  
South Korea ◽  
Hidden Markov ◽  
Hidden Markov Chain ◽  
Markov Chain Models

scholarly journals On the use of Markovian stick-breaking priors

2021 ◽  
pp. 153-174
Author(s):  
William Lippitt ◽  
Sunder Sethuraman
Keyword(s):  
Markov Chain ◽  
Simulated Annealing ◽  
Dirichlet Process ◽  
Test Cases ◽  
Content Type ◽  
Inference Test ◽  
Irreducible Markov Chain ◽  
Class Of Priors ◽  
Distributional Limits

Recently, a ‘Markovian stick-breaking’ process which generalizes the Dirichlet process ( μ , θ ) (\mu , \theta ) with respect to a discrete base space X \mathfrak {X} was introduced. In particular, a sample from from the ‘Markovian stick-breaking’ processs may be represented in stick-breaking form ∑ i ≥ 1 P i δ T i \sum _{i\geq 1} P_i \delta _{T_i} where { T i } \{T_i\} is a stationary, irreducible Markov chain on X \mathfrak {X} with stationary distribution μ \mu , instead of i.i.d. { T i } \{T_i\} each distributed as μ \mu as in the Dirichlet case, and { P i } \{P_i\} is a GEM ( θ ) (\theta ) residual allocation sequence. Although the previous motivation was to relate these Markovian stick-breaking processes to empirical distributional limits of types of simulated annealing chains, these processes may also be thought of as a class of priors in statistical problems. The aim of this work in this context is to identify the posterior distribution and to explore the role of the Markovian structure of { T i } \{T_i\} in some inference test cases.

scholarly journals Availability of periodically inspected systems with Markovian wear and shocks

2006 ◽  
Vol 43 (02) ◽  
pp. 303-317 ◽  
Author(s):  
Jeffrey P. Kharoufeh ◽  
Daniel E. Finkelstein ◽  
Dustin G. Mixon
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Lifetime Distribution ◽  
Time To Failure ◽  
Continuous Time Markov Chain ◽  
Mean Time To Failure ◽  
Numerical Examples ◽  
Shock Process ◽  
Hidden Failures ◽  
Mean Time

We analyze a periodically inspected system with hidden failures in which the rate of wear is modulated by a continuous-time Markov chain and additional damage is induced by a Poisson shock process. We explicitly derive the system's lifetime distribution and mean time to failure, as well as the limiting average availability. The main results are illustrated in two numerical examples.

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