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Lirong Cui - One of the best experts on this subject based on the ideXlab platform.
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extended phase type models for multistate competing risk Systems
Reliability Engineering & System Safety, 2019Co-Authors: Lirong CuiAbstract:Abstract Two extended Phase-type models with competing risks for failures of Markov Repairable Systems with absorbing states are presented in this article. We divide the states into three subsets: perfect, imperfect and failure (absorption) for a Markov Repairable System. Two models are developed in terms of the proposed failure criteria of the Repairable System. For model 1, the System failure criteria of the Repairable System are, whichever occurs first, (1) when the System goes into the failure state (absorption state), or (2) when the System transfers from imperfect states to other states, and before that time the transitions from perfect to imperfect states reached a specified number. For model 2, there still are two criteria whichever occurs first. The first one is the same as failure criterion (1) in model 1, but failure criterion (2) is replaced by (3) which is when the sojourn time in imperfect states exceeds a given threshold. Under two models, two distributions are proposed, which are extensions of the well-known Phase-type distribution. Some reliability indexes under two models, such as the distributions of lifetimes, the point-wise availabilities, various interval availabilities, are given. Finally, some numerical examples are presented to illustrate the results obtained in this article.
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a cold standby Repairable System with the repairman having multiple vacations and operational repair and vacation times following phase type distributions
Communications in Statistics-theory and Methods, 2016Co-Authors: Baoliang Liu, Lirong Cui, Yanqing Wen, Furi GuoAbstract:ABSTRACTThis paper studies a cold standby Repairable System with two identical components and one repairman having multiple vacations applying matrix-analytic methods. The lifetime of the component follows a phase-type distribution. The repair times and the vacation times of the repairman are governed by different phase-type distributions, respectively. For this System, the Markov process governing the System is constructed. The System is studied in a transient and stationary regime, the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated, respectively. A numerical application is performed to illustrate the calculations.
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a cold standby Repairable System with working vacations and vacation interruption following markovian arrival process
Reliability Engineering & System Safety, 2015Co-Authors: Baoliang Liu, Lirong Cui, Yanqing Wen, Jingyuan ShenAbstract:Abstract This paper studies a cold standby Repairable System with working vacations and vacation interruptions. The repairman׳s multiple vacation, the working vacation policy and the vacation interruption policy are considered simultaneously. The lifetime of component follows a Phase-type (PH) distribution. The repair time in the regular repair period and the working vacation period are other two Phase-type distributions with different representations, and the successive vacation times are governed by a Markovian arrival process (MAP). For this System, a vector-valued Markov process is constructed. We obtain several important performance measures for the System in transient and stationary regimes applying the matrix-analytic method. Finally, a numerical example is given to illustrate the results obtained in the paper.
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multi point and multi interval availabilities
IEEE Transactions on Reliability, 2013Co-Authors: Lirong Cui, Baoliang LiuAbstract:Availability is an important measure of performance for Repairable Systems because it can describe the probability of a Repairable System being in working states. Single point and interval availability measurements (availabilities) have been widely used, but they cannot meet the requirements of all applications. In this paper, multi-point, multi-interval, and mixed multi-point-interval availabilities are introduced, which are extensions of the single point and interval availabilities. The multi-interval availability formula was given by Csenki in 2007 by using the induction method in which the multi-interval availability was called the joint interval reliability, but a new simple technique is provided to present the formula of multi-interval availability in this paper. We also consider the steady-state situations for all new availabilities. For Markov Repairable Systems, the calculation formulae are presented for the new availabilities, and some properties of new availabilities are discussed too. Finally, some special cases and numerical examples are given to illustrate the results obtained in the paper.
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a study on reliability for a two item cold standby markov Repairable System with neglected failures
Communications in Statistics-theory and Methods, 2012Co-Authors: Xinzhuo Bao, Lirong CuiAbstract:This article studies reliability for a Markov Repairable two-item cold standby System with neglected failures. In the System, if a failed time of the System is too short (less than a given critical value) to cause the System to fail, then the failed time may be omitted from the downtime record, i.e., the failure effect could be neglected. In ion-channel modeling, this situation is called the time interval omission problem. The availability indices and the mean downtime are presented as two measures of reliability for this Repairable System. Some numerical examples are shown to illustrate the results obtained in this article.
Guan Jun Wang - One of the best experts on this subject based on the ideXlab platform.
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a geometric process repair model for a Repairable cold standby System with priority in use and repair
Reliability Engineering & System Safety, 2009Co-Authors: Yuan Lin Zhang, Guan Jun WangAbstract:In this paper, a deteriorating cold standby Repairable System consisting of two dissimilar components and one repairman is studied. For each component, assume that the successive working times form a decreasing geometric process while the consecutive repair times constitute an increasing geometric process, and component 1 has priority in use and repair. Under these assumptions, we consider a replacement policy N based on the number of repairs of component 1 under which the System is replaced when the number of repairs of component 1 reaches N. Our problem is to determine an optimal policy N* such that the average cost rate (i.e. the long-run average cost per unit time) of the System is minimized. The explicit equation of the average cost rate of the System is derived and the corresponding optimal replacement policy N* can be determined analytically or numerically. Finally, a numerical example with Weibull distribution is given to illustrate some theoretical results in this paper.
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a geometric process repair model for a series Repairable System with k dissimilar components
Applied Mathematical Modelling, 2007Co-Authors: Yuan Lin Zhang, Guan Jun WangAbstract:Abstract In this paper, a geometric process repair model for a k-dissimilar-component series Repairable System with one repairman is proposed. For each component, the successive operating times form a decreasing geometric process whereas the consecutive repair times constitute an increasing geometric process. Under this assumption, we consider a replacement policy M = (N1, N2, … , Nk) based respectively on the number of failures of component 1, component 2, …, and component k. Our problem is to determine an optimal replacement policy M ∗ = ( N 1 ∗ , N 2 ∗ , … , N k ∗ ) such that the average cost rate (i.e. the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, an appropriate numerical example is given to illustrate some issues included the sensitivity analysis and the uniqueness of the optimal replacement policy M∗.
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an optimal replacement policy for a two component series System assuming geometric process repair
Computers & Mathematics With Applications, 2007Co-Authors: Guan Jun Wang, Yuan Lin ZhangAbstract:This article studies a series Repairable System consisting of two non-identical components and one repairer. It is assumed that each component after repair in the System is not ''as good as new''. Under this assumption, by using a geometric process repair model, a replacement policy (M,N) is considered, based on the number of failures of component 1 and component 2. The problem is to determine an optimal replacement policy (M^*,N^*) such that the long-run expected cost per unit time is minimized. The explicit expression for the long-run expected cost per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, an appropriate numerical example is given to illustrate some theoretical results included the sensitivity analysis and the uniqueness of the optimal replacement policy (M^*,N^*).
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a shock model with two type failures and optimal replacement policy
International Journal of Systems Science, 2005Co-Authors: Guan Jun Wang, Yuan Lin ZhangAbstract:In this paper, a shock model for a Repairable System with two-type failures is studied. Assume that two kinds of shock in a sequence of random shocks will make the System failed, one based on the inter-arrival time between two consecutive shocks less than a given positive value δ and the other based on the shock magnitude of single shock more than a given positive value γ. Under this assumption, we obtain some reliability indices of the shock model such as the System reliability and the mean working time before System failure. Assume further that the System after repair is 'as good as new', but the consecutive repair times of the System form a stochastic increasing geometric process. On the basis of the above assumptions, we consider a replacement policy N based on the number of failure of the System. Our problem is to determine an optimal replacement policy N* such that the long-run average cost per unit time is minimised. The explicit expression of long-run average cost per unit time is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, a numerical example is given.
Yuan Lin Zhang - One of the best experts on this subject based on the ideXlab platform.
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a geometric process repair model for a Repairable cold standby System with priority in use and repair
Reliability Engineering & System Safety, 2009Co-Authors: Yuan Lin Zhang, Guan Jun WangAbstract:In this paper, a deteriorating cold standby Repairable System consisting of two dissimilar components and one repairman is studied. For each component, assume that the successive working times form a decreasing geometric process while the consecutive repair times constitute an increasing geometric process, and component 1 has priority in use and repair. Under these assumptions, we consider a replacement policy N based on the number of repairs of component 1 under which the System is replaced when the number of repairs of component 1 reaches N. Our problem is to determine an optimal policy N* such that the average cost rate (i.e. the long-run average cost per unit time) of the System is minimized. The explicit equation of the average cost rate of the System is derived and the corresponding optimal replacement policy N* can be determined analytically or numerically. Finally, a numerical example with Weibull distribution is given to illustrate some theoretical results in this paper.
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a geometric process repair model for a series Repairable System with k dissimilar components
Applied Mathematical Modelling, 2007Co-Authors: Yuan Lin Zhang, Guan Jun WangAbstract:Abstract In this paper, a geometric process repair model for a k-dissimilar-component series Repairable System with one repairman is proposed. For each component, the successive operating times form a decreasing geometric process whereas the consecutive repair times constitute an increasing geometric process. Under this assumption, we consider a replacement policy M = (N1, N2, … , Nk) based respectively on the number of failures of component 1, component 2, …, and component k. Our problem is to determine an optimal replacement policy M ∗ = ( N 1 ∗ , N 2 ∗ , … , N k ∗ ) such that the average cost rate (i.e. the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, an appropriate numerical example is given to illustrate some issues included the sensitivity analysis and the uniqueness of the optimal replacement policy M∗.
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an optimal replacement policy for a two component series System assuming geometric process repair
Computers & Mathematics With Applications, 2007Co-Authors: Guan Jun Wang, Yuan Lin ZhangAbstract:This article studies a series Repairable System consisting of two non-identical components and one repairer. It is assumed that each component after repair in the System is not ''as good as new''. Under this assumption, by using a geometric process repair model, a replacement policy (M,N) is considered, based on the number of failures of component 1 and component 2. The problem is to determine an optimal replacement policy (M^*,N^*) such that the long-run expected cost per unit time is minimized. The explicit expression for the long-run expected cost per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, an appropriate numerical example is given to illustrate some theoretical results included the sensitivity analysis and the uniqueness of the optimal replacement policy (M^*,N^*).
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a bivariate optimal replacement policy for a multistate Repairable System
Reliability Engineering & System Safety, 2007Co-Authors: Yuan Lin Zhang, Richard C M Yam, M J ZuoAbstract:Abstract In this paper, a deteriorating simple Repairable System with k + 1 states, including k failure states and one working state, is studied. It is assumed that the System after repair is not “as good as new” and the deterioration of the System is stochastic. We consider a bivariate replacement policy, denoted by ( T , N ) , in which the System is replaced when its working age has reached T or the number of failures it has experienced has reached N, whichever occurs first. The objective is to determine the optimal replacement policy ( T , N ) * such that the long-run expected profit per unit time is maximized. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. We prove that the optimal policy ( T , N ) * is better than the optimal policy N * for a multistate simple Repairable System. We also show that a general monotone process model for a multistate simple Repairable System is equivalent to a geometric process model for a two-state simple Repairable System in the sense that they have the same structure for the long-run expected profit (or cost) per unit time and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results.
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a shock model with two type failures and optimal replacement policy
International Journal of Systems Science, 2005Co-Authors: Guan Jun Wang, Yuan Lin ZhangAbstract:In this paper, a shock model for a Repairable System with two-type failures is studied. Assume that two kinds of shock in a sequence of random shocks will make the System failed, one based on the inter-arrival time between two consecutive shocks less than a given positive value δ and the other based on the shock magnitude of single shock more than a given positive value γ. Under this assumption, we obtain some reliability indices of the shock model such as the System reliability and the mean working time before System failure. Assume further that the System after repair is 'as good as new', but the consecutive repair times of the System form a stochastic increasing geometric process. On the basis of the above assumptions, we consider a replacement policy N based on the number of failure of the System. Our problem is to determine an optimal replacement policy N* such that the long-run average cost per unit time is minimised. The explicit expression of long-run average cost per unit time is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, a numerical example is given.
Baoliang Liu - One of the best experts on this subject based on the ideXlab platform.
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a cold standby Repairable System with the repairman having multiple vacations and operational repair and vacation times following phase type distributions
Communications in Statistics-theory and Methods, 2016Co-Authors: Baoliang Liu, Lirong Cui, Yanqing Wen, Furi GuoAbstract:ABSTRACTThis paper studies a cold standby Repairable System with two identical components and one repairman having multiple vacations applying matrix-analytic methods. The lifetime of the component follows a phase-type distribution. The repair times and the vacation times of the repairman are governed by different phase-type distributions, respectively. For this System, the Markov process governing the System is constructed. The System is studied in a transient and stationary regime, the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated, respectively. A numerical application is performed to illustrate the calculations.
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a cold standby Repairable System with working vacations and vacation interruption following markovian arrival process
Reliability Engineering & System Safety, 2015Co-Authors: Baoliang Liu, Lirong Cui, Yanqing Wen, Jingyuan ShenAbstract:Abstract This paper studies a cold standby Repairable System with working vacations and vacation interruptions. The repairman׳s multiple vacation, the working vacation policy and the vacation interruption policy are considered simultaneously. The lifetime of component follows a Phase-type (PH) distribution. The repair time in the regular repair period and the working vacation period are other two Phase-type distributions with different representations, and the successive vacation times are governed by a Markovian arrival process (MAP). For this System, a vector-valued Markov process is constructed. We obtain several important performance measures for the System in transient and stationary regimes applying the matrix-analytic method. Finally, a numerical example is given to illustrate the results obtained in the paper.
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multi point and multi interval availabilities
IEEE Transactions on Reliability, 2013Co-Authors: Lirong Cui, Baoliang LiuAbstract:Availability is an important measure of performance for Repairable Systems because it can describe the probability of a Repairable System being in working states. Single point and interval availability measurements (availabilities) have been widely used, but they cannot meet the requirements of all applications. In this paper, multi-point, multi-interval, and mixed multi-point-interval availabilities are introduced, which are extensions of the single point and interval availabilities. The multi-interval availability formula was given by Csenki in 2007 by using the induction method in which the multi-interval availability was called the joint interval reliability, but a new simple technique is provided to present the formula of multi-interval availability in this paper. We also consider the steady-state situations for all new availabilities. For Markov Repairable Systems, the calculation formulae are presented for the new availabilities, and some properties of new availabilities are discussed too. Finally, some special cases and numerical examples are given to illustrate the results obtained in the paper.
Min Xie - One of the best experts on this subject based on the ideXlab platform.
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generalized confidence interval for the scale parameter of the power law process
Communications in Statistics-theory and Methods, 2013Co-Authors: Bing Xing Wang, Min Xie, Jun Xing ZhouAbstract:The power-law process is widely used in the analysis of Repairable System reliability. In this article, interval estimation for the scale parameter is investigated under some general conditions. A procedure to derive a generalized confidence interval for the scale parameter is presented. We also study the accuracy of the generalized confidence interval by Monte Carlo simulation. Finally, two examples are shown to illustrate the proposed procedure.
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state probability of a series parallel Repairable System with two types of failure states
International Journal of Systems Science, 2006Co-Authors: Gregory Levitin, Tao Zhang, Min XieAbstract:This paper presents a method for the analysis of a series-parallel safety-critical System where the System states can be distinguished into failure-safe and failure-dangerous. The method incorporates the Markov chain and universal generating function technique. In the model considered, both periodic inspection and repair (perfect and imperfect) of System elements are taken into account. The System state distributions and the overall System safety function are derived, based on the developed model. The proposed method is applicable to complex Systems for analysing state distributions and it is also useful in decision-making such as determining the optimal proof-test interval or repair resource allocation. An illustrative example is given.
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a comparative study of neural network and box jenkins arima modeling in time series prediction
Annual Conference on Computers, 2002Co-Authors: Min Xie, T N GohAbstract:This paper aims to investigate suitable time series models for Repairable System failure analysis. A comparative study of the Box-Jenkins autoregressive integrated moving average (ARIMA) models and the artificial neural network models in predicting failures are carried out. The neural network architectures evaluated are the multi-layer feed-forward network and the recurrent network. Simulation results on a set of compressor failures showed that in modeling the stochastic nature of reliability data, both the ARIMA and the recurrent neural network (RNN) models outperform the feed-forward model; in terms of lower predictive errors and higher percentage of correct reversal detection. However, both models perform better with short term forecasting. The effect of varying the damped feedback weights in the recurrent net is also investigated and it was found that RNN at the optimal weighting factor gives satisfactory performances compared to the ARIMA model.
