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Zhe-george Zhang - One of the best experts on this subject based on the ideXlab platform.
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Optimal periodic preventive maintenance policy for a system subject to failures/repairs which follow the non-homogeneous Pure Birth Process
Quality Technology & Quantitative Management, 2020Co-Authors: Yuhung Chien, Zhe-george Zhang, Shey-huei SheuAbstract:This paper considers a periodic preventive maintenance policy for a deteriorating and repairable system. The system is subject to random failures and is repaired at each failure. To improve the rel...
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optimal periodic preventive maintenance policy for a system subject to failures repairs which follow the non homogeneous Pure Birth Process
Quality Technology and Quantitative Management, 2020Co-Authors: Yuhung Chien, Shey-huei Sheu, Zhe-george ZhangAbstract:This paper considers a periodic preventive maintenance policy for a deteriorating and repairable system. The system is subject to random failures and is repaired at each failure. To improve the rel...
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Optimal number of repairs before replacement for a two-unit system subject to non-homogeneous Pure Birth Process
Computers & Industrial Engineering, 2014Co-Authors: Shey-huei Sheu, Zhe-george Zhang, Tzu-hsin Liu, Tsan-ming ChangAbstract:We consider a discrete replacement model for a two-unit system subject to failure rate interaction and shocks. Two types of shocks occur according to a non-homogeneous Pure Birth Process and can affect the two-unit system. Type I shock causes unit A to fail and can be rectified by a general repair, while type II shock results in a non-repairable failure and must be fixed by a replacement. Two-unit systems also exhibit failure rate interactions between the units: each failure of unit A causes some damage to unit B, while each failure of unit B causes unit A into an instantaneous failure. The occurrence of a particular type of shock is dependent on the number of shocks occurred since the last replacement. The objective of this paper is to determine the optimal number of minor failures before replacement that minimizes the expected cost rate. A numerical example is presented to illustrate application of the model.
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Age replacement policy with lead-time for a system subject to non-homogeneous Pure Birth shocks
Applied Mathematical Modelling, 2013Co-Authors: Shey-huei Sheu, Yuhung Chien, Zhe-george Zhang, Tsun-hung HuangAbstract:Abstract A system is subject to shocks that arrive according to a non-homogeneous Pure Birth Process. Whenever a shock occurs, the system enters one of the two types of failure states. Type I failure (minor failure) is fixed by a minimal repair. Type II failure (catastrophic failure) is removed by a replacement. We consider an age replacement policy which replaces the system whenever its age reaches T and a spare for replacement is available. The optimal cost minimization age T ∗ is derived under a cost structure. We demonstrate that this model includes more realistic factors and is a generalization of several previous models in the literature.
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Optimal Number of Repairs Before Replacement for a System Subject to Shocks of a Non-Homogeneous Pure Birth Process
IEEE Transactions on Reliability, 2013Co-Authors: Shey-huei Sheu, Chinchih Chang, Yen-luan Chen, Zhe-george ZhangAbstract:We consider a system subject to shocks that arrive according to a nonhomogeneous Pure Birth Process (NHPBP). As a shock occurs, the system has two types of failures. Type-I failure (minor failure) is rectified by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The probabilities of these two types of failures depend on the number of shocks since the last replacement. We consider a policy with which the system is replaced at the n th type-I failure, or at any type-II failure. The aim of this paper is to determine the optimal policy n*, the number of minor failures up to replacement that minimizes the expected cost rate of the system subject to NHPBP shocks. The model is a generalization of the existing models, and is more applicable in practice. We present some numerical examples, and show that several classical models are the special cases of our model.
Shey-huei Sheu - One of the best experts on this subject based on the ideXlab platform.
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Optimal periodic preventive maintenance policy for a system subject to failures/repairs which follow the non-homogeneous Pure Birth Process
Quality Technology & Quantitative Management, 2020Co-Authors: Yuhung Chien, Zhe-george Zhang, Shey-huei SheuAbstract:This paper considers a periodic preventive maintenance policy for a deteriorating and repairable system. The system is subject to random failures and is repaired at each failure. To improve the rel...
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optimal periodic preventive maintenance policy for a system subject to failures repairs which follow the non homogeneous Pure Birth Process
Quality Technology and Quantitative Management, 2020Co-Authors: Yuhung Chien, Shey-huei Sheu, Zhe-george ZhangAbstract:This paper considers a periodic preventive maintenance policy for a deteriorating and repairable system. The system is subject to random failures and is repaired at each failure. To improve the rel...
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Optimal number of repairs before replacement for a two-unit system subject to non-homogeneous Pure Birth Process
Computers & Industrial Engineering, 2014Co-Authors: Shey-huei Sheu, Zhe-george Zhang, Tzu-hsin Liu, Tsan-ming ChangAbstract:We consider a discrete replacement model for a two-unit system subject to failure rate interaction and shocks. Two types of shocks occur according to a non-homogeneous Pure Birth Process and can affect the two-unit system. Type I shock causes unit A to fail and can be rectified by a general repair, while type II shock results in a non-repairable failure and must be fixed by a replacement. Two-unit systems also exhibit failure rate interactions between the units: each failure of unit A causes some damage to unit B, while each failure of unit B causes unit A into an instantaneous failure. The occurrence of a particular type of shock is dependent on the number of shocks occurred since the last replacement. The objective of this paper is to determine the optimal number of minor failures before replacement that minimizes the expected cost rate. A numerical example is presented to illustrate application of the model.
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Age replacement policy with lead-time for a system subject to non-homogeneous Pure Birth shocks
Applied Mathematical Modelling, 2013Co-Authors: Shey-huei Sheu, Yuhung Chien, Zhe-george Zhang, Tsun-hung HuangAbstract:Abstract A system is subject to shocks that arrive according to a non-homogeneous Pure Birth Process. Whenever a shock occurs, the system enters one of the two types of failure states. Type I failure (minor failure) is fixed by a minimal repair. Type II failure (catastrophic failure) is removed by a replacement. We consider an age replacement policy which replaces the system whenever its age reaches T and a spare for replacement is available. The optimal cost minimization age T ∗ is derived under a cost structure. We demonstrate that this model includes more realistic factors and is a generalization of several previous models in the literature.
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Optimal Number of Repairs Before Replacement for a System Subject to Shocks of a Non-Homogeneous Pure Birth Process
IEEE Transactions on Reliability, 2013Co-Authors: Shey-huei Sheu, Chinchih Chang, Yen-luan Chen, Zhe-george ZhangAbstract:We consider a system subject to shocks that arrive according to a nonhomogeneous Pure Birth Process (NHPBP). As a shock occurs, the system has two types of failures. Type-I failure (minor failure) is rectified by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The probabilities of these two types of failures depend on the number of shocks since the last replacement. We consider a policy with which the system is replaced at the n th type-I failure, or at any type-II failure. The aim of this paper is to determine the optimal policy n*, the number of minor failures up to replacement that minimizes the expected cost rate of the system subject to NHPBP shocks. The model is a generalization of the existing models, and is more applicable in practice. We present some numerical examples, and show that several classical models are the special cases of our model.
Yuhung Chien - One of the best experts on this subject based on the ideXlab platform.
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optimal periodic preventive maintenance policy for a system subject to failures repairs which follow the non homogeneous Pure Birth Process
Quality Technology and Quantitative Management, 2020Co-Authors: Yuhung Chien, Shey-huei Sheu, Zhe-george ZhangAbstract:This paper considers a periodic preventive maintenance policy for a deteriorating and repairable system. The system is subject to random failures and is repaired at each failure. To improve the rel...
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Optimal periodic preventive maintenance policy for a system subject to failures/repairs which follow the non-homogeneous Pure Birth Process
Quality Technology & Quantitative Management, 2020Co-Authors: Yuhung Chien, Zhe-george Zhang, Shey-huei SheuAbstract:This paper considers a periodic preventive maintenance policy for a deteriorating and repairable system. The system is subject to random failures and is repaired at each failure. To improve the rel...
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Age replacement policy with lead-time for a system subject to non-homogeneous Pure Birth shocks
Applied Mathematical Modelling, 2013Co-Authors: Shey-huei Sheu, Yuhung Chien, Zhe-george Zhang, Tsun-hung HuangAbstract:Abstract A system is subject to shocks that arrive according to a non-homogeneous Pure Birth Process. Whenever a shock occurs, the system enters one of the two types of failure states. Type I failure (minor failure) is fixed by a minimal repair. Type II failure (catastrophic failure) is removed by a replacement. We consider an age replacement policy which replaces the system whenever its age reaches T and a spare for replacement is available. The optimal cost minimization age T ∗ is derived under a cost structure. We demonstrate that this model includes more realistic factors and is a generalization of several previous models in the literature.
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a note on replacement policy for a system subject to non homogeneous Pure Birth shocks
European Journal of Operational Research, 2012Co-Authors: Shey-huei Sheu, Zhe-george Zhang, Chinchih Chang, Yuhung ChienAbstract:Abstract A system is subject to shocks that arrive according to a non-homogeneous Pure Birth Process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T . The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.
Chinchih Chang - One of the best experts on this subject based on the ideXlab platform.
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Optimal Number of Repairs Before Replacement for a System Subject to Shocks of a Non-Homogeneous Pure Birth Process
IEEE Transactions on Reliability, 2013Co-Authors: Shey-huei Sheu, Chinchih Chang, Yen-luan Chen, Zhe-george ZhangAbstract:We consider a system subject to shocks that arrive according to a nonhomogeneous Pure Birth Process (NHPBP). As a shock occurs, the system has two types of failures. Type-I failure (minor failure) is rectified by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The probabilities of these two types of failures depend on the number of shocks since the last replacement. We consider a policy with which the system is replaced at the n th type-I failure, or at any type-II failure. The aim of this paper is to determine the optimal policy n*, the number of minor failures up to replacement that minimizes the expected cost rate of the system subject to NHPBP shocks. The model is a generalization of the existing models, and is more applicable in practice. We present some numerical examples, and show that several classical models are the special cases of our model.
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a note on replacement policy for a system subject to non homogeneous Pure Birth shocks
European Journal of Operational Research, 2012Co-Authors: Shey-huei Sheu, Zhe-george Zhang, Chinchih Chang, Yuhung ChienAbstract:Abstract A system is subject to shocks that arrive according to a non-homogeneous Pure Birth Process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T . The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.
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A Block Replacement Policy for Systems Subject to Non-homogeneous Pure Birth Shocks
IEEE Transactions on Reliability, 2012Co-Authors: Shey-huei Sheu, Chinchih Chang, Yen-luan Chen, Zhe-george ZhangAbstract:This note studies the block replacement policy with general repairs for an operating system subject to shocks occurring according to a non-homogeneous Pure Birth Process. A shock causes the system to fail. There are two types of failures: a type-I failure (minor failure) is fixed by a general repair, whereas a type-II failure (catastrophic failure) is removed by an unplanned (or unscheduled) replacement. The failure type probabilities depend on the number of type-I failure shocks that occurred since the last replacement. Under the block replacement policy, the operating system is replaced every time units to reduce the chances of more expensive unplanned replacements due to type-II failures. The aim of this note is to determine the optimal block interval T*, which minimizes the expected cost rate and the expected total discounted cost rate of the proposed policy. As the shock Process is a more general non-homogeneous Pure Birth Process, several previous models become the special cases of our model.
Nestor Ruben Barraza - One of the best experts on this subject based on the ideXlab platform.
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ICSE (Companion Volume) - A new homogeneous Pure Birth Process based software reliability model
Proceedings of the 38th International Conference on Software Engineering Companion, 2016Co-Authors: Nestor Ruben BarrazaAbstract:A new Software Reliability model based on a Pure Birth Process is proposed. In our novel approach, the Birth (failure) rate of the Process is considered to be non dependent on time but dependent non linearly on the previous number of Births (failures), contrarily to non homogeneous Pure Birth Processes, as it is usually done in the literature. We use the empirical Bayes framework in order to get the Birth (failure) rate. Our approach allows either to estimate the mean time to failure MTTF or to simulate the stochastic failure Process. We analyze both, the discrete and continuous time case and apply the first to a real case.
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a new homogeneous Pure Birth Process based software reliability model
International Conference on Software Engineering, 2016Co-Authors: Nestor Ruben BarrazaAbstract:A new Software Reliability model based on a Pure Birth pro- cess is proposed. In our novel approach, the Birth (failure) rate of the Process is considered to be non dependent on time but dependent non linearly on the previous number of Births (failures), contrarily to non homogeneous Pure Birth Processes, as it is usually done in the literature. We use the empirical Bayes framework in order to get the Birth (fail- ure) rate. Our approach allows either to estimate the mean time to failure MTTF or to simulate the stochastic failure Process. We analyze both, the discrete and continuous time case and apply the first to a real case.
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ISSRE Workshops - Software Reliability Modeled on Contagion
2016 IEEE International Symposium on Software Reliability Engineering Workshops (ISSREW), 2016Co-Authors: Nestor Ruben BarrazaAbstract:A new software reliability model based on the Polya contagion stochastic Process is proposed. We model the failure detection Process as a Pure Birth Process with a failure rate that depends not just on time but on the number of failures previously detected, as it happens in the Polya Process obtained as the asymptotic limit of the Polya urn model for contagion. Since the contagion proposes an increasing failure (Birth) rate, this model is suitable to be applied at the beginning of the testing Process or when some code has been added to the project, situations where the S-shaped model is usually used. The result of applying our model to real data is also shown.
