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Yuan Lin Zhang - One of the best experts on this subject based on the ideXlab platform.
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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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optimal periodic preventive repair and Replacement Policy assuming geometric process repair
IEEE Transactions on Reliability, 2006Co-Authors: Guan Jun Wang, Yuan Lin ZhangAbstract:In this paper, a simple deteriorating system with repair is studied. When failure occurs, the system is replaced at high cost. To extend the operating life, the system can be repaired preventively. However, preventive repair does not return the system to a "good as new" condition. Rather, the successive operating times of the system after preventive repair form a stochastically decreasing geometric process, while the consecutive preventive repair times of the system form a stochastically increasing geometric process. We consider a bivariate preventive repair Policy to solve the efficiency for a deteriorating & valuable system. Thus, the objective of this paper is to determine an optimal bivariate Replacement Policy 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 numerically. An example is given where the operating time of the system is given by a Weibull distribution.
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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.
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optimal Replacement Policy for a multistate repairable system
Journal of the Operational Research Society, 2002Co-Authors: Yuan Lin Zhang, Richard C M Yam, M J ZuoAbstract:In this paper, a deteriorating simple repairable system with k + 1 states, including k failure states and one working state, is studied. The system after repair is not ‘as good as new’ and the deterioration of the system is stochastic. Under these assumptions, we study a Replacement Policy, called Policy N, based on the failure number of the system. The objective is to maximize the long-run expected profit per unit time. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal solution may be determined analytically or numerically. Furthermore, we prove that the model for the multistate system in this paper forms a general monotone process model which includes the geometric process repair model as a special case. A numerical example is given to illustrate the theoretical results.
Shey-huei Sheu - One of the best experts on this subject based on the ideXlab platform.
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Optimal two-threshold Replacement Policy in a cumulative damage model
Annals of Operations Research, 2016Co-Authors: Shey-huei Sheu, Tzu-hsin Liu, Zhe-george Zhang, Hsin-nan Tsai, Jung-chih ChenAbstract:In this paper, a two-unit system with failure interactions is studied. The system is subject to two types of shocks (I and II) and the probabilities of these two shock types are age-dependent. A type I shock, rectified by a minimal repair, causes a minor failure of unit A and type II shock causes a complete system failure that calls for a Replacement. Each unit A minor failure also results in an amount of damage to unit B. The damages to unit B caused by type I shocks can be accumulated to trigger a preventive Replacement or a corrective Replacement action. Besides, unit B with cumulative damage of level z may become minor failed with probability $$\pi (z)$$ π ( z ) at each unit A minor failure and rectified by a minimal repair. We consider a more general Replacement Policy. Under this Policy, the system is preventively replaced at the N th type I shock, or at the time when the total damage to unit B exceeds a pre-specified level Z (but less than a failure level K where $$K>Z$$ K > Z ) or is replaced correctively at first type II shock or when the total damage to unit B exceeding a failure level K , whichever occurs first. To minimize the expected cost per unit time, the optimal Replacement Policy $$(N^{*}$$ ( N ∗ , $$Z^{*})$$ Z ∗ ) is derived analytically and determined numerically. We also show that several previous maintenance models in the literature are 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 multi criteria optimal Replacement Policy for a system subject to shocks
Computers & Industrial Engineering, 2011Co-Authors: Chinchih Chang, Shey-huei Sheu, Yenluan Chen, Zhe-george ZhangAbstract:A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As these shocks occur, the system experiences one of two types of failures: a type-I failure (minor), rectified by a minimal repair; or a type-II failure (catastrophic) that calls for a Replacement. In this study, we consider a multi-criteria Replacement Policy based on system age, nature of failure, and entire repair-cost history. Under such a Policy, the system is replaced at planned life time T, or at the nth type-I failure, or at the kth type-I failure (k
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An age Replacement Policy via the Bayesian method
International Journal of Systems Science, 2011Co-Authors: Shey-huei Sheu, Chaun-hung Chiu, Tsung-shin HsuAbstract:This article aims to estimate the probability of item Replacement on an age Replacement Policy. An item is replaced until time T, or until a first non-repairable catastrophic failure occurs-whichever comes first. Because the sample size is relatively small under the Replacement Policy, we use a Bayesian approach to estimate probability. A prior choice is undoubtedly closely related to the problem under consideration. Here, we consider the (Jeffreys (1961), Theory of Probability, Oxford: Clarendon Press) prior and the conjugate prior that are justified to some extent. We also derive some approximations of the posterior and discuss certain special cases. Our objective is to determine an optimal Replacement Policy in which the long-run average cost per unit time is minimised. We also assume that some catastrophic failures can be repaired. On the spectrum of long-run average costs per unit time, our cost is smaller than others. Here, we use numerical examples to illustrate some known models, and make some comparisons as well.
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optimal age Replacement Policy with age dependent minimal repair and random leadtime
IEEE Transactions on Reliability, 2001Co-Authors: Shey-huei Sheu, William S GriffithAbstract:A generalized age-Replacement Policy with age-dependent minimal repair and random leadtime is considered. A model is developed for the average cost per unit time and is based on the stochastic behavior of the assumed system and reflects the cost of storing a spare as well as the cost of system downtime. Determination of the minimum-cost Policy time is described and illustrated with a numerical example. Because the model and its analysis are general, several existing results are shown to be subsumed by this model.
Yuhung Chien - One of the best experts on this subject based on the ideXlab platform.
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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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optimal age Replacement Policy under an imperfect renewing free Replacement warranty
IEEE Transactions on Reliability, 2008Co-Authors: Yuhung ChienAbstract:This paper investigates the effects of an imperfect renewing free-Replacement warranty (RFRW) on the classical age-Replacement Policy for a product with an increasing failure rate. Under the imperfect RFRW, whenever a product fails during the warranty period, it is replaced by a repaired one from an infinite stock of refurbished items, at no cost to the purchaser, with a new full warranty. We assume that the failure potential of the repaired product is inferior to that of a new product; that is, the repaired product is less reliable than a new one. Long-run expected cost rates for the age-Replacement Policy are developed for two cases: when the preventive Replacement age occurs before, and when it occurs after the warranty expires. The optimal Replacement ages that minimize the cost rates are determined, and the impact of an imperfect RFRW on the optimal Replacement age is illustrated with a numerical example. We review the literature dealing with warranty and maintenance against this framework, and conclude with some discussions on topics for research in the future. The imperfect RFRW proposed in this paper is practical, and novel; and this study represents a useful extension of Yeh that promises to be of interest to reliability engineers, managers, and theoreticians.
Ruey-huei Yeh - One of the best experts on this subject based on the ideXlab platform.
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Optimal Single Replacement Policy for Products with Free-Repair Warranty Under a Finite Planning Horizon
Quality Technology and Quantitative Management, 2016Co-Authors: Ruey-huei Yeh, Nani Kurniati, Wen Liang ChangAbstract:AbstractThis paper investigates the optimal single Replacement Policy for products with free-repair warranty (FRW) under a finite planning horizon (FPH) from the consumer’s perspective. Within the planning horizon, the product is replaced once by a new product. During FRW, when the product fails, the failed product is rectified using minimal repair without any cost to the consumer. After FRW, any failure of the product incurs a fixed repair cost to the consumer. However, each failure incurs a fixed downtime cost to the consumer over the planning horizon. Under this maintenance scheme, the Replacement of the product is investigated for two separate cases: before FRW and after FRW. Then, two cost models from the consumer’s perspective are derived and the optimal Replacement Policy is obtained such that the expected total disbursement cost is minimized. Finally, numerical examples are given to illustrate the features of the optimal Replacement Policy under various warranties and planning horizons.
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optimal periodic Replacement Policy for repairable products under free repair warranty
European Journal of Operational Research, 2007Co-Authors: Ruey-huei Yeh, Mingyuh Chen, Chenyi LinAbstract:This paper investigates the effects of a free-repair warranty on the periodic Replacement Policy for a repairable product. Cost models are developed for both a warranted and a non-warranted product, and the corresponding optimal periodic Replacement policies are derived such that the long-run expected cost rate is minimized. For a product with an increasing failure rate function, structural properties of these optimal policies are obtained. By comparing these optimal policies, we show that the optimal Replacement period for a warranted product should be adjusted toward the end of the warranty period. Finally, examples are given to numerically illustrate the impact of a product warranty on the optimal periodic Replacement Policy.
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optimal age Replacement Policy for nonrepairable products under renewing free Replacement warranty
IEEE Transactions on Reliability, 2005Co-Authors: Ruey-huei Yeh, Gaungcheng Chen, Mingyuh ChenAbstract:This paper investigates the effects of a renewing free-Replacement warranty on the age Replacement Policy for a nonrepairable product. For both warranted, and nonwarranted products, cost models are developed, and the corresponding optimal Replacement ages are derived such that the long-run expected cost rate is minimized. Furthermore, we show that the optimal Replacement age for a warranted product is closer to the end of the warranty period than for a nonwarranted product. Finally, numerical examples are given to evaluate the impact of a product warranty on the optimal Replacement age.
Guan Jun Wang - One of the best experts on this subject based on the ideXlab platform.
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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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optimal periodic preventive repair and Replacement Policy assuming geometric process repair
IEEE Transactions on Reliability, 2006Co-Authors: Guan Jun Wang, Yuan Lin ZhangAbstract:In this paper, a simple deteriorating system with repair is studied. When failure occurs, the system is replaced at high cost. To extend the operating life, the system can be repaired preventively. However, preventive repair does not return the system to a "good as new" condition. Rather, the successive operating times of the system after preventive repair form a stochastically decreasing geometric process, while the consecutive preventive repair times of the system form a stochastically increasing geometric process. We consider a bivariate preventive repair Policy to solve the efficiency for a deteriorating & valuable system. Thus, the objective of this paper is to determine an optimal bivariate Replacement Policy 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 numerically. An example is given where the operating time of the system is given by a Weibull distribution.
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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.
