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ABSTRACT: The dynamics of a system represented by a finite-state Markov process operating under two alternating regimes, for example, day/night, machine working/machine idling, etc., are modeled in this article. The transition rate matrices under the two regimes will usually be different. Also, the set of states of the system that are regarded as satisfactory may depend on the regime in operation: for example, a particular state of the system that may be regarded as satisfactory by day might not be tolerated at night (e.g., the headlights on a car not working). It is assumed that the regime durations are random variables and results are obtained for the availability of such a system and probability distributions for uptimes. Results and numerical examples are also given for two special cases: (i) when the regimes are of fixed duration; and (ii) when the regime durations have negative exponential distributions.
IIE Transactions 11/2011; 43(11):761-772. · 0.86 Impact Factor
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ABSTRACT: A linear connected-(r, s)-out-of-(m, n) : F system consists of m×n components arranged in m rows by n columns, and it fails iff there exists a r × s subsystem in which all components are failed. The linear connected-(r, s)-out-of-(m, n) : F system can be used for modeling engineering systems such as temperature feeler systems, supervision systems, etc. In this paper, a general method is proposed based on the finite Markov chain imbedding approach to study the exact reliability of a linear connected-(r, s)-out-of-(m, n) : F system. Then a new more efficient method, which reduces the size of the state space by combining some states into one state, is presented to reduce the computing time. Furthermore, three numerical examples are given. The first two numerical examples show that the proposed algorithm is efficient not only when the component states are i.i.d., but also when the component states are statistically independent and non-identically distributed. And the last numerical example shows that our method can be used to compute not only the reliability, but also the component importance.
IEEE Transactions on Reliability 10/2011; · 1.28 Impact Factor
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IEEE Transactions on Reliability. 01/2011; 60:689-698.
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ABSTRACT: Most studies on k-out-of-n systems are in the binary context. The k-out-of-n system has failed if and only if at least k components have failed. The generalised multi-state k-out-of-n: G and F system models are defined by Huang et al. [Huang, J., Zuo, M.J., and Wu, Y.H. (2000), ‘Generalized Multi-state k-out-of-n: G Systems’, IEEE Transactions on reliability, 49, 105–111] and Zuo and Tian [Zuo, M.J., and Tian, Z.G. (2006), ‘Performance Evaluation of Generalized Multi-state k-out-of-n Systems’, IEEE Transactions on Reliability, 55, 319–327], respectively. In this article, by using the finite Markov chain imbedding (FMCI) approach, we present a unified formula with the product of matrices for evaluating the system state distribution for generalised multi-state k-out-of-n: F systems which include the decreasing multi-state F system, the increasing multi-state F system and the non-monotonic multi-state F system. Our results can be extended to the generalised multi-state k-out-of-n: G system. Three numerical examples are presented to illustrate the results.
International Journal of Systems Science. 12/2010; 41(12):1437-1443.
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Int. J. Systems Science. 01/2010; 41:1437-1443.
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IEEE Transactions on Reliability. 01/2010; 59:685-690.
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ABSTRACT: A linear consecutive- (2, 2) -out-of-(m, n) : F system is a special two-dimensional system, which consists of m à n components, and fails if and only if all components in a 2 à 2 sub-matrix are failed. This system can be treated as a reliability model for video monitoring systems, phased-array radar systems, and wireless communication networks etc. An effective method has been developed for evaluating the exact system reliability, but that method can only give a recursive algorithm that can not be used for system optimization. In this paper, a finite Markov chain imbedding approach is used to obtain the reliability analytic formulas of that system. Numerical examples show that the method can be used for not only the system with independent identical distribution components, but also with independent non-identical distribution components.
Industrial Engineering and Engineering Management, 2009. IE&EM '09. 16th International Conference on; 11/2009
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IEEE Transactions on Reliability. 01/2009; 58:383-388.
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ABSTRACT: Detects on Nano/Micro integrated circuits wafer (ICW) tend to cluster and the spatial patterns of these defect clusters usually contain important information for quality engineers to remove the root causes of failures. In this paper, a new method consisting of noise filter, defect clustering by using chameleon method and model-based pattern recognition is proposed for automatic defect spatial pattern recognition on Nano/Micro ICW. The new method can not only find the number of defect clusters, and identify the pattern of each cluster, but also provide valuable information for the yield and reliability study. The method can recognize not only the linear/curvilinear patterns, ellipsoidal patterns, but also the ring spatial patterns.
Nano/Micro Engineered and Molecular Systems, 2008. NEMS 2008. 3rd IEEE International Conference on; 02/2008
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ABSTRACT: We introduce the system of consecutive failures with sparse d which is a natural extension of consecutive-k systems. Then a series of generalizations of consecutive-k systems are discussed, such as consecutive-k-out-n:F systems with sparse d, M consecutive-k-out-of-n:F systems with sparse d, and (n, f, k) :F systems with sparse d. We present the formulation for the system reliability of these generalized consecutive-k systems with various component settings in terms of the finite Markov chain imbedding idea, along with two numerical examples.
IEEE Transactions on Reliability 10/2007; · 1.28 Impact Factor
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IEEE Transactions on Reliability. 01/2007; 56:516-524.
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ABSTRACT: This paper introduces a new model for a single-unit Markov repairable system in which repair times that are sufficiently short (less than some critical value) do not result in system failure. We can say that such a repair interval is omitted from the downtime record. First we suppose that the critical repair time is a constant. The model is then generalized to allow the critical repair time to be a non-negative random variable. We calculate system availability for these new models as a measure of reliability. Some numerical examples are given to illustrate the results in the paper.
IEEE Transactions on Reliability 07/2006; · 1.28 Impact Factor
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ABSTRACT: Renewal-type equations are frequently encountered in the study of reliability, warranty analysis, replacement and maintenance policies, and inventory control. Renewal equations usually do not have analytical solutions, and hence, bounds or approximations are very useful. In this article, analytical bounds are studied based on a simple iterative procedure which provides some analytical results and nice convergence properties when the number of iteration increases. Bounds and approximations are also investigated for a recursive algorithm for numerical computation. In addition, some interesting monotonicity properties are introduced and discussed. The approximation error, which is important for determining the stopping rule of the iterative procedure and the numerical algorithm, is also studied.
Communication in Statistics- Theory and Methods 01/2006; 35(10):1815-1827. · 0.27 Impact Factor
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ABSTRACT: The effect of a repair of a complex system can usually be approximated by the following two types: minimal repair for which the system is restored to its functioning state with minimum effort, or perfect repair for which the system is replaced or repaired to a good-as-new state. When both types of repair are possible, an important problem is to determine the repair policy; that is, the type of repair which should be carried out after a failure. In this paper, an optimal allocation problem is studied for a monotonic failure rate repairable system under some resource constraints. In the first model, the numbers of minimal & perfect repairs are fixed, and the optimal repair policy maximizing the expected system lifetime is studied. In the second model, the total amount of repair resource is fixed, and the costs of each minimal & perfect repair are assumed to be known. The optimal allocation algorithm is derived in this case. Two numerical examples are shown to illustrate the procedures.
IEEE Transactions on Reliability 07/2004; · 1.28 Impact Factor
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IEEE Transactions on Reliability. 01/2004; 53:193-199.
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ABSTRACT: In this paper, some recursive equations of reliability for linear consecutive-k -out-of-n : F systems with spares d are introduced. The system of consecutive failures with sparse d is a generalized extension of consecutive-k systems, which was proposed by Zhao et al. (2007) in which the reliability formulas of these systems were presented by using finite Markov Chain imbedding approach. To facilitate the use, two theorems and some special cases on recursive equations for the system reliability are given.
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ABSTRACT: The availability of systems undergoing periodic inspections is studied in this paper. A perfect repair or replacement of a failed system is carried out requiring either a constant or a random length of time. In Model A, the system is assumed to be as good as new on completion of inspection or repair. For Model B, no maintenance or corrective actions are taken at the time of inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. Unlike that studied in a related paper by Sarkar and Sarkar (J. Statist. Plann. Inference 91 (2000) 77.), our model assumes that the periodic inspections take place at fixed time points after repair or replacement in case of failure. Some general results on the instantaneous availability and the steady-state availability for the two models are presented under the assumption of random repair or replacement time.
Journal of Statistical Planning and Inference.
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ABSTRACT: In this paper, the instantaneous availability of a system maintained under periodic inspection is investigated using random walk models. Two cases are considered. In the first model, the system is repaired or modified and it is assumed to be as good as new upon periodic inspection and maintenance. In the second model, the system is not modified after the inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. For both models the failures only can be found through the inspection. Perfect repair or replacement of a failed system is assumed to be carried out, but the time it takes can be constant or of a random length. The relationship between this problem and the random walk model in a two-dimensional plane is described. Several new results are also shown.
