The Experts below are selected from a list of 2457 Experts worldwide ranked by ideXlab platform
Bhupendra Singh - One of the best experts on this subject based on the ideXlab platform.
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an additive perks weibull model with bathtub shaped Hazard Rate Function
Communications in Mathematics and Statistics, 2016Co-Authors: Bhupendra SinghAbstract:In this article, an additive Perks–Weibull model capable of modeling lifetime data with bathtub-shaped Hazard Rate Function is proposed. The model is derived by the sum of the Hazard Rates of Perks and Weibull distributions. Some statistical properties including shapes of density and Hazard Rate Functions, moments, and order statistics are explored. The method of maximum likelihood estimation is used for estimating the model parameters. The goodness-of-fit of the model for three real datasets having bathtub-shaped Hazard Rate Functions has been illustRated. Finally, an application for competing risk data is also given to show the flexibility of the proposed model.
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An Additive Perks–Weibull Model with Bathtub-Shaped Hazard Rate Function
Communications in Mathematics and Statistics, 2016Co-Authors: Bhupendra SinghAbstract:In this article, an additive Perks–Weibull model capable of modeling lifetime data with bathtub-shaped Hazard Rate Function is proposed. The model is derived by the sum of the Hazard Rates of Perks and Weibull distributions. Some statistical properties including shapes of density and Hazard Rate Functions, moments, and order statistics are explored. The method of maximum likelihood estimation is used for estimating the model parameters. The goodness-of-fit of the model for three real datasets having bathtub-shaped Hazard Rate Functions has been illustRated. Finally, an application for competing risk data is also given to show the flexibility of the proposed model.
R. Zitikis - One of the best experts on this subject based on the ideXlab platform.
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Useful periods for lifetime distributions with bathtub shaped Hazard Rate Functions
IEEE Transactions on Reliability, 2006Co-Authors: M. Bebbington, R. ZitikisAbstract:We propose computationally tractable formal mathematical definitions for the 'useful period' of lifetime distributions with bathtub shaped Hazard Rate Functions. Detailed analysis of the reduced additive Weibull Hazard Rate Function illustRates its utility for identifying such useful periods. Examples of several other bathtub shaped Hazard Rate Functions are also presented with applications to lifetime data. The suggestion is made of defining and considering analogous 'stable periods' in the case of the corresponding upside-down bathtub shaped mean residual life Functions.
Donghua Zhou - One of the best experts on this subject based on the ideXlab platform.
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Optimal Imperfect Periodic Preventive Maintenance for Systems in Time-Varying Environments
IEEE Transactions on Reliability, 2012Co-Authors: Xiaofei Lu, Maoyin Chen, Donghua ZhouAbstract:Manufacturing systems run in time-varying environmental and operational conditions. For the effective manager to make a long-term preventive maintenance decision, it is necessary to integRate the time-varying environment into preventive maintenance (PM) policies. This paper considers PM for systems running in the time-varying environment, modeled as a two-state homogeneous Markov process, where one state represents a typical condition, and the other represents a severe condition. Environmental conditions affect the Hazard Rate Function through a proportional Hazard model. To avoid sudden failures in a system due to either minor failures or catastrophic failures, an extended periodic imperfect preventive maintenance model is carried out, and the maintenance effect is modeled with an age reduction factor, and a Hazard improvement factor. We prove the discontinuity of the Hazard Rate Function of the system in a time-varying environment through a Markov additive process. We also give a method to compute the probability density Function of failure at any time. Further, the s-expected cost Rate of the system in the time-varying environment is compared with the s-expected cost Rates of the system always working in typical, and severe conditions. Finally, numerical examples fully verify our main results.
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Exact Results on the Statistically Expected Total Cost and Optimal Solutions for Extended Periodic Imperfect Preventive Maintenance
IEEE Transactions on Reliability, 2012Co-Authors: Xiaofei Lu, Maoyin Chen, Donghua ZhouAbstract:Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) presented an interesting extended periodic imperfect preventive maintenance (EPIPM) model for a system with age-dependent failure type. Many cases studied previously are special cases of the EPIPM model. In the Errata (IEEE Trans. Rel., vol. 60, no. 2, 2011), Sheu and Chang showed that the proposed effective age and the proposed Hazard Rate Function after the PM are incorrect. In this paper, based on the correct failure characteristics (effective age and Hazard Rate Function after PM), the correct s -expected total cost per unit time for the EPIPM model is presented. By assigning three types of failure characteristics for the EPIPM model, we analyse and compare the corresponding s -expected total costs per unit time. We find that the s-expected total cost per unit time developed by Sheu and Chang (IEEE Trans. Rel., vol. 58, no. 2, pp. 397-404, 2009) is only one upper bound of the exact s-expected total cost per unit time. In addition, we also give some results on the existence of the optimal solution for the exact s -expected total cost.
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Cooperative predictive maintenance of repairable systems with dependent failure modes and resource constraint
IEEE Transactions on Reliability, 2011Co-Authors: Hongdong Fan, Changhua Hu, Maoyin Chen, Donghua ZhouAbstract:Many works on condition-based maintenance of repairable systems apply to either a single failure mode, or statistically independent failure modes. Different from these works, this paper considers the problem of predictive maintenance of repairable systems with dependent failure modes, and resource constraints. Assume that (i) a repairable system is subject to two statistically dependent failure modes bidirectionally affecting each other, (ii) imperfect maintenance actions are cooperatively performed on two dependent failure modes by allocating insufficient resources spent for maintenance, and (iii) future maintenance scheduled at the current time depend on both the predicted number of future failures and the minimization of the expected maintenance cost Rate defined in the long term. To resolve the above problem, a novel cooperative predictive maintenance model is proposed. Its basis is the incorporation of the Hazard-Rate Function, and effective age. In this model, two failure modes are statistically dependent in such a way that the Hazard Rate of one failure mode depends on the accumulated number of failures of the other failure mode. The effect of imperfect maintenance is interpreted in terms of how the Hazard Rate Function and the effective age are changed by maintenance actions. The age reduction factor for each failure mode due to maintenance has some deterministic relation to the degree of resources cooperatively allocated to perform maintenance. The decision variables in the maintenance policy, namely the number of maintenance actions to be performed, the interval between successive maintenance actions, and the cooperatively allocated degree of resources, can be recursively updated when new monitored information arrives. This approach relies on both the predicted number of future failures, and the minimization of the expected maintenance cost Rate defined in the long term.
D.n.p. Murthy - One of the best experts on this subject based on the ideXlab platform.
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Modelling N- and W-shaped Hazard Rate Functions without mixing distributions
Proceedings of the Institution of Mechanical Engineers Part O: Journal of Risk and Reliability, 2008Co-Authors: Mark Bebbington, D.n.p. Murthy, Ričardas ZitikisAbstract:The presence of non-conforming components instead of, or in addition to, the usual assembly errors results in N- or W-shaped Hazard Rate (HR) Functions rather than the usual bathtub (i.e. U-shaped) ones. Although there have been numerous models for bathtub-shaped HR Functions, N- and W-shaped HR Functions are usually modelled using mixtures of two or more distributions. While this approach does sometimes lead to tidy interpretation, there can be a degree of overparameterization, with consequent problems in stability and fitting. For this reason, the present paper revisits the natural approach of modelling N- and W-shaped HR Functions using polynomial Functions of degree three or four. Although the non-negativity of the Hazard Rate Function becomes non-trivial, this ensures a minimal number of parameters. The polynomial approach also allows the use of a parametric model without imposing a particular shape of Hazard Rate Function on the data, which usually requires a non-parametric approach. The possible Hazard Rate shapes obtainable are characterized, and detailed formulae for local minima and maxima of the Functions provided. The performance of the models is compared to that of several generalizations of the Weibull distribution, with promising results.
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A modified Weibull distribution
IEEE Transactions on Reliability, 2003Co-Authors: D.n.p. MurthyAbstract:A new lifetime distribution capable of modeling a bathtub-shaped Hazard-Rate Function is proposed. The proposed model is derived as a limiting case of the Beta IntegRated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped Hazard-Rate Function.
M. Bebbington - One of the best experts on this subject based on the ideXlab platform.
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Useful periods for lifetime distributions with bathtub shaped Hazard Rate Functions
IEEE Transactions on Reliability, 2006Co-Authors: M. Bebbington, R. ZitikisAbstract:We propose computationally tractable formal mathematical definitions for the 'useful period' of lifetime distributions with bathtub shaped Hazard Rate Functions. Detailed analysis of the reduced additive Weibull Hazard Rate Function illustRates its utility for identifying such useful periods. Examples of several other bathtub shaped Hazard Rate Functions are also presented with applications to lifetime data. The suggestion is made of defining and considering analogous 'stable periods' in the case of the corresponding upside-down bathtub shaped mean residual life Functions.
