On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

Xu, Meng; Droguett, Enrique López; Lins, Isis Didier; Moura, Márcio das Chagas

doi:10.1016/j.ress.2016.10.012

Cited by 28 publications

(31 citation statements)

References 41 publications

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“…[9,20]. Xu et al [10] obtained the CIs for the q-Weibull parameters according to this approximation. Here, we derive the expected values.…”

Section: The Asymptotic Cismentioning

confidence: 99%

“…the q-Weibull distribution, has been more focused than others. The q-Weibull distribution can describe complex systems with long-range interactions and long-term memory [10]. The Weibull distribution can only exhibit monotonic and constant shapes for its hazard rate function.…”

Section: Introductionmentioning

confidence: 99%

“…The Weibull distribution can only exhibit monotonic and constant shapes for its hazard rate function. However, the q-Weibull distribution can exhibit unimodal, bathtub-shaped, monotonically decreasing, monotonically increasing and constant shapes [7,10] for its hazard rate function. Hence, it is a useful generalization of the Weibull distribution [11].…”

Section: Introductionmentioning

confidence: 99%

“…Several methods have been proposed to estimate the q-Weibull parameters, including moment estimates [14], maximum likelihood estimates (MLEs) [10] and least-squares estimates (LSEs) [7,16,17]. The confidence intervals (CIs) for the q-Weibull parameters were considered only by Xu et al [10]. These developments motivate us to compare the different estimates and propose CIs for the q-Weibull parameters.…”

Section: Introductionmentioning

confidence: 99%

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Inference on q-Weibull parameters

Jia

Nadarajah

2017

Stat Papers

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The q-Weibull distribution is a generalization of the Weibull distribution and could describe complex systems. We firstly point out how to derive the maximum likelihood estimates (MLEs) and least-squares estimates (LSEs) of the q-Weibull parameters. Next, three confidence intervals (CIs) for the q-Weibull parameters are constructed based on bootstrap methods and asymptotic normality of the MLEs. Explicit expressions for the Fisher information matrix necessary for the asymptotic CIs are derived. A Monte Carlo simulation study is conducted to compare the performances of the MLEs and LSEs as well as the different CIs. The simulation results show that the MLEs are superior to the LSEs in terms of both bias and mean squared error. The bootstrap CIs based on the MLEs are shown to have good coverage probabilities and average interval widths. Finally, a real data example is provided to illustrate the proposed methods.

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“…[9,20]. Xu et al [10] obtained the CIs for the q-Weibull parameters according to this approximation. Here, we derive the expected values.…”

Section: The Asymptotic Cismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Inference on q-Weibull parameters

Jia

Nadarajah

2017

Stat Papers

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“…Due to the complicated first derivatives, along with constraints over parameters' values to guarantee the models' probabilistic validity, derivative-based optimization methods may fail. Alternatively, derivative-free and nature-based heuristics (e.g., artificial bee colony (ABC) [19,20], particle swarm optimization (PSO) [21,22], among others) can be used in the quest for proper parameters' ML estimates. The search procedure associated with these heuristics are governed by direct evaluations of the objective function, as derivative information is not required.…”

Section: Introductionmentioning

confidence: 99%

Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

Lins

Moura

Droguett

et al. 2018

Entropy

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Abstract:The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsallis' non-extensive entropy, namely the q-Exponential and the q-Weibull distributions. The q-Exponential and Weibull distributions can model decreasing, constant or increasing failure intensity functions. However, the power law behavior of the q-Exponential probability density function for specific parameter values is an advantage over the Weibull distribution when adjusting data containing extreme values. The q-Weibull probability distribution, in turn, can also fit data with bathtub-shaped or unimodal failure intensities in addition to the behaviors already mentioned. Therefore, the q-Exponential-GRP is an alternative for the Weibull-GRP model and the q-Weibull-GRP generalizes both. The method of maximum likelihood is used for their parameters' estimation by means of a particle swarm optimization algorithm, and Monte Carlo simulations are performed for the sake of validation. The proposed models and algorithms are applied to examples involving reliability-related data of complex systems and the obtained results suggest GRP plus q-distributions are promising techniques for the analyses of repairable systems.

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Reliability analysis of computed tomography equipment using the q‐Weibull distribution

Litian

Zhi

Ling

et al. 2023

Engineering Reports

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Inspired by the successful application of the q‐Weibull distribution in other research fields, we took the lead to use it in the field of medical devices in this work. The parameter estimation of the q‐Weibull distribution was performed using the probability plot method. The CT failure data from Nanfang Hospital in Guangzhou, China, were used to study the reliability of CT equipment at two levels: the CT system and its seven main components. In terms of evaluation accuracy, the mean squared error, Akaike's information criterion, and the determination coefficient were used to compare the accuracy of fitting of different distribution models. The results show that the accuracy of fitting the q‐Weibull distribution is higher than that of the Weibull distribution in terms of determination coefficient and mean squared error. When considering the complexity of the model, the fit accuracy of the Weibull distribution is better. The results were analyzed using reliability and failure rate plots. The q‐Weibull distribution gives a good fit for the failure data of the CT system and components. Though the Weibull distribution fits better in a few cases, the q‐Weibull distribution can describe the entire “bathtub curve” with only a set of parameters. The findings of this study can be extended to other medical devices.

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On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

Cited by 28 publications

References 41 publications

Inference on q-Weibull parameters

Inference on q-Weibull parameters

Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

Reliability analysis of computed tomography equipment using the q‐Weibull distribution

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