Classical and Bayesian estimations of improved Weibull–Weibull distribution for complete and censored failure times data

Wang, Hong; Abba, Badamasi; Pan, Jianxin

doi:10.1002/asmb.2698

Cited by 7 publications

(8 citation statements)

References 44 publications

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“…Thus, we use the scaled TTT-transform plot to check the appropriateness of the proposed AGW model for analysing the three sets of data employed. See Wang et al 42 for a more recent discussion on the roles of the scaled TTT-transform plot in model selection.…”

Section: Reliability Data Applicationsmentioning

confidence: 99%

A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation

Abba

Wang

2023

Proceedings of the Institution of Mechanical Engineers, Part O:

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This paper presents an additive Gompertz-Weibull (AGW) distribution, a four-parameter hybrid probability distribution, and its applications in reliability engineering. The failure rate (FR) function of the proposed model demonstrates an increasing trend and a variety of bathtub shapes with or without a low and yet long-stable segment, making it appropriate for modelling a wide variety of real-world problems. Some relationships between the AGW’s FR and its mean residual life functions are examined. For parameter estimation, maximum likelihood and Bayesian inferences are considered. For posterior simulations, we use Hamiltonian Monte Carlo to evaluate the Bayes estimators of the AGW parameters. We evaluate the performance of the proposed AGW model to that of other recent bathtub distributions constructed following the same approach on three failure time datasets. The first two datasets represent device failure times, while the third represents early cable-joint failure times, all with bathtub FR. For comparison, five parametric and nonparametric evaluation criteria and the fitted FR and mean residual life curves were employed. The results indicated that the AGW model would be the best choice for describing failure times, especially when the bathtub-shaped FR of the presented dataset exhibits its three segments.

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Section: Reliability Data Applicationsmentioning

confidence: 99%

A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation

Abba

Wang

2023

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…More recent works that discuss the roles of the TTT plot in model selection are available in the literature (see, e.g., Refs. 26, 27).…”

Section: Applications To Reliability Datamentioning

confidence: 99%

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

Bakouch,

Abba,

Jónás

et al. 2023

Quality & Reliability Eng

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In this study, a two‐parameter, upper‐bounded probability distribution called the tau distribution is introduced and its applications in reliability engineering are presented. Each of the parameters of the tau distribution has a clear semantic meaning. Namely, one of them determines the upper bound of the distribution, while the value of the other parameter influences the shape of the cumulative distribution function. A remarkable property of this new probability distribution is that its probability density function, survival function, hazard rate function (HRF), and quantile function can all be expressed in terms of its cumulative distribution function. The HRF of the proposed probability distribution can exhibit an increasing trend and various bathtub shapes with or without a low and long‐flat phase (useful time phase), which makes this new distribution suitable for modeling a wide range of real‐world problems. The constraint maximum likelihood estimation, percentile estimation, approximate Bayesian computation, and approximate quantile estimation computation are proposed to calculate the unknown parameters of the model. The suitability of the estimation methods is verified with the aid of simulation and real‐world data results. The modeling capability of the tau distribution was compared with that of some well‐known two‐ and three‐parameter probability distributions using two data sets known from the literature of reliability engineering: time between failures data of a machining center, and time to failure of data acquisition system cards. Based on empirical results, the new distribution may be viewed as a viable competitor to the Weibull, Gamma, Chen, and modified Weibull distributions.

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“…Based on Weibull, some better models have been developed recently 12–17 . Among them, the q‐Weibull model, which describes the bathtub and unimodal curves with only one set of parameter values is widely popular in the research field 18 …”

Section: Introductionmentioning

confidence: 99%

“…4 Based on Weibull, some better models have been developed recently. [12][13][14][15][16][17] Among them, the q-Weibull model, which describes the bathtub and unimodal curves with only one set of parameter values is widely popular in the research field. 18 To our knowledge, there has not been any reported CT reliability analysis using the q-Weibull model.…”

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confidence: 99%

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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Classical and Bayesian estimations of improved Weibull–Weibull distribution for complete and censored failure times data

Cited by 7 publications

References 44 publications

A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation

A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

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

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