The Maxwell–Weibull Distribution in Modeling Lifetime Datasets

Ishaq, Aliyu Ismail; Abiodun, Alfred Adewole

doi:10.1007/s40745-020-00288-8

Cited by 31 publications

(28 citation statements)

References 33 publications

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“…Weibull models are used to describe various phenomena, including the failure of components. They are widely used in reliability and survival analyses [43][44][45]. Nowadays, many types of modifications, extensions, and variations of the model are used [46][47][48][49][50][51][52].…”

Section: Weibull Distributionmentioning

confidence: 99%

Influence of Disinfectants on Airport Conveyor Belts

et al. 2021

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The coronavirus disease has influenced almost all of our everyday activities. Traveling and transportation have been influenced significantly and there is no doubt that air transportation has been restricted and therefore reduced considerably. It is predicted that the change back to pre-pandemic conditions will take several years, and so it is a reasonable assumption that disinfectants will be used more frequently for a long time. The presented article initially deals with the possible impacts of the pandemic on aircraft infrastructure—namely, on the influence of disinfectants on the rubber materials used, for example, in conveyor belts. The proposed methodology is based on the Weibull analysis for conveyor belt lifetime prediction regarding the impact of disinfectants. The Weibull distribution is a continuous probability distribution that can be applied as a theoretical model for statistical data processing. It was named after Weibull, who suggested shape, scale, and location parameters that made the distribution meaningful and useful. Currently, this distribution is applied in many areas, such as biology, economics, and hydrology. In engineering applications, it can be used for reliability and survival analysis. It is used mainly in cases where failure time is dependent on the operating hours, cycles, or age of the component. In the reliability area, it can be used, for example, to predict the lifetime or failure time of a component. To show the consequences of material changes due to the use of disinfectants, this article also presents a CAE (Computer Aided Engineering) analysis that was used for the evaluation of other hyperelastic material characteristics. This research is based on the results of experimental measurements, during which the influence of the types of disinfectant commonly used for the elimination of the coronavirus disease on airport conveyor belt rubber segments was tested. From the performed analysis, it was found that the influence of disinfectants on the material characteristics, including material hardness, elasticity, and static and dynamic loading, could be significant. Therefore, the probability of mechanical damage to the rubber part of the conveyor belt becomes higher, and time intervals for the maintenance or repair of airport conveyor belts should be considered.

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Section: Weibull Distributionmentioning

confidence: 99%

Influence of Disinfectants on Airport Conveyor Belts

et al. 2021

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“…As proposed by Ishaq and Abiodun [17], the cumulative distribution function of Maxwell generalized family of distributions is given by ( 𝑇 (𝑥; 𝜙)…”

Section: Maxwell Generalized Family Of Distributionsmentioning

confidence: 99%

“…Therefore, the maximum likelihood estimator of the scale parameter 𝑐 can be obtained by differentiating (17) partially with respect to parameter 𝑐 and setting the result to zero as…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…i. to propose a new continuous probability distribution referred to as Maxwell-Mukherjee Islam distribution by using Maxwell generalized family of distribution introduced by Ishaq and Abiodun [17] ii. to test the validity of the proposed Maxwell-Mukherjee Islam distribution iii.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian estimation of the parameter of Maxwell-Mukherjee Islam distribution using assumptions of the Extended Jeffrey's, Inverse-Rayleigh and Inverse-Nakagami priors under the three loss functions

Ishaq

Abiodun

Falgore

2021

Heliyon

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A three-parameter Maxwell-Mukherjee Islam distribution was proposed by applying Maxwell generalized family of distributions introduced by Ishaq and Abiodun [17]. The probability density and cumulative distribution functions of the proposed distribution were defined. The validity test was derived from its cumulative distribution function. The study aimed to obtain a Bayesian estimation of the scale parameter of Maxwell-Mukherjee Islam distribution by using assumptions of the Extended Jeffrey's (Uniform, Jeffrey's and Hartigan's), Inverse-Rayleigh and Inverse-Nakagami priors under the loss functions, namely, Squared Error Loss Function (SELF), Precautionary Loss Function (PLF) and Quadratic Loss Function (QLF), and their performances were compared. The posterior distribution under each prior and its corresponding loss functions was derived. The performance of the Bayesian estimation was illustrated from the basis of quantile function by using a simulation study and application to real life data set. For different sample sizes and parameter values, the QLF and SELF under Jeffrey's and Hartigan's priors produced the same estimates, bias and Mean Squared Error (MSE) just as we observed in their mathematical derivatives. Similarly, the SELF, PLF and QLF under Inverse-Rayleigh and Inverse-Nakagami priors provided the same performance when some parameter values are equal. For some parameter values, the QLF under Inverse-Nakagami and Inverse-Rayleigh priors produced the least values of MSE. In the application to real life data set, the QLF and SELF under Jeffrey's and Hartigan's priors; the SELF, PLF and QLF under Inverse-Rayleigh and Inverse-Nakagami priors provided similar results as observed in the simulation study. Therefore, the study concluded that the QLF under Inverse-Rayleigh and Inverse-Nakagami priors could effectively be used in the estimation of scale parameter of Maxwell-Mukherjee Islam distribution using Bayesian approach.

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