The modified exponentiated-Weibull distribution for life-time modeling

Gera, Amos E.

doi:10.1109/rams.1997.571690

Cited by 13 publications

(11 citation statements)

References 3 publications

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“…In addition to the exponentiated method, there have been different alternatives to generate different types of flexible families of distributions using different functions of F ( x ), including Gera135 defined F E = exp(− λx γ ) F,λ,γ > 0. Cancho and Bolfarine136 defined F M = λ − λ [1 − F ( x )] ,λ ∈ (0,1). Note that one can consider this as a mixture method. The Kw‐G family discussed previously can be defined as an exponentiated method by F Kw − G = 1−[1− F λ ( x )] θ ,λ,θ > 0.…”

Section: Methods Of Adding Parametersmentioning

confidence: 99%

Methods for generating families of univariate continuous distributions in the recent decades

Lee

Famoye

Alzaatreh

2013

WIREs Computational Stats

147

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There has been a renewed interest in developing more flexible statistical distributions in recent decades. A major milestone in the methods for generating statistical distributions is undoubtedly the system of differential equation approach. There is a recent renewed interest in generating skewed distributions. Generally speaking, the methods developed prior to 1980s may be summarized into three categories: (1) method of differential equation, (2) method of transformation, and (3) quantile method. Techniques developed since 1980s may be categorized as ‘methods of combination’ for the reason that these methods attempt to combine existing distributions into new distributions or adding new parameters to an existing distribution. This article discusses five general methods of combination and their variations. These five are (1) method of generating skew distributions, (2) method of adding parameters (e.g., exponentiation), (3) beta generated method, (4) transformed‐transformer method, and (5) composite method. WIREs Comput Stat 2013, 5:219–238. doi: 10.1002/wics.1255 This article is categorized under: Algorithms and Computational Methods > Random Number Generation Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

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Section: Methods Of Adding Parametersmentioning

confidence: 99%

Methods for generating families of univariate continuous distributions in the recent decades

Lee

Famoye

Alzaatreh

2013

WIREs Computational Stats

147

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“…The Weibull distribution is a continuous distribution which can adequately describe observed failure data of many different types of components and phenomena. In the product life test, the Weibull distribution is the commonly used life distribution model in statistical methods [12]. The Weibull distribution is proposed in 1951.…”

Section: A Statistical Methodsmentioning

confidence: 99%

Investigation on data-driven life prediction methods

Yang

Liu

Zhou

et al. 2012

2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering

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The theory of life prediction is the key foundation of the safety service of electromechanical device, and it is also an important aspect of modern mechanical design and manufacturing. Life prediction for major mechanical equipment has great significance for economic development and defense construction. This paper aims at the investigation of characteristics and applications of electromechanical device life prediction techniques. It summarizes the current progress of life prediction based on data-driven methods. The challenges of electromechanical device life prediction include theoretic models, experimental validation, data accumulation. It provides a possible direction for further research on life forecasting method.

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“…So it is necessary to develop a more precise failure model. Currently, different functions are applied to model failures of different assets, such as the well-known Weibull distribution [21][22][23]. Paper [24] brings forward an S-PLP to depict the failure pattern of a complex repairable equipment, which shows a bathtub behaviour of the intensity function.…”

Section: Unit Failure Model Analysismentioning

confidence: 99%

Optimal maintenance scheduling of power producers considering unexpected unit failure

Feng

Wang

2009

IET Generation, Transmission &Amp; Distribution

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A novel unit maintenance scheduling (UMS) problem formulation for a generation producer is presented, to maximise its benefit while thoroughly considering the risk associated with unexpected unit failures. First, the unit failure is characterised by a more practical bathtub-shaped failure behaviour from the modified superposed power law process. Its parameters are estimated from the historical data by solving a nonlinear least-squaresfitting problem via Gauss -Newton iteration method. On the basis of the unit failure analysis, the new UMS formulation is solved by a combination of linear programming and genetic algorithms (GAs), and its impact on the producer's benefit is analysed in detail, including expected profit of selling energy, expected renewal cost of damaged components and maintenance cost. Compared with the current models, the proposed UMS model takes into consideration the influences of market factors as well as unexpected unit failures to strike the right balance between profits and costs related with potential unit failures. Numerical examples on a four-unit producer are utilised to demonstrate the effectiveness of the proposed scheme. NomenclatureThe main mathematical symbols used in this paper are classified as follows:maintenance cost at period t E Profit (t) expected energy-selling profit at period t E Renewal (t) expected renewal cost at period t h( j, t, x j ) failure rate of unit j at period t p m (t) probability of unit operating state m at period t P m ( j, t) generation of unit j in unit operating state m at period t

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The modified exponentiated-Weibull distribution for life-time modeling

Cited by 13 publications

References 3 publications

Methods for generating families of univariate continuous distributions in the recent decades

Methods for generating families of univariate continuous distributions in the recent decades

Investigation on data-driven life prediction methods

Optimal maintenance scheduling of power producers considering unexpected unit failure

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