Graphical representation of two mixed-Weibull distributions

Jiang, Suhua; Kececioglu, Dimitri

doi:10.1109/24.257789

Cited by 65 publications

(41 citation statements)

References 6 publications

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“…The detailed analysis of the model and parameter estimation can be referred to [9,10,[31][32][33]38]. From equation (61), it is derived that…”

Section: Mixed Weibull Distributionmentioning

confidence: 99%

“…These include modified Weibull distribution and its extension models [1][2][3][4][5], exponentiated Weibull family [6][7][8], mixture models [9][10], competing risk models, multiplicative models and sectional models [11][12][13][14]. These models can be utilized to analyze a given data set whose fitting plot on WPP is concave, convex, S-shaped or further other shapes.…”

Section: Introductionmentioning

confidence: 99%

“…It has been recognized for more than four decades that the mixed Weibull distribution is an appropriate distribution to use in modeling the lifetimes of units that have more than one failure cause [31]. Jiang and Kececioglu [9,32] 1. It is mathematically tractable and yields a bathtub shape for the failure rate function.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Choosing an optimal model for failure data analysis by graphical approach

Zhang

Dwight

2013

Reliability Engineering & System Safety

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Many models involving combination of multiple Weibull distributions, modification of Weibull distribution or extension of its modified ones, etc. have been developed to model a given set of failure data. The application of these models to modeling a given data set can be based on plotting the data on Weibull probability paper (WPP). Of them, two or more models are appropriate to model one typical shape of the fitting plot, whereas a specific model may be fit for analyzing different shapes of the plots. Hence, a problem arises, that is how to choose an optimal model for a given data set and how to model the data. The motivation of this paper is to address this issue. This paper summarizes the characteristics of Weibull-related models with more than three parameters including sectional models involving two or three Weibull distributions, competing risk model and mixed Weibull model. The models as discussed in this present paper are appropriate to model the data of which the shapes of plots on WPP can be concave, convex, S-shaped or inversely S-shaped. Then, the method for model selection is proposed, which is based on the shapes of the fitting plots. The main procedure for parameter estimation of the models is described accordingly. In addition, the range of data plots on WPP is clearly highlighted from the practical point of view. To note this is important as mathematical analysis of a model with neglecting the applicable range of the model plot will incur discrepancy or big errors in model selection and parameter estimates. © 2013 Elsevier Ltd. All rights reserved. The application of these models to modeling a given data set can be based on plotting the data on Weibull probability paper (WPP). Of them, two or more models are appropriate to model one typical shape of the fitting plot, whereas a specific model may be fit for analyzing different shapes of the plots. Hence, a problem arises, that is how to choose an optimal model for a given data set and how to model the data. The motivation of this paper is to address this issue. This paper summarizes the characteristics of Weibull-related models with more than three parameters including sectional models involving two or three Weibull distributions, competing risk model and mixed Weibull model. The models as discussed in this present paper are appropriate to model the data of which the shapes of plots on WPP can be concave, convex, S-shaped or inversely S-shaped. Then, the method for model selection is proposed, which is based on the shapes of the fitting plots. The main procedure for parameter estimation of the models is described accordingly. In addition, the range of data plots on WPP is clearly highlighted from the practical point of view. To note this is important as mathematical analysis of a model with neglecting the applicable range of the model plot will incur discrepancy or big errors in model selection and parameter estimates.Keywords: Weibull models, Failure data analysis, Model selection, Parameter estimation, Weibull probability paper NOTATION...

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“…The detailed analysis of the model and parameter estimation can be referred to [9,10,[31][32][33]38]. From equation (61), it is derived that…”

Section: Mixed Weibull Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Choosing an optimal model for failure data analysis by graphical approach

Zhang

Dwight

2013

Reliability Engineering & System Safety

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“…There are also several other studies that investigated the combination of two Weibull distributions for bathtub shape failure rate function, such as the competing risk model, multiplicate model, and sectional model given in Chen (2000). Graphical methods and representations of the mixed Weibull distributions were discussed in Murthy (1995, 1999), Jiang and Kececioglu (1992) and recently Lai, et.al (2001).…”

Section: Introductionmentioning

confidence: 99%

New Solution and Its Impact on Increasing, Decreasing and Bathtub Shaped Failure Rate Model

Alam¹

2009

Pak.j.stat.oper.res.

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The maximum likelihood equations of IDB distribution can't be solved analytically. Solutions of the MLE equations can be obtained numerically. But the problem is to detect the initial value of the parameters to solve the nonlinear MLE equations. A technique is developed for formulating the initial value of the parameter to solve the MLE equations of IDB distribution. Considering all the facts, though IDB distribution is not suitable for graduating mortality data but the model can graduate mortality data of Bangladesh in the age range of 0-8 very well.

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“…Cheng and Fu (1982) proposed a parametric mixture model of Weibull distribution where they employed the weighted least squares method to estimate the parameters. Jiang and Kececioglu (1992a) estimated the parameters of a mixture model of Weibull distribution using graphical approach. They (Jiang & Kececioglu, 1992b) also developed a new procedure to estimate the parameters of a mixture model of Weibull.…”

Section: Introductionmentioning

confidence: 99%

A Simulation Study of a Parametric Mixture Model of Three Different Distributions to Analyze Heterogeneous Survival Data

Mohammed¹,

Yatim²,

Ismail³

2013

MAS

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In this paper a simulation study of a parametric mixture model of three different distributions is considered to model heterogeneous survival data. Some properties of the proposed parametric mixture of Exponential, Gamma and Weibull are investigated. The Expectation Maximization Algorithm (EM) is implemented to estimate the maximum likelihood estimators of three different postulated parametric mixture model parameters. The simulations are performed by simulating data sampled from a population of three component parametric mixture of three different distributions, and the simulations are repeated 10, 30, 50, 100 and 500 times to investigate the consistency and stability of the EM scheme. The EM Algorithm scheme developed is able to estimate the parameters of the mixture which are very close to the parameters of the postulated model. The repetitions of the simulation give parameters closer and closer to the postulated models, as the number of repetitions increases, with relatively small standard errors.

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Graphical representation of two mixed-Weibull distributions

Cited by 65 publications

References 6 publications

Choosing an optimal model for failure data analysis by graphical approach

Choosing an optimal model for failure data analysis by graphical approach

New Solution and Its Impact on Increasing, Decreasing and Bathtub Shaped Failure Rate Model

A Simulation Study of a Parametric Mixture Model of Three Different Distributions to Analyze Heterogeneous Survival Data

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