Non-informative and practical Bayesian confidence bounds for reliable life in the Weibull model

Erto, Pasquale; Rapone, M.

doi:10.1016/0143-8174(84)90016-7

Cited by 33 publications

(18 citation statements)

References 12 publications

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“…Therefore, here we derive an expression for the moments of an IWPS distribution. Suppose that X ∼ IWPS(α, β, θ), then by using Equation (2), the kth moment of X is given by…”

Section: The Class Of Iwps Distributionsmentioning

confidence: 99%

“…For the situations in which empirical studies indicate that the hazard function (HF) might be unimodal, the IW distribution would be an appropriate model. The IW model has been derived as a suitable model for describing the degradation phenomena of mechanical components, such as the dynamic components of diesel engines, see, for example, Murthy et al [1] The physical failure process given by Erto and Rapone [2] also leads to the IW model. Erto and Rapone [2] showed that the IW model provides a good fit to survival data such as the time to breakdown of an insulating fluid subject to the action of constant tension, see also Nelson.…”

Section: Introductionmentioning

confidence: 99%

“…The IW model has been derived as a suitable model for describing the degradation phenomena of mechanical components, such as the dynamic components of diesel engines, see, for example, Murthy et al [1] The physical failure process given by Erto and Rapone [2] also leads to the IW model. Erto and Rapone [2] showed that the IW model provides a good fit to survival data such as the time to breakdown of an insulating fluid subject to the action of constant tension, see also Nelson. [3] Calabria and Pulcini [4] provided an interpretation of the IW distribution in the context of a load-strength relationship for a component.…”

Section: Introductionmentioning

confidence: 99%

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Inverse Weibull power series distributions: properties and applications

Shafiei

Darijani

Saboori

2015

Journal of Statistical Computation and Simulation

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Inverse Weibull (IW) distribution is one of the widely used probability distributions for nonnegative data modelling, specifically, for describing degradation phenomena of mechanical components. In this paper, by compounding IW and power series distributions we introduce a new lifetime distribution. The compounding procedure follows the same set-up carried out by Adamidis and Loukas [A lifetime distribution with decreasing failure rate. Stat Probab Lett. 1998;39:35-42]. We provide mathematical properties of this new distribution such as moments, estimation by maximum likelihood with censored data, inference for a large sample and the EM algorithm to determine the maximum likelihood estimates of the parameters. Furthermore, we characterize the proposed distributions using a simple relationship between two truncated moments and maximum entropy principle under suitable constraints. Finally, to show the flexibility of this type of distributions, we demonstrate applications of two real data sets.

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“…Therefore, here we derive an expression for the moments of an IWPS distribution. Suppose that X ∼ IWPS(α, β, θ), then by using Equation (2), the kth moment of X is given by…”

Section: The Class Of Iwps Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inverse Weibull power series distributions: properties and applications

Shafiei

Darijani

Saboori

2015

Journal of Statistical Computation and Simulation

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show abstract

“…The inverse Weibull model has been derived as a suitable model for describing the degradation phenomena of mechanical components, such as the dynamic components of diesel engines, see for example Murthy et al [18]. The physical failure process given by Erto and Rapone [13] also leads to the inverse Weibull model. Erto and Rapone [13] showed that the inverse Weibull model provides a good fit to survival data such as the times to breakdown of an insulating fluid subject to the action of constant tension, see also Nelson [19].…”

Section: The Inverse Weibull Distributionmentioning

confidence: 99%

“…The physical failure process given by Erto and Rapone [13] also leads to the inverse Weibull model. Erto and Rapone [13] showed that the inverse Weibull model provides a good fit to survival data such as the times to breakdown of an insulating fluid subject to the action of constant tension, see also Nelson [19]. Calabria and Pulcini [9] provided an interpretation of the inverse Weibull distribution in the context of a load-strength relationship for a component.…”

Section: The Inverse Weibull Distributionmentioning

confidence: 99%

Bayesian Inference Based on Multiply Type-II Censored Sample from a General Class of Distributions

Shafay¹,

El-Din²,

Abdel-Aty³

2018

JSTA

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In this paper, we consider a general form for the underlying distribution and a general conjugate prior, and develop a general procedure for Bayesian estimation based on an observed multiply Type-II censored sample. The problem of predicting the order statistics from a future sample are also discussed from a Bayesian viewpoint. For the illustration of the developed results, the inverse Weibull distribution is used as example. Finally, two numerical examples are presented for illustrating all the inferential procedures developed here.

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Comparison of Estimation Methods for Inverse Weibull Distribution

Akgül

Şenoğlu

2018

Contributions to Statistics

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Non-informative and practical Bayesian confidence bounds for reliable life in the Weibull model

Cited by 33 publications

References 12 publications

Inverse Weibull power series distributions: properties and applications

Inverse Weibull power series distributions: properties and applications

Bayesian Inference Based on Multiply Type-II Censored Sample from a General Class of Distributions

Comparison of Estimation Methods for Inverse Weibull Distribution

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