On Shrinkage Estimation for the Scale Parameter of Weibull Distribution

Prakash, Gyan; Singh, D.C.; Sinha, Sanjeev

doi:10.2481/dsj.7.125

Cited by 6 publications

(5 citation statements)

References 22 publications

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“…14. Comparing results of Figs 1 to 9 with the tables given in references [15] and [21] to [23], it is seen that our proposed testimator is much better in terms of higher relative efficiency. 15.…”

Section: Comparisonsmentioning

confidence: 72%

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Some testimators for the scale parameter and reliability function of Weibull lifetime data

Al-Hemyari

2010

Proceedings of the Institution of Mechanical Engineers, Part O:

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Section: Comparisonsmentioning

confidence: 72%

“…Since under H 0 , T ðbÞ has chi-square distribution with 2r degrees of freedom, it can be seen that [5,21,24,25]…”

Section: The Ssstbmentioning

confidence: 99%

Some testimators for the scale parameter and reliability function of Weibull lifetime data

Al-Hemyari

2010

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…For shape parameter β=2, it is approximate to Rayleigh distribution. While for the value of β in the range 3≤β≤4, the shape of Weibull distribution is close to normal distribution [26]. In the meanwhile, the scale parameter θ does not affect the shape of Weibull distribution, and only has an impact on the timescale of pdf curves.…”

Section: Reliability Assessment Of Cutting Tools 21 Tool Life Distrimentioning

confidence: 79%

Reliability assessment of cutting tools based on zero-failure data

Yang¹,

Guo²,

Feng³

et al. 2020

Preprint

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Titanium alloys are widely utilized in aeronautical monolithic components due to their excellent mechanical properties. However, the low machinability of titanium alloys results in an uncertain lifetime of cutting tools. Reliability assessment on cutting tools has become more and more significant to the effectiveness and stability of machining systems. Considering that cutting tools are often replaced well before the end of their useful lifetime to avoid failures and thus few tools failure data can be obtained during the machining process of titanium alloys, a reliability assessment model based on zero-failure data is developed to evaluate the reliability of cutting tools. A Weibull distribution model is chosen to describe the life distribution of cutting tools for reliability evaluation. Matching distribution curve method and weighted least squares method are used to estimate the distribution parameters. A novel approach using hierarchical Bayesian method for estimating the prior distribution of failure probability with zero-failure data is proposed by combining the characteristics of Weibull distribution and Incomplete Beta distribution. Reliability analysis for cutting tools with zero-failure data is performed using the proposed method. By comparing with the experience of experts and adopting stochastic simulation, the results of point estimation show plausibility of the proposed approach.

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“…At the same time, it is noted that the scale parameter ϑ in the Weibull distribution affects the failure probability curve on the timescale. The increase of the scale parameter is accompanied by the improvement of product reliability when the shape parameter is fixed . At last, the parameter γ affects the position of the Weibull distribution curve in the coordinate system, which does not have any effect on the change of the curve shape, and can only translate the curve in the horizontal axis direction.…”

Section: Significance Of the Parameter About Weibull Distributionmentioning

confidence: 99%

“…The increase of the scale parameter is accompanied by the improvement of product reliability when the shape parameter is fixed. 32 At last, the parameter γ affects the position of the Weibull distribution curve in the coordinate system, which does not have any effect on the change of the curve shape, and can only translate the curve in the horizontal axis direction. The product has not been used has been invalid when the parameter γ < 0.…”

Section: Significance Of the Parameter About Weibull Distributionmentioning

confidence: 99%

Reliability assessment of high‐quality and long‐life products based on zero‐failure data

Xie

et al. 2018

Quality & Reliability Eng

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For a period of mission time, only zero‐failure data can be obtained for high‐quality long‐life products. In the case of zero‐failure data reliability assessment, the point estimates and confidence interval estimates of distribution parameters cannot be obtained simultaneously by the current reliability assessment models, and the credibility of the assessment results may be reduced if they are obtained at the same time. A new model is proposed for consistency problem in this paper. In the proposed model, the point estimates of reliability can be obtained by the lifetime probability distribution derived from matching distribution curve method, while the confidence interval estimates of reliability can be obtained by using new samples generated from the lifetime probability distribution according to parameter bootstrap method. By analyzing the zero‐failure data of the torque motors after real operation, the results show that the new model not only meets the requirements of reliability assessment but also improves the accuracy of reliability interval estimation.

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On Shrinkage Estimation for the Scale Parameter of Weibull Distribution

Cited by 6 publications

References 22 publications

Some testimators for the scale parameter and reliability function of Weibull lifetime data

Some testimators for the scale parameter and reliability function of Weibull lifetime data

Reliability assessment of cutting tools based on zero-failure data

Reliability assessment of high‐quality and long‐life products based on zero‐failure data

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