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

Al-Hemyari, Zuhair A.

doi:10.1243/1748006xjrr299

Cited by 9 publications

(4 citation statements)

References 15 publications

(14 reference statements)

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“…As shown in Table 3, the lower reliability percentiles of the S-N curve are the minimum strength values given in the column 𝜂𝜂 (𝜎𝜎𝑢𝑢) of Table 5. Due to the column 𝜂𝜂 (𝜎𝜎𝑢𝑢) of Table 3 represents the minimum strength values that the designed element must have to present the desired reliability, then the reliability percentiles of the S-N curve can be used as the accelerated levels in and ALT test to demonstrate the product presents the intended reliability [17].…”

Section: Numerical Analysismentioning

confidence: 99%

Weibull strength distribution and reliability S-N percentiles for tensile tests

Baro¹,

Piña‐Monarrez

Barraza-Contreras

2022

Rev. Ci. Tec.

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Based on the true stress, the ultimate material’s strength, and the fatigue slope b values, the probabilistic percentiles of the S-N curve of ductile materials are formulated. The Weibull β and η parameters used to determine the product’s reliability are determined directly from the material’s strength values corresponding to 103 and 106 cycles. And since in Table corresponding to the properties of this A538 A (b) steel and collected by table 23-A of Shigley Mechanical Engineering Design book; authors present the σt, Sut, and b values of several materials, then the Weibull parameters for each one of these materials as well as the 95% and 5% reliability percentiles of their S-N curves are given. A step-by-step application to the steel A538 A (b) material is presented. And based on the maximum and minimum applied stress values, the corresponding Weibull stress distribution was fitted and used with the Weibull strength distribution, in the stress/strength reliability function to determine the element’s reliability.

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Section: Numerical Analysismentioning

confidence: 99%

Weibull strength distribution and reliability S-N percentiles for tensile tests

Baro¹,

Piña‐Monarrez

Barraza-Contreras

2022

Rev. Ci. Tec.

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“…Inference upon reliability is widely studied in literature. We refer to Al-Hemyari and Al-Dolami, 1 Jia et al, 2 and Al-Hemyari 3 for some useful results on this aspect. Initial discussion on a stress-strength model (SM) is given in Birnbaum, 4 see also, Birnbaum and McCarty.…”

Section: Introductionmentioning

confidence: 99%

Estimation in a multicomponent stress-strength model for progressive censored lognormal distribution

Singh

Mahto

Tripathi

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part O:

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We consider estimation of multicomponent stress-strength reliability under classical as well as Bayesian approaches when stress-strength components follow lognormal distributions and data are observed under progressive censoring. Various estimates are obtained by sequentially considering one parameter common and unknown. Different expressions for the reliability are evaluated under these cases. For both the cases, we obtain different estimates of considered parametric function using likelihood, Lindley and repeated sampling methods. Asymptotic and credible intervals are also obtained. Extensive simulations are conducted to examine the behavior of all estimates under various censoring schemes. We finally present analysis of a real life example from application purposes.

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“…Introducing additional information or knowledge, for example, Bayesian approaches 14–17 and re-sampling techniques; 9…”

Section: Introductionmentioning

confidence: 99%

A novel parameter estimation method for the Weibull distribution on heavily censored data

Jiang

2019

Proceedings of the Institution of Mechanical Engineers, Part O:

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It is desired to build the life distribution models of critical components (which are assumed to be non-repairable) of a repairable system as early as possible based on field failure data in order to optimize the operation and maintenance decisions of the components. When the number of the systems under observation is large and the observation duration is relatively short, the samples obtained for modeling are large and heavily censored. For such samples, the classical parameter estimation methods (e.g. maximum likelihood method and least square method) do not provide robust estimates. To address this issue, this article develops a hybrid censoring index to quantitatively describe censoring characteristics of a data set, proposes a novel parameter estimation method based on information extracted from censored observations, and evaluates the accuracy and robustness of the proposed method through a numerical experiment. Its applicable range in terms of the hybrid censoring index is determined through an accuracy analysis. The experiment results show that the proposed approach provides much accurate estimates than the classical methods for heavily censored data. A real-world example is also included.

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

Cited by 9 publications

References 15 publications

Weibull strength distribution and reliability S-N percentiles for tensile tests

Weibull strength distribution and reliability S-N percentiles for tensile tests

Estimation in a multicomponent stress-strength model for progressive censored lognormal distribution

A novel parameter estimation method for the Weibull distribution on heavily censored data

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