Estimation of some lifetime parameters of generalized Gompertz distribution under progressively type-II censored data

Ahmed, Essam A.

doi:10.1016/j.apm.2015.01.023

Cited by 30 publications

(17 citation statements)

References 27 publications

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“…ese data were analyzed by many authors assuming GG distribution under different sampling schemes (see, for example, Ahmed [7] and El-Gohary et al [4]). e GG distribution was found to fit the data fairly well and better than other candidate distributions such as Gompertz and generalized exponential and exponential distributions.…”

Section: Real Data Examplementioning

confidence: 99%

“…Demir and Saracoglu [6] studied maximum likelihood estimation of the GG distribution parameters under progressively type II censored data. Ahmed [7] studied maximum likelihood and Bayesian estimation of the lifetime parameters of the GG distribution under progressively type II censored data. Based on the GG distribution, Borges [5] developed a regression model for survival data.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

Obeidat

Al‐Nasser

Al-Omari

2020

Journal of Probability and Statistics

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This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.

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Section: Real Data Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

Obeidat

Al‐Nasser

Al-Omari

2020

Journal of Probability and Statistics

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“…Accordingly, the Gumbel, Gamma, and Gaussian models were compared to obtain the best approximation model. In general, the AIC formulation is assumed when the sample size is adequately large, but if the division of the sample size over the number of parameters is quite small ( n k < ∼ 40), then the AIC is formulated as follows [39,40]:…”

Section: Approximate Best Model Compared With Other Modelsmentioning

confidence: 99%

Fatigue Reliability Assessment of an Automobile Coil Spring under Random Strain Loads Using Probabilistic Technique

Manouchehrynia

Abdullah

Singh

2019

Metals

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This paper presents a mathematical model to estimate strain-life probabilistic modeling based on the fatigue reliability prediction of an automobile coil spring under random strain loads. The proposed technique was determined using a probabilistic method of the Gumbel distribution for strain-life models of automobile suspension systems. Strain signals from different road excitations in experimental tests were measured. The probability density function of the Gumbel distribution was considered to estimate model parameters using maximum likelihood estimation (MLE). The Akaike information criterion (AIC) method was performed to specify which model can estimate the best fit model parameters. Results demonstrated a good agreement between the predicted fatigue lives of the proposed probabilistic model and the measured strain fatigue life models. The root-mean-square errors (RMSE) based on the Coffin–Manson, Morrow, and Smith–Watson–Topper strain-life models were approximately 0.00114, 0.00107, and 0.00509, respectively, indicating a high correlation with the proposed model and experimental data. The results demonstrated that the proposed probabilistic model is effective for the fatigue life prediction of automobile coil springs using strain and stress fatigue life approaches.

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“…By quantification and relativity concept, boundary conditions, and compatibility, the validity of candidate damage equations/quantities on S-N plane for prediction of fatigue life could be evaluated. 28 A MCM with discrete ray tracing was developed to simulate radiative transfer in a medium with a refractive-index distribution given at a set of discrete points by Hung-Yi Tseng et al 29 With available raw experimental data, Naryanan et al 30 performed the variations in fatigue life and its most influencing parameters based on Monte Carlo simulation by varying the random life samples. In the second stage, linear elastic fracture mechanics was used to evaluate the possibility of long crack arrest.…”

mentioning

confidence: 99%

“…The Monte Carlo method (MCM) was used in numerous areas of science such as biology, quantum chemistry, 27 and quantum mechanics. 28 A MCM with discrete ray tracing was developed to simulate radiative transfer in a medium with a refractive-index distribution given at a set of discrete points by Hung-Yi Tseng et al 29 With available raw experimental data, Naryanan et al 30 performed the variations in fatigue life and its most influencing parameters based on Monte Carlo simulation by varying the random life samples. The predictions showed that with more number of random samples, the results convergence much better.…”

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confidence: 99%

An improved damage model using the construction technology of virtual load spectrum and its statistical analysis

Deng

et al. 2018

Fatigue Fract Eng Mat Struct

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In this work, an improved damage model based on construction technology of virtual load spectrum is developed. A predetermined reliability index is used as the termination criterion to calculate the fatigue life, and the results of statistical analysis have shown that the accuracy of fatigue life prediction result has been greatly improved. The model is targeting cyclic loading applications. The main advantage of the model is the use of construction technology of virtual load spectrum for expanding load spectrum and the Monte Carlo method for correcting fatigue damage. Another advantage concerns the link between predetermined reliability criterion and the fatigue life, which puts forward a new method of calculating fatigue life. The convergence proof of the model is presented, and physical experiment data are shown for validation. Several illustrative examples are presented to confirm the accuracy and efficiency of the proposed damage model.

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Estimation of some lifetime parameters of generalized Gompertz distribution under progressively type-II censored data

Cited by 30 publications

References 27 publications

Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

Fatigue Reliability Assessment of an Automobile Coil Spring under Random Strain Loads Using Probabilistic Technique

An improved damage model using the construction technology of virtual load spectrum and its statistical analysis

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