Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

Shi, Xiaolin; Shi, Yimin

doi:10.1002/qre.3298

Quality & Reliability Eng

2023

DOI: 10.1002/qre.3298

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Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

Xiaolin Shi

Yimin Shi

Abstract: In this paper, we investigate classical and Bayes estimates for stress-strength reliability (SSR) based on two independent progressive first failure censored samples from beta log Weibull distributions with different shape and scale parameters.The maximum likelihood estimation of SSR and its asymptotic confidence interval are obtained. Bayes estimates of SSR are derived under two different loss functions using the Tierney-Kadane's approximation algorithm. In addition, two different bootstrap confidence interva… Show more

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Cited by 4 publications

References 39 publications

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On Estimation of Stress-Strength Reliability with Zero-Inflated Poisson Distribution

Amrin,

Biswas,

Hazarika

et al. 2024

J Indian Soc Probab Stat

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On Estimation of Stress-Strength Reliability with Zero-Inflated Poisson Distribution

Amrin,

Biswas,

Hazarika

et al. 2024

J Indian Soc Probab Stat

View full text Add to dashboard Cite

Estimation of the Reliability Function of the Generalized Rayleigh Distribution under Progressive First-Failure Censoring Model

Gong,

Chen,

Ren

et al. 2024

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This study investigates the statistical inference of the parameters, reliability function, and hazard function of the generalized Rayleigh distribution under progressive first-failure censoring samples, considering factors such as long product lifetime and challenging experimental conditions. Firstly, the progressive first-failure model is introduced, and the maximum likelihood estimation for the parameters, reliability function, and hazard function under this model are discussed. For interval estimation, confidence intervals have been constructed for the parameters, reliability function, and hazard function using the bootstrap method. Next, in Bayesian estimation, considering informative priors and non-information priors, the Bayesian estimation of the parameters, reliability function, and hazard function under symmetric and asymmetric loss functions is obtained using the MCMC method. Finally, Monte Carlo simulation is conducted to compare mean square errors, evaluating the superiority of the maximum likelihood estimation and Bayesian estimation under different loss functions. The performance of the estimation methods used in the study is illustrated through illustrative examples. The results indicate that Bayesian estimation outperforms maximum likelihood estimation.

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Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an Application

Ramadan,

EL-Sagheer,

Abd-El-Monem

2024

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This paper investigates statistical methods for estimating unknown lifetime parameters using a progressive first-failure censoring dataset. The failure mode’s lifetime distribution is modeled by the odd-generalized-exponential–inverse-Weibull distribution. Maximum-likelihood estimators for the model parameters, including the survival, hazard, and inverse hazard rate functions, are obtained, though they lack closed-form expressions. The Newton–Raphson method is used to compute these estimations. Confidence intervals for the parameters are approximated via the normal distribution of the maximum-likelihood estimation. The Fisher information matrix is derived using the missing information principle, and the delta method is applied to approximate the confidence intervals for the survival, hazard rate, and inverse hazard rate functions. Bayes estimators were calculated with the squared error, linear exponential, and general entropy loss functions, utilizing independent gamma distributions for informative priors. Markov-chain Monte Carlo sampling provides the highest-posterior-density credible intervals and Bayesian point estimates for the parameters and reliability characteristics. This study evaluates these methods through Monte Carlo simulations, comparing Bayes and maximum-likelihood estimates based on mean squared errors for point estimates, average interval widths, and coverage probabilities for interval estimators. A real dataset is also analyzed to illustrate the proposed methods.

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Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

Cited by 4 publications

References 39 publications

On Estimation of Stress-Strength Reliability with Zero-Inflated Poisson Distribution

On Estimation of Stress-Strength Reliability with Zero-Inflated Poisson Distribution

Estimation of the Reliability Function of the Generalized Rayleigh Distribution under Progressive First-Failure Censoring Model

Estimating the Lifetime Parameters of the Odd-Generalized-Exponential–Inverse-Weibull Distribution Using Progressive First-Failure Censoring: A Methodology with an Application

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