Stress–Strength Reliability for the Generalized Inverted Exponential Distribution Using MRSS

Hassan, Amal S.; Al-Omari, Amer Ibrahim; Nagy, Heba F.

doi:10.1007/s40995-020-01033-9

Cited by 29 publications

(11 citation statements)

References 23 publications

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“…Many authors have recently used likelihood and Bayesian estimation approaches to estimate R = P ( Y < X = x ) for various life testing schemes based on various distributions [ 25 – 31 ].…”

Section: Stress-strength Reliability Computationsmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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A two-parameter continuous distribution, namely, power-modified Lindley (PML), is proposed. Various structural properties of the new distribution, including moments, moment-generating function, conditional moments, mean deviations, mean residual lifetime, and mean past lifetime, are provided. The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent. Maximum-likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Bayesian estimation methods of the parameters with independent gamma prior are discussed based on symmetric and asymmetric loss functions. We proposed using the MCMC technique with the Metropolis–Hastings algorithm to approximate the posteriors of the stress-strength parameters for Bayesian calculations. The confidence interval for likelihood and the Bayesian estimation method is obtained for the parameter of the model and stress-strength reliability. We prove empirically the importance and flexibility of the new distribution in modeling with real data applications.

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Section: Stress-strength Reliability Computationsmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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“…Studies about the GIE distribution were discussed by several researchers (for instance see [31][32][33][34][35]). Note that for , the CDF (Equation ( 3)) reduces to the IE distribution.…”

Section: Model Specification and The Reliability Of The Structurementioning

confidence: 99%

Reliability Estimation in Multicomponent Stress-Strength for Generalized Inverted Exponential Distribution Based on Ranked Set Sampling

Soliman

Nagy

2022

Gazi University Journal of Science

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“…The two data sets were first published by Bader and Priest [ 37 ]; and they reflected the GPA strength of single carbon fibers with lengths of 10 mm (Data Set I) and 10 mm (Data Set II), respectively, with sample sizes of n = 63 and m = 69. These data were analyzed previously by Hassan et al [ 38 ]. The following are the data sets: Data Set I (length of 10 mm): X ( n = 63): “1.901, 2.132, 2.203, 2.228, 2.257, 2.350, 2.361, 2.396, 2.397, 2.445, 2.454, 2.474, 2.518, 2.522, 2.525, 2.532, 2.575, 2.614, 2.616, 2.618, 2.624, 2.659, 2.675, 2.738, 2.740, 2.856, 2.917, 2.928, 2.937, 2.937, 2.977, 2.996, 3.030, 3.125, 3.139, 3.145, 3.220, 3.223, 3.235, 3.243, 3.264, 3.272, 3.294, 3.332, 3.346, 3.377, 3.408, 3.435, 3.493, 3.501, 3.537, 3.554, 3.562, 3.628, 3.852, 3.871, 3.886, 3.971, 4.024, 4.027, 4.225, 4.395, 5.020.” Data Set II (length of 20 mm): Y ( m = 69): “1.312, 1.314, 1.479, 1.552, 1.700, 1.803, 1.861, 1.865, 1.944, 1.958, 1.966, 1.997, 2.006, 2.021, 2.027, 2.055, 2.063, 2.098, 2.14, 2.179, 2.224, 2.240, 2.253, 2.270, 2.272, 2.274, 2.301, 2.301, 2.359, 2.382, 2.382, 2.426, 2.434, 2.435, 2.478, 2.490, 2.511, 2.514, 2.535, 2.554, 2.566, 2.57, 2.586, 2.629, 2.633, 2.642, 2.648, 2.684, 2.697, 2.726, 2.770, 2.773, 2.800, 2.809, 2.818, 2.821, 2.848, 2.88, 2.954, 3.012, 3.067, 3.084, 3.090, 3.096, 3.128, 3.233, 3.433, 3.585, 3.585.” …”

Section: Application Of Real Datamentioning

confidence: 99%

Stress‐Strength Reliability for Exponentiated Inverted Weibull Distribution with Application on Breaking of Jute Fiber and Carbon Fibers

Azm

Almetwally

Alghamdi

et al. 2021

Computational Intelligence and Neuroscience

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For the first time and by using an entire sample, we discussed the estimation of the unknown parameters θ 1 , θ 2 , and β and the system of stress-strength reliability R = P Y < X for exponentiated inverted Weibull (EIW) distributions with an equivalent scale parameter supported eight methods. We will use maximum likelihood method, maximum product of spacing estimation (MPSE), minimum spacing absolute-log distance estimation (MSALDE), least square estimation (LSE), weighted least square estimation (WLSE), method of Cramér-von Mises estimation (CME), and Anderson-Darling estimation (ADE) when X and Y are two independent a scaled exponentiated inverted Weibull (EIW) distribution. Percentile bootstrap and bias-corrected percentile bootstrap confidence intervals are introduced. To pick the better method of estimation, we used the Monte Carlo simulation study for comparing the efficiency of the various estimators suggested using mean square error and interval length criterion. From cases of samples, we discovered that the results of the maximum product of spacing method are more competitive than those of the other methods. A two real‐life data sets are represented demonstrating how the applicability of the methodologies proposed in real phenomena.

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Stress–Strength Reliability for the Generalized Inverted Exponential Distribution Using MRSS

Cited by 29 publications

References 23 publications

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Reliability Estimation in Multicomponent Stress-Strength for Generalized Inverted Exponential Distribution Based on Ranked Set Sampling

Stress‐Strength Reliability for Exponentiated Inverted Weibull Distribution with Application on Breaking of Jute Fiber and Carbon Fibers

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