On reliability estimation p (X1 < Y < X2) following Rayleigh-Pareto distribution in stress-strength model
In this paper, the reliability system R = P(X1 < Y < X2), of the stress-strength model was derived having strength (Y) subject to two stresses X1 and X2 follows the two parameters Rayleigh - Pareto distribution such as δ (scale) known and λ (shape) unknown parameters. We estimate the reliabili...
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| Published in | AIP conference proceedings Vol. 2394; no. 1 |
|---|---|
| Main Authors | , |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
Melville
American Institute of Physics
08.11.2022
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0094-243X 1551-7616 |
| DOI | 10.1063/5.0128655 |
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| Abstract | In this paper, the reliability system R = P(X1 < Y < X2), of the stress-strength model was derived having strength (Y) subject to two stresses X1 and X2 follows the two parameters Rayleigh - Pareto distribution such as δ (scale) known and λ (shape) unknown parameters. We estimate the reliability function by using three estimation methods as maximum likelihood (ML), Percentile estimation (PE), and two shrinkage methods such that Shrinkage weight Estimator (SMW), and Shrinkage Function Estimator (SMF). To obtain the best estimate of the reliability function by using the Monte Carlo method depend on mean square error (MSE) criteria. The comparison showed that the (SMW) method is the best among the other methods. |
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| AbstractList | In this paper, the reliability system R = P(X1 < Y < X2), of the stress-strength model was derived having strength (Y) subject to two stresses X1 and X2 follows the two parameters Rayleigh - Pareto distribution such as δ (scale) known and λ (shape) unknown parameters. We estimate the reliability function by using three estimation methods as maximum likelihood (ML), Percentile estimation (PE), and two shrinkage methods such that Shrinkage weight Estimator (SMW), and Shrinkage Function Estimator (SMF). To obtain the best estimate of the reliability function by using the Monte Carlo method depend on mean square error (MSE) criteria. The comparison showed that the (SMW) method is the best among the other methods. |
| Author | Haddad, Emad Sh. M. Batah, Feras Sh. M. |
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| Editor | Mohammed, Mohammed Ahmed |
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| References | Chandra, Owen (c4) 1975 Patowary, Sriwastav, Hazarika (c12) 2016; 12 Birnbaum (c2) 1956; I Birnbaum, McCarty (c3) 1958 Kao (c10) 1958 Singh (c5) 1980 Jyothi (c7) 2019 Jebeli, Deiri (c13) 2019; 54 Kao (c8) 1958 Al-Joboori (c11) 2014; 38 Kundu, Gupta (c9) 2006 |
| References_xml | – start-page: 15 year: 1958 ident: c8 article-title: computer methods for estimating weibull Parameters in Reliability studies publication-title: transaction of IRE-Reliability and Quality control – start-page: 31 year: 1975 ident: c4 article-title: On estimating the reliability of a component subject to several different stresses (strengths) publication-title: Naval Research Logistics Quarterly – volume: 54 start-page: 1 year: 2019 ident: c13 article-title: Estimation Methods For The Probability Density Function and The Cumulative Distribution Function of The Pareto – Rayleigh Distribution publication-title: Statistics: A Journal of Theoretical and Applied Statistics – volume: I start-page: 13 year: 1956 ident: c2 article-title: On a use of the Mann-Whitney statistic publication-title: proceedings of the third Berkeley symposium on mathematical statistics and probability – volume: 12 start-page: 18 year: 2016 ident: c12 article-title: Inference of R=P(X<Y<Z) For n-Stand by System: A Monte Carlo Simulation Approach publication-title: Journal of Mathematics. – start-page: 2053 year: 2019 ident: c7 article-title: Reliability Computation of System Reliability for the New Rayleigh Pareto Distribution publication-title: International Journal of Science and Research (IJSR) – start-page: 270 year: 2006 ident: c9 article-title: Estimation of P(Y<X) for Weibull distribution publication-title: IEEE Transactions on Reliability – start-page: 15 year: 1958 ident: c10 article-title: Computer Methods for Estimating Weibull Parameters in Reliability Studies publication-title: IRE-Reliability and Quality control – start-page: 1551 year: 1980 ident: c5 article-title: On the estimation of p(X <Y< X ) publication-title: Communication in Statistics Theory & Methods – volume: 38 start-page: 1127 year: 2014 ident: c11 article-title: Single and Double Stage Shrinkage Estimators for the Normal Mean with the Variance Cases publication-title: International Journal of statistics – start-page: 557 year: 1958 ident: c3 article-title: distribution free upper confidence bound for Pr (Y<X), based on independent samples of X and Y publication-title: Annals of Mathematical Statistics |
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| Snippet | In this paper, the reliability system R = P(X1 < Y < X2), of the stress-strength model was derived having strength (Y) subject to two stresses X1 and X2... |
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| SubjectTerms | Mathematical models Maximum likelihood estimation Monte Carlo simulation Parameter estimation |
| Title | On reliability estimation p (X1 < Y < X2) following Rayleigh-Pareto distribution in stress-strength model |
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