Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application
In this study, we look at how to estimate stress–strength reliability models, <i>R</i><sub>1</sub> = P (<i>Y</i> < <i>X</i>) and <i>R</i><sub>2</sub> = P (<i>Y</i> < <i>X</i>), where the strength &l...
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| Format: | Article |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/2/318 |
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| author | Amal S. Hassan Ibrahim M. Almanjahie Amer Ibrahim Al-Omari Loai Alzoubi Heba Fathy Nagy |
| author_facet | Amal S. Hassan Ibrahim M. Almanjahie Amer Ibrahim Al-Omari Loai Alzoubi Heba Fathy Nagy |
| author_sort | Amal S. Hassan |
| collection | DOAJ |
| description | In this study, we look at how to estimate stress–strength reliability models, <i>R</i><sub>1</sub> = P (<i>Y</i> < <i>X</i>) and <i>R</i><sub>2</sub> = P (<i>Y</i> < <i>X</i>), where the strength <i>X</i> and stress <i>Y</i> have the same distribution in the first model, <i>R</i><sub>1</sub>, and strength <i>X</i> and stress <i>Z</i> have different distributions in the second model, <i>R</i><sub>2</sub>. Based on the first model, the stress <i>Y</i> and strength <i>X</i> are assumed to have the Lomax distributions, whereas, in the second model, <i>X</i> and <i>Z</i> are assumed to have both the Lomax and inverse Lomax distributions, respectively. With the assumption that the variables in both models are independent, the median-ranked set sampling (MRSS) strategy is used to look at different possibilities. Using the maximum likelihood technique and an MRSS design, we derive the reliability estimators for both models when the strength and stress variables have a similar or dissimilar set size. The simulation study is used to verify the accuracy of various estimates. In most cases, the simulation results show that the reliability estimates for the second model are more efficient than those for the first model in the case of dissimilar set sizes. However, with identical set sizes, the reliability estimates for the first model are more efficient than the equivalent estimates for the second model. Medical data are used for further illustration, allowing the theoretical conclusions to be verified. |
| first_indexed | 2024-03-09T11:46:43Z |
| format | Article |
| id | doaj.art-a48a16053bcd421bb76f619ec647388e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:46:43Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a48a16053bcd421bb76f619ec647388e2023-11-30T23:20:32ZengMDPI AGMathematics2227-73902023-01-0111231810.3390/math11020318Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and ApplicationAmal S. Hassan0Ibrahim M. Almanjahie1Amer Ibrahim Al-Omari2Loai Alzoubi3Heba Fathy Nagy4Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptDepartment of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Al Albayt University, Mafraq 25113, JordanDepartment of Mathematics, Faculty of Science, Al Albayt University, Mafraq 25113, JordanFaculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, EgyptIn this study, we look at how to estimate stress–strength reliability models, <i>R</i><sub>1</sub> = P (<i>Y</i> < <i>X</i>) and <i>R</i><sub>2</sub> = P (<i>Y</i> < <i>X</i>), where the strength <i>X</i> and stress <i>Y</i> have the same distribution in the first model, <i>R</i><sub>1</sub>, and strength <i>X</i> and stress <i>Z</i> have different distributions in the second model, <i>R</i><sub>2</sub>. Based on the first model, the stress <i>Y</i> and strength <i>X</i> are assumed to have the Lomax distributions, whereas, in the second model, <i>X</i> and <i>Z</i> are assumed to have both the Lomax and inverse Lomax distributions, respectively. With the assumption that the variables in both models are independent, the median-ranked set sampling (MRSS) strategy is used to look at different possibilities. Using the maximum likelihood technique and an MRSS design, we derive the reliability estimators for both models when the strength and stress variables have a similar or dissimilar set size. The simulation study is used to verify the accuracy of various estimates. In most cases, the simulation results show that the reliability estimates for the second model are more efficient than those for the first model in the case of dissimilar set sizes. However, with identical set sizes, the reliability estimates for the first model are more efficient than the equivalent estimates for the second model. Medical data are used for further illustration, allowing the theoretical conclusions to be verified.https://www.mdpi.com/2227-7390/11/2/318Lomax and inverse Lomax distributionsstress–strength modelmaximum likelihood methodmedian ranked set sample |
| spellingShingle | Amal S. Hassan Ibrahim M. Almanjahie Amer Ibrahim Al-Omari Loai Alzoubi Heba Fathy Nagy Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application Mathematics Lomax and inverse Lomax distributions stress–strength model maximum likelihood method median ranked set sample |
| title | Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application |
| title_full | Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application |
| title_fullStr | Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application |
| title_full_unstemmed | Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application |
| title_short | Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application |
| title_sort | stress strength modeling using median ranked set sampling estimation simulation and application |
| topic | Lomax and inverse Lomax distributions stress–strength model maximum likelihood method median ranked set sample |
| url | https://www.mdpi.com/2227-7390/11/2/318 |
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