Inference of fuzzy reliability model for inverse Rayleigh distribution
In this paper, the question of inference of the reliability parameter of fuzzy stress strength R-F = P (Y < X) is attached to the difference between stress and strength values when X and Y are independently distributed from inverse Rayleigh random variables. Including fuzziness in the stress-stre...
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| Veröffentlicht in: | AIMS Mathematics 2021-01, Vol.6 (9), p.9770-9785 |
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| creator | Sabry, Mohamed A. H. Almetwally, Ehab M. Alamri, Osama Abdulaziz Yusuf, M. Almongy, Hisham M. Eldeeb, Ahmed Sedky |
| description | In this paper, the question of inference of the reliability parameter of fuzzy stress strength R-F = P (Y < X) is attached to the difference between stress and strength values when X and Y are independently distributed from inverse Rayleigh random variables. Including fuzziness in the stress-strength interference enables researchers to make more sensitive and precise analyses about the underlying systems. The maximum product of the spacing method for the reliability of fuzzy stress intensity inference has been introduced. As classical estimation methods and Bayesian estimation methods are used to estimate the reliability parameter R-F , the maximum product of spacing and maximum likelihood estimation methods is used. The maximum product of spacing under fuzzy reliability of stress strength model is introducing in this paper. Markov Chain Monte Carlo approach is used to obtain Bayesian estimators of traditional and fuzzy reliability of stress strength for inverse Rayleigh model by using the Metropolis-Hastings algorithm. Using an extensive Monte Carlo simulation analysis, the outputs of the fuzzy reliability and traditional reliability estimators are contrasted. Finally, for example, and to verify the efficiency of the proposed estimators, a genuine data application is used. |
| doi_str_mv | 10.3934/math.2021568 |
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H. ; Almetwally, Ehab M. ; Alamri, Osama Abdulaziz ; Yusuf, M. ; Almongy, Hisham M. ; Eldeeb, Ahmed Sedky ; Faculty of Commerce, Mansoura University, Mansoura 35516, Egypt ; Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt ; Department of Statistics, Mathematics and Insurance, Alexandria University, Egypt ; Faculty of Business Administration, Delta University for Science and Technology, Mansoura 11152, Egypt ; Statistics Department, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia ; Mathematics Department, Helwan University, Egypt ; Department of Business Administration, College of Business, King Khaled University, Saudi Arabia</creatorcontrib><description>In this paper, the question of inference of the reliability parameter of fuzzy stress strength R-F = P (Y < X) is attached to the difference between stress and strength values when X and Y are independently distributed from inverse Rayleigh random variables. 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H.</creatorcontrib><creatorcontrib>Almetwally, Ehab M.</creatorcontrib><creatorcontrib>Alamri, Osama Abdulaziz</creatorcontrib><creatorcontrib>Yusuf, M.</creatorcontrib><creatorcontrib>Almongy, Hisham M.</creatorcontrib><creatorcontrib>Eldeeb, Ahmed Sedky</creatorcontrib><creatorcontrib>Faculty of Commerce, Mansoura University, Mansoura 35516, Egypt</creatorcontrib><creatorcontrib>Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt</creatorcontrib><creatorcontrib>Department of Statistics, Mathematics and Insurance, Alexandria University, Egypt</creatorcontrib><creatorcontrib>Faculty of Business Administration, Delta University for Science and Technology, Mansoura 11152, Egypt</creatorcontrib><creatorcontrib>Statistics Department, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia</creatorcontrib><creatorcontrib>Mathematics Department, Helwan University, Egypt</creatorcontrib><creatorcontrib>Department of Business Administration, College of Business, King Khaled University, Saudi Arabia</creatorcontrib><title>Inference of fuzzy reliability model for inverse Rayleigh distribution</title><title>AIMS Mathematics</title><addtitle>AIMS MATH</addtitle><description>In this paper, the question of inference of the reliability parameter of fuzzy stress strength R-F = P (Y < X) is attached to the difference between stress and strength values when X and Y are independently distributed from inverse Rayleigh random variables. Including fuzziness in the stress-strength interference enables researchers to make more sensitive and precise analyses about the underlying systems. The maximum product of the spacing method for the reliability of fuzzy stress intensity inference has been introduced. As classical estimation methods and Bayesian estimation methods are used to estimate the reliability parameter R-F , the maximum product of spacing and maximum likelihood estimation methods is used. The maximum product of spacing under fuzzy reliability of stress strength model is introducing in this paper. Markov Chain Monte Carlo approach is used to obtain Bayesian estimators of traditional and fuzzy reliability of stress strength for inverse Rayleigh model by using the Metropolis-Hastings algorithm. Using an extensive Monte Carlo simulation analysis, the outputs of the fuzzy reliability and traditional reliability estimators are contrasted. Finally, for example, and to verify the efficiency of the proposed estimators, a genuine data application is used.</description><subject>bayesian</subject><subject>fuzzy set</subject><subject>inverse rayleigh distribution</subject><subject>Markov processes</subject><subject>Mathematics</subject><subject>Mathematics, Applied</subject><subject>maximum likelihood</subject><subject>maximum product of spacing</subject><subject>Monte Carlo method</subject><subject>Physical Sciences</subject><subject>reliability stress-strength</subject><subject>Science & Technology</subject><issn>2473-6988</issn><issn>2473-6988</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>HGBXW</sourceid><sourceid>DOA</sourceid><recordid>eNqNkU9LAzEQxRdRUGpvfoC9a2uSyW42x1L8UygIouclyU5qZLuRbKq0n96sW8SjzGGG4fdewrwsu6JkDhL47VbFtzkjjBZldZJdMC5gVsqqOv0zn2fTvn8nJFGMM8EvsvtVZzFgZzD3Nre7w2GfB2yd0q51cZ9vfYNtbn3IXfeJocf8We1bdJu3vHF9DE7vovPdZXZmVdvj9Ngn2ev93cvycbZ-elgtF-uZAVHFmQIjiSlANwBQGc2RiMIQxYREVNLIsjCcMgFoNBEUCxRIqGFJRwyjGibZavRtvHqvP4LbqrCvvXL1z8KHTa1CdKbFWhOwJW-I5I3kpQUlYXhCa0tLqSwkr_notVEJd531MSiTqsGtM75D69J-UUqgRUUpT4KbUWCC7_uA9vcDlNRDBvWQQX3MIOHXI_6F2tveuOHKv5IUQmI4rUSaaJno6v_00kU1nH3pd12Eb6M0m20</recordid><startdate>20210101</startdate><enddate>20210101</enddate><creator>Sabry, Mohamed A. 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H. ; Almetwally, Ehab M. ; Alamri, Osama Abdulaziz ; Yusuf, M. ; Almongy, Hisham M. ; Eldeeb, Ahmed Sedky</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c378t-a3c90c53bd3338cb4e075c0a279eea9c965c41273ecb071e5e7e01c2a3c0c21b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>bayesian</topic><topic>fuzzy set</topic><topic>inverse rayleigh distribution</topic><topic>Markov processes</topic><topic>Mathematics</topic><topic>Mathematics, Applied</topic><topic>maximum likelihood</topic><topic>maximum product of spacing</topic><topic>Monte Carlo method</topic><topic>Physical Sciences</topic><topic>reliability stress-strength</topic><topic>Science & Technology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sabry, Mohamed A. H.</creatorcontrib><creatorcontrib>Almetwally, Ehab M.</creatorcontrib><creatorcontrib>Alamri, Osama Abdulaziz</creatorcontrib><creatorcontrib>Yusuf, M.</creatorcontrib><creatorcontrib>Almongy, Hisham M.</creatorcontrib><creatorcontrib>Eldeeb, Ahmed Sedky</creatorcontrib><creatorcontrib>Faculty of Commerce, Mansoura University, Mansoura 35516, Egypt</creatorcontrib><creatorcontrib>Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt</creatorcontrib><creatorcontrib>Department of Statistics, Mathematics and Insurance, Alexandria University, Egypt</creatorcontrib><creatorcontrib>Faculty of Business Administration, Delta University for Science and Technology, Mansoura 11152, Egypt</creatorcontrib><creatorcontrib>Statistics Department, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia</creatorcontrib><creatorcontrib>Mathematics Department, Helwan University, Egypt</creatorcontrib><creatorcontrib>Department of Business Administration, College of Business, King Khaled University, Saudi Arabia</creatorcontrib><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>Web of Science - Science Citation Index Expanded - 2021</collection><collection>CrossRef</collection><collection>Gale Academic OneFile</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>AIMS Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sabry, Mohamed A. H.</au><au>Almetwally, Ehab M.</au><au>Alamri, Osama Abdulaziz</au><au>Yusuf, M.</au><au>Almongy, Hisham M.</au><au>Eldeeb, Ahmed Sedky</au><aucorp>Faculty of Commerce, Mansoura University, Mansoura 35516, Egypt</aucorp><aucorp>Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt</aucorp><aucorp>Department of Statistics, Mathematics and Insurance, Alexandria University, Egypt</aucorp><aucorp>Faculty of Business Administration, Delta University for Science and Technology, Mansoura 11152, Egypt</aucorp><aucorp>Statistics Department, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia</aucorp><aucorp>Mathematics Department, Helwan University, Egypt</aucorp><aucorp>Department of Business Administration, College of Business, King Khaled University, Saudi Arabia</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Inference of fuzzy reliability model for inverse Rayleigh distribution</atitle><jtitle>AIMS Mathematics</jtitle><stitle>AIMS MATH</stitle><date>2021-01-01</date><risdate>2021</risdate><volume>6</volume><issue>9</issue><spage>9770</spage><epage>9785</epage><pages>9770-9785</pages><issn>2473-6988</issn><eissn>2473-6988</eissn><abstract>In this paper, the question of inference of the reliability parameter of fuzzy stress strength R-F = P (Y < X) is attached to the difference between stress and strength values when X and Y are independently distributed from inverse Rayleigh random variables. Including fuzziness in the stress-strength interference enables researchers to make more sensitive and precise analyses about the underlying systems. The maximum product of the spacing method for the reliability of fuzzy stress intensity inference has been introduced. As classical estimation methods and Bayesian estimation methods are used to estimate the reliability parameter R-F , the maximum product of spacing and maximum likelihood estimation methods is used. The maximum product of spacing under fuzzy reliability of stress strength model is introducing in this paper. Markov Chain Monte Carlo approach is used to obtain Bayesian estimators of traditional and fuzzy reliability of stress strength for inverse Rayleigh model by using the Metropolis-Hastings algorithm. Using an extensive Monte Carlo simulation analysis, the outputs of the fuzzy reliability and traditional reliability estimators are contrasted. 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| subjects | bayesian fuzzy set inverse rayleigh distribution Markov processes Mathematics Mathematics, Applied maximum likelihood maximum product of spacing Monte Carlo method Physical Sciences reliability stress-strength Science & Technology |
| title | Inference of fuzzy reliability model for inverse Rayleigh distribution |
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