{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T09:25:26Z","timestamp":1769851526731,"version":"3.49.0"},"reference-count":45,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T00:00:00Z","timestamp":1680825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Prince Sattam bin Abdulaziz University","award":["PNURSP2023R443"],"award-info":[{"award-number":["PNURSP2023R443"]}]},{"name":"Prince Sattam bin Abdulaziz University","award":["PSAU\/2023\/R\/1444"],"award-info":[{"award-number":["PSAU\/2023\/R\/1444"]}]},{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia and Prince Sattam bin Abdulaziz University","award":["PNURSP2023R443"],"award-info":[{"award-number":["PNURSP2023R443"]}]},{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia and Prince Sattam bin Abdulaziz University","award":["PSAU\/2023\/R\/1444"],"award-info":[{"award-number":["PSAU\/2023\/R\/1444"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is agreed by industry experts that manufacturing processes are evaluated using quantitative indicators of units produced from this process. For example, the Cpy process capability index is usually unknown and therefore estimated based on a sample drawn from the requested process. In this paper, Cpy process capability index estimates were generated using two iterative methods and a Bayesian method of estimation based on stepwise controlled type II data from the Pareto model. In iterative methods, besides the traditional probability-based estimation, there are other competitive methods, known as bootstrap, which are alternative methods to the common probability method, especially in small samples. In the Bayesian method, we have applied the Gibbs sampling procedure with the help of the significant sampling technique. Moreover, the approximate and highest confidence intervals for the posterior intensity of Cpy were also obtained. Massive simulation studies have been performed to evaluate the behavior of Cpy. Ultimately, application to real-life data is seen to demonstrate the proposed methodology and its applicability.<\/jats:p>","DOI":"10.3390\/sym15040879","type":"journal-article","created":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T03:49:29Z","timestamp":1681098569000},"page":"879","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["The Process Capability Index of Pareto Model under Progressive Type-II Censoring: Various Bayesian and Bootstrap Algorithms for Asymmetric Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7828-3536","authenticated-orcid":false,"given":"Rashad M.","family":"EL-Sagheer","sequence":"first","affiliation":[{"name":"Mathematics Department, Faculty of Science, Al-Azhar University, Naser City 11884, Egypt"},{"name":"High Institute of Computer and Management Information System, First Statement, New Cairo 11865, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"Mahmoud","family":"El-Morshedy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2788-8946","authenticated-orcid":false,"given":"Laila A.","family":"Al-Essa","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khaled M.","family":"Alqahtani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5619-210X","authenticated-orcid":false,"given":"Mohamed S.","family":"Eliwa","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"},{"name":"Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,7]]},"reference":[{"key":"ref_1","unstructured":"Montgomery, D.C. 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