{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T22:36:49Z","timestamp":1777502209255,"version":"3.51.4"},"reference-count":54,"publisher":"Wiley","issue":"8","license":[{"start":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T00:00:00Z","timestamp":1753488000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah Bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2025R404"],"award-info":[{"award-number":["PNURSP2025R404"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Quality &amp; Reliability Eng"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>The development of new statistical distributions is essential for modeling complex real\u2010world phenomena, especially when existing models fail to capture skewness, heavy tails, or censoring. This paper introduces the QR distribution, a flexible extension of the one\u2010parameter Ailamujia distribution (AD), designed to model positive data with diverse asymmetry and failure rate behaviors. The study explores the properties of the QR distribution under Type\u2010II censoring (T\u2010II C), a common scenario in resource\u2010constrained experiments. Parameter estimation is conducted using both classical and Bayesian approaches. In Bayesian analysis the Tierney\u2013Kadane (T\u2010K) approximation and Markov Chain Monte Carlo (MCMC) techniques are employed to derive Bayes estimators (BEs). For interval estimation, the study incorporates the percentile Bootstrap method (BootP) and the Bootstrap\u2010T method (BootT) and Bayesian highest posterior density (HPD) intervals, allowing a comprehensive assessment of parameter uncertainty under censored settings. A key application of the proposed QR distribution is demonstrated using real\u2010world aircraft windshield failure data, where the model effectively captures the censored nature and variability of the observed lifetimes. The QR distribution demonstrates superior performance in modeling aircraft windshield failure times compared to existing distributions. Bayesian methods, particularly the T\u2010K approximation under the LINEX\u2010based loss function (LBLF), consistently provide more accurate parameter estimates. Real\u2010data applications confirm the QR distribution's effectiveness in analyzing censored data and reliability problems, establishing it as a robust tool for statistical modeling in diverse\u00a0fields.<\/jats:p>","DOI":"10.1002\/qre.70028","type":"journal-article","created":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T09:20:18Z","timestamp":1753521618000},"page":"3458-3490","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bayesian and Classical Insights into a Novel Probability Model for Aircraft Windshield Failures"],"prefix":"10.1002","volume":"41","author":[{"given":"Kainat","family":"Ashraf","sequence":"first","affiliation":[{"name":"Department of Statistics University of Sargodha Sargodha Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6151-4844","authenticated-orcid":false,"given":"Noureen","family":"Akhtar","sequence":"additional","affiliation":[{"name":"Department of Statistics University of Sargodha Sargodha Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4203-7798","authenticated-orcid":false,"given":"Qasim","family":"Ramzan","sequence":"additional","affiliation":[{"name":"Department of Statistics University of Sargodha Sargodha Pakistan"},{"name":"Department of Statistics Government Graduate College Jauharabad Khushab Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2073-918X","authenticated-orcid":false,"given":"Hafiz Zafar","family":"Nazir","sequence":"additional","affiliation":[{"name":"Department of Statistics University of Sargodha Sargodha Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0776-2652","authenticated-orcid":false,"given":"Tmader","family":"Alballa","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences College of Science Princess Nourah bint Abdulrahman University Riyadh Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,7,26]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1965.10480783"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1969.10500967"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40745-019-00192-w"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.6339\/JDS.201810_16(4).00004"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.3934\/math.2021579"},{"key":"e_1_2_11_7_1","first-page":"48","article-title":"On the Extended Generalized Inverted Kumaraswamy Distribution","volume":"6","author":"Ramzan Q.","year":"2022","journal-title":"Computational Intelligence and Neuroscience"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1080\/02331880801983876"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177731607"},{"key":"e_1_2_11_10_1","first-page":"48","article-title":"Ailamujia Distribution and Its Application in Supportability Data Analysis","volume":"16","author":"Lv H. 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