{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T15:08:46Z","timestamp":1764688126313,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T00:00:00Z","timestamp":1731024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Deanship of Scientific Research, Princess Nourah bint Abdulrahman University","award":["44-PRFA-P-142"],"award-info":[{"award-number":["44-PRFA-P-142"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The Bayesian approach offers a flexible, interpretable and powerful framework for statistical analysis, making it a valuable tool to help in making optimal decisions under uncertainty. It incorporates prior knowledge or beliefs about the parameters, which can lead to more accurate and informative results. Also, it offers credible intervals as a measure of uncertainty, which are often more interpretable than confidence intervals. Hence, the Bayesian approach is utilized to estimate the parameters, reliability function, hazard rate function and reversed hazard rate function of a new competing risks model. A squared error loss function as a symmetric loss function and a linear exponential loss function as an asymmetric loss function are employed to derive the Bayesian estimators. Credible intervals of the parameters, reliability function, hazard rate function and reversed hazard rate function are obtained. Predicting future observations is important in many fields, from finance and weather forecasting to healthcare and engineering. Thus, two-sample prediction (as a special case of the multi-sample prediction) for future observation is considered. An adaptive Metropolis algorithm is applied to conduct a simulation study to evaluate the performance of the Bayes estimates and predictors. Moreover, two applications of medical and engineering data sets are used to test and validate the theoretical results, ensuring that they are accurate, applicable to real-world scenarios and contribute to the understanding of the world and inform decision-making.<\/jats:p>","DOI":"10.3390\/sym16111502","type":"journal-article","created":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T03:53:14Z","timestamp":1731383594000},"page":"1502","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Medical and Engineering Applications for Estimation and Prediction of a New Competing Risks Model: A Bayesian Approach"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7017-8336","authenticated-orcid":false,"given":"Hebatalla H.","family":"Mohammad","sequence":"first","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":"Heba N.","family":"Salem","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Cairo 11651, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3247-2013","authenticated-orcid":false,"given":"Abeer A.","family":"EL-Helbawy","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls\u2019 Branch), Cairo 11651, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0312-8731","authenticated-orcid":false,"given":"Faten S.","family":"Alamri","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"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0951-8320(95)00149-2","article-title":"Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function","volume":"52","author":"Xie","year":"1996","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/S0951-8320(00)00066-1","article-title":"A new model with bathtub-shaped failure rate using an additive Burr XII distribution","volume":"70","author":"Wang","year":"2000","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.ress.2012.10.018","article-title":"A new modified Weibull distribution","volume":"111","author":"Almalki","year":"2013","journal-title":"Reliab. Eng. Syst. 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