{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:20:07Z","timestamp":1760149207035,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,16]],"date-time":"2023-07-16T00:00:00Z","timestamp":1689465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","doi-asserted-by":"publisher","award":["PNURSP2023R175"],"award-info":[{"award-number":["PNURSP2023R175"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A new two-parameter weighted-exponential (WE) distribution, as a beneficial competitor model to other lifetime distributions, namely: generalized exponential, gamma, and Weibull distributions, is studied in the presence of adaptive progressive Type-II hybrid data. Thus, based on different frequentist and Bayesian estimation methods, we study the inferential problem of the WE parameters as well as related reliability indices, including survival and failure functions. In frequentist setups, besides the standard likelihood-based estimation, the product of spacing (PS) approach is also taken into account for estimating all unknown parameters of life. Making use of the delta method and the observed Fisher information of the frequentist estimators, approximated asymptotic confidence intervals for all unknown parameters are acquired. In Bayes methodology, from the squared-error loss with independent gamma density priors, the point and interval estimates of the unknown parameters are offered using both joint likelihood and the product of spacings functions. Because a closed solution to the Bayes estimators is not accessible, the Metropolis\u2013Hastings sampler is presented to approximate the Bayes estimates and also to create their associated highest interval posterior density estimates. To figure out the effectiveness of the developed approaches, extensive Monte Carlo experiments are implemented. To highlight the applicability of the offered methodologies in practice, one real-life data set consisting of 30 failure times of repairable mechanical equipment is analyzed. This application demonstrated that the offered WE model provides a better fit compared to the other eight lifetime models.<\/jats:p>","DOI":"10.3390\/axioms12070690","type":"journal-article","created":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T01:06:36Z","timestamp":1689555996000},"page":"690","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Analysis of WE Parameters of Life Using Adaptive-Progressively Type-II Hybrid Censored Mechanical Equipment Data"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9916-259X","authenticated-orcid":false,"given":"Ahmed","family":"Elshahhat","sequence":"first","affiliation":[{"name":"Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3888-1275","authenticated-orcid":false,"given":"Ehab M.","family":"Almetwally","sequence":"additional","affiliation":[{"name":"Faculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6900-8233","authenticated-orcid":false,"given":"Sanku","family":"Dey","sequence":"additional","affiliation":[{"name":"Department of Statistics, St. Anthony\u2019s College, Shillong 793001, Meghalaya, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heba S.","family":"Mohammed","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":[[2023,7,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Balakrishnan, N., and Cramer, E. (2014). The Art of Progressive Censoring, Springer.","DOI":"10.1007\/978-0-8176-4807-7"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1016\/j.csda.2005.05.002","article-title":"Analysis of Type-II progressively hybrid censored data","volume":"50","author":"Kundu","year":"2006","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1002\/nav.20371","article-title":"Statistical analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme","volume":"56","author":"Ng","year":"2009","journal-title":"Nav. Res. Logist."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.1007\/s00180-021-01065-8","article-title":"Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data","volume":"36","author":"Elshahhat","year":"2021","journal-title":"Comput. Stat."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1080\/00949655.2022.2127149","article-title":"Analysis of adaptive Type-II progressively hybrid censoring with binomial removals","volume":"93","author":"Elshahhat","year":"2023","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1111\/j.2517-6161.1983.tb01268.x","article-title":"Estimating parameters in continuous univariate distributions with a shifted origin","volume":"45","author":"Cheng","year":"1983","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_7","first-page":"93","article-title":"The maximum spacing method. An estimation method related to the maximum likelihood method","volume":"11","author":"Ranneby","year":"1984","journal-title":"Scand. J. Stat."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1017\/S0266466605050255","article-title":"An alternative to maximum likelihood based on spacings","volume":"21","author":"Anatolyev","year":"2005","journal-title":"Econom. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"124251","DOI":"10.1016\/j.physa.2020.124251","article-title":"Progressive Type-II hybrid censored schemes based on maximum product spacing with application to Power Lomax distribution","volume":"553","author":"Almetwally","year":"2020","journal-title":"Physica A Stat. Mech. Its Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1080\/02331880802605346","article-title":"A new class of weighted exponential distributions","volume":"43","author":"Gupta","year":"2009","journal-title":"Statistics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3641","DOI":"10.1080\/00949655.2014.992346","article-title":"Weighted exponential distribution: Properties and different methods of estimation","volume":"85","author":"Dey","year":"2015","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1080\/03610918.2012.733471","article-title":"Bayesian statistical inference for weighted exponential distribution","volume":"43","author":"Farahani","year":"2014","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3426","DOI":"10.1080\/00949655.2021.1928128","article-title":"Inference of weighted exponential distribution under progressively Type-II censored competing risks model with electrodes data","volume":"91","author":"Tian","year":"2021","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s00180-010-0217-1","article-title":"maxLik: A package for maximum likelihood estimation in R","volume":"26","author":"Henningsen","year":"2011","journal-title":"Comput. Stat."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lawless, J.F. (2003). Statistical Models and Methods For Lifetime Data, John Wiley and Sons. [2nd ed.].","DOI":"10.1002\/9781118033005"},{"key":"ref_16","unstructured":"Greene, W.H. (2000). Econometric Analysis, Prentice-Hall. [4th ed.]."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2004). Bayesian Data Analysis, Chapman and Hall\/CRC. [2nd ed.].","DOI":"10.1201\/9780429258480"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lynch, S.M. (2007). Introduction to Applied Bayesian Statistics and Estimation for Social Scientists, Springer.","DOI":"10.1007\/978-0-387-71265-9"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1080\/10618600.1999.10474802","article-title":"Monte Carlo estimation of Bayesian credible and HPD intervals","volume":"8","author":"Chen","year":"1999","journal-title":"J. Comput. Graph. Stat."},{"key":"ref_20","first-page":"7","article-title":"CODA: Convergence diagnosis and output analysis for MCMC","volume":"6","author":"Plummer","year":"2006","journal-title":"R News"},{"key":"ref_21","unstructured":"Murthy, D.N.P., Xie, M., and Jiang, R. (2004). Weibull Models, Wiley."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Alotaibi, R., Nassar, M., and Elshahhat, A. (2023). Estimations of modified Lindley parameters using progressive Type-II censoring with applications. Axioms, 12.","DOI":"10.3390\/axioms12020171"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1115\/1.4010337","article-title":"A statistical distribution function of wide applicability","volume":"18","author":"Weibull","year":"1951","journal-title":"J. Appl. Mech."},{"key":"ref_24","unstructured":"Johnson, N., Kotz, S., and Balakrishnan, N. (1994). Continuous Univariate Distributions, John Wiley and Sons. [2nd ed.]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1080\/02331881003678678","article-title":"An extension of the exponential distribution","volume":"45","author":"Nadarajah","year":"2011","journal-title":"Statistics"},{"key":"ref_26","first-page":"133","article-title":"A weighted Nadarajah and Haghighi distribution","volume":"80","author":"Khan","year":"2018","journal-title":"UPB Sci. Bull. Ser. A Appl. Math. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"6543","DOI":"10.1080\/03610926.2015.1130839","article-title":"A new method for generating distributions with an application to exponential distribution","volume":"46","author":"Mahdavi","year":"2017","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.3923\/jas.2015.1305.1311","article-title":"The Weibull-exponential distribution: Its properties and applications","volume":"15","author":"Oguntunde","year":"2015","journal-title":"J. Appl. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1214\/aoms\/1177704481","article-title":"A Generalization of the Gamma Distribution","volume":"33","author":"Stacy","year":"1962","journal-title":"Ann. Math. Stat."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/0304-4076(94)01612-4","article-title":"A generalization of the beta distribution with applications","volume":"66","author":"McDonald","year":"1995","journal-title":"J. Econom."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/690\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:12:50Z","timestamp":1760127170000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/690"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,16]]},"references-count":30,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["axioms12070690"],"URL":"https:\/\/doi.org\/10.3390\/axioms12070690","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,7,16]]}}}