{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T18:04:36Z","timestamp":1774980276586,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T00:00:00Z","timestamp":1750291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2025R745"],"award-info":[{"award-number":["PNURSP2025R745"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In lifetime testing, the failure times of highly reliable products under normal usage conditions are often impractically long, making direct reliability assessment impractical. To overcome this, step-stress partially accelerated life testing is employed to reduce testing time while preserving data quality. This paper develops a Bayesian model based on Type II censored data, assuming that item lifetimes follow the Topp\u2013Leone inverted Kumaraswamy distribution, a flexible alternative to classical lifetime models due to its ability to capture various hazard rate shapes and to model bounded and skewed lifetime data more effectively than traditional models observed in real-world reliability data. Bayes estimators of the model parameters and acceleration factor are derived under both symmetric (balanced squared error) and asymmetric (balanced linear exponential) loss functions using informative priors. The novelty of this work lies in the integration of the Topp\u2013Leone inverted Kumaraswamy distribution within the Bayesian step-stress partially accelerated life testing framework, which has not been explored previously, offering improved modeling capability for complex lifetime data. The proposed method is validated through comprehensive simulation studies under various censoring schemes, demonstrating robustness and superior estimation performance compared to traditional models. A real-data application involving COVID-19 mortality data further illustrates the practical relevance and improved fit of the model. Overall, the results highlight the flexibility, efficiency, and applicability of the proposed Bayesian approach in reliability analysis.<\/jats:p>","DOI":"10.3390\/axioms14060476","type":"journal-article","created":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T09:57:48Z","timestamp":1750327068000},"page":"476","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Bayesian Approach to Step-Stress Partially Accelerated Life Testing for a Novel Lifetime Distribution"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0646-9443","authenticated-orcid":false,"given":"Mervat K.","family":"Abd Elaal","sequence":"first","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, Al-Azhar University, (Girls\u2019 Branch), Cairo 11751, Egypt"},{"name":"Canal High Institute of Engineering and Technology, Suez 43511, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7017-8336","authenticated-orcid":false,"given":"Hebatalla H.","family":"Mohammad","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7040-5623","authenticated-orcid":false,"given":"Zakiah I.","family":"Kalantan","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"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 11751, Egypt"},{"name":"Higher Institute of Marketing, Commerce & Information Systems (MCI), Cairo 11511, Egypt"}]},{"given":"Gannat R.","family":"AL-Dayian","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, Al-Azhar University, (Girls\u2019 Branch), Cairo 11751, Egypt"}]},{"given":"Sara M.","family":"Behairy","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, Al-Azhar University, (Girls\u2019 Branch), Cairo 11751, Egypt"}]},{"given":"Reda M.","family":"Refaey","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Commerce, Al-Azhar University, (Girls\u2019 Branch), Cairo 11751, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1080\/00401706.1962.10490020","article-title":"Optimal accelerated life designs for estimation","volume":"4","author":"Chernoff","year":"1962","journal-title":"Technometrics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1080\/00401706.1962.10490019","article-title":"An optimal sequential accelerated life test","volume":"4","author":"Bessler","year":"1962","journal-title":"Technometrics"},{"key":"ref_3","first-page":"722","article-title":"Constant and step-stress accelerated life test of VFD under Weibull distribution case","volume":"7","author":"Zhang","year":"2005","journal-title":"J. Zhejiang Univ. Sci. B"},{"key":"ref_4","first-page":"1227","article-title":"Unbiased estimations for the exponential distribution based on step-stress accelerated life testing data","volume":"173","author":"Wang","year":"2006","journal-title":"Appl. Math. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4172","DOI":"10.1016\/j.jspi.2008.03.036","article-title":"Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type II censoring","volume":"138","author":"Balakrishnan","year":"2008","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2706","DOI":"10.1016\/j.jspi.2010.03.033","article-title":"Interval estimation for exponential progressive Type-II censored step-stress accelerated life-testing","volume":"140","author":"Wang","year":"2010","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1496","DOI":"10.9734\/BJMCS\/2014\/7560","article-title":"Statistical inference for a simple step-stress model based on censored data from Kumaraswamy Weibull distribution","volume":"4","author":"Rezk","year":"2014","journal-title":"Br. J. Math. Comput. Sci."},{"key":"ref_8","first-page":"1","article-title":"Optimizing the simple step stress accelerated life test with Fr\u00e9chet data","volume":"15","author":"Hakamipour","year":"2017","journal-title":"Revstat. Stat. J."},{"key":"ref_9","first-page":"629","article-title":"On step-stress accelerated life testing for power generalized Weibull distribution under progressive Type II censoring","volume":"8","year":"2020","journal-title":"Ann. Data Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1080\/00949650701447084","article-title":"Step partially accelerated life tests under finite mixture models","volume":"78","year":"2008","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_11","first-page":"1509","article-title":"Optimal planning of failure-step stress partially accelerated life tests under Type II censoring","volume":"3","author":"Ismail","year":"2009","journal-title":"Int. J. Math. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4021","DOI":"10.5897\/SRE10.1060","article-title":"Planning step-stress life tests with Type II censored data","volume":"6","author":"Ismail","year":"2011","journal-title":"Sci. Res. Essays"},{"key":"ref_13","first-page":"2097581","article-title":"Bayesian inference for step-stress partially accelerated competing failure model under Type II progressive censoring","volume":"2016","author":"Shi","year":"2016","journal-title":"Math. Probl. Eng. Copy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"225","DOI":"10.12988\/ijcms.2017.7725","article-title":"Estimating costs of maintenance service policy using step stress partially accelerated life testing for the extension of exponential distribution under Type II censoring","volume":"12","year":"2017","journal-title":"Int. J. Contemp. Math. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"137","DOI":"10.18576\/jsap\/070113","article-title":"Estimating the modified Weibull parameters in presence of step-stress partially accelerated life testing","volume":"7","author":"Mahmoud","year":"2018","journal-title":"J. Stat. Appl. Prob."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1016\/j.aej.2020.01.022","article-title":"Estimations with step-stress partially accelerated life tests for competing risks Burr XII lifetime model under Type-II censored data","volume":"59","author":"Aljohani","year":"2020","journal-title":"Alex Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"147","DOI":"10.18576\/amis\/150206","article-title":"Multiply censored partially accelerated life testing for power function model","volume":"15","author":"Lone","year":"2021","journal-title":"Appl. Math. Inf. Sci."},{"key":"ref_18","first-page":"1","article-title":"Maximum likelihood estimation based on step stress-partially accelerated life testing for Topp Leone-inverted Kumaraswamy distribution","volume":"4","author":"Behairy","year":"2024","journal-title":"J. Econom. Stat."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"113067","DOI":"10.1016\/j.asoc.2025.113067","article-title":"Strategic integration of adaptive sampling and ensemble techniques in federated learning for aircraft engine remaining useful life prediction","volume":"175","author":"Xu","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1080\/24725854.2024.2389538","article-title":"A multivariate student-t process model for dependent tail-weighted degradation data","volume":"57","author":"Xu","year":"2024","journal-title":"IISE Trans."},{"key":"ref_21","first-page":"93","article-title":"Topp Leone-inverted Kumaraswamy distribution: Properties, estimation and prediction","volume":"15","author":"Behairy","year":"2020","journal-title":"J. Appl. Probab. Stat."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Behairy, S.M., Refaey, R.M., AL-Dayian, G.R., and EL-Helbawy, A.A. (2020, January 9\u201311). Estimation and prediction based on constant stress-partially accelerated life testing for Topp Leone-inverted Kumaraswamy distribution. Proceedings of the 54th Annual Conference on Statistics, Computer Sciences and Operation Research, Giza, Egypt.","DOI":"10.9734\/jamcs\/2021\/v36i330344"},{"key":"ref_23","first-page":"11","article-title":"Bayesian estimation and prediction based on constant stress-partially accelerated life testing for Topp Leone-inverted Kumaraswamy distribution","volume":"36","author":"Refaey","year":"2021","journal-title":"J. Adv. Math. Comput. Sci."},{"key":"ref_24","first-page":"003","article-title":"The important role of Bayesian statistics in the decision making process and management of insurance companies","volume":"8","author":"Pinda","year":"2013","journal-title":"Manag. Inf. Syst."},{"key":"ref_25","unstructured":"Berger, J.O., and Gupta, S.S. (1994). Bayesian and non-Bayesian estimation using balanced loss functions. Statistical Decision Theory and Methods, Springer."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/j.spl.2005.10.026","article-title":"On estimation with weighted balanced-Type loss function","volume":"76","author":"Jozani","year":"2006","journal-title":"Stat. Probab. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1180","DOI":"10.1016\/j.jspi.2008.07.008","article-title":"Bayes estimation based on k-record data from a general class of distributions under balanced type loss functions","volume":"139","author":"Ahmadi","year":"2009","journal-title":"J. Stat. Plan. Infer."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"28","DOI":"10.4236\/ojs.2012.21004","article-title":"Estimation under a finite mixture of exponentiated exponential components model and balanced square error loss","volume":"2","author":"Hussein","year":"2012","journal-title":"Open J. Stat."},{"key":"ref_29","first-page":"431541","article-title":"On parameters estimation of Lomax distribution under general progressive censoring","volume":"2013","year":"2013","journal-title":"J. Qual. Reliab. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"323","DOI":"10.4236\/ojs.2017.72024","article-title":"Inference on constant-partially accelerated life tests for mixture of Pareto distributions under progressive Type-II censoring","volume":"7","author":"Abushal","year":"2017","journal-title":"Open J. Stat."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"223","DOI":"10.2307\/3318737","article-title":"An adaptive Metropolis algorithm","volume":"7","author":"Haario","year":"2001","journal-title":"Bernoulli"},{"key":"ref_32","first-page":"537","article-title":"The Topp-Leone generator of distributions: Properties and inferences","volume":"38","author":"Sangsanit","year":"2016","journal-title":"Songklanakarin J. Sci. Technol."},{"key":"ref_33","unstructured":"Murthy, D.N.P., Xie, M., and Jiang, R. (2004). Weibull Models, John Wiley and Sons, Inc."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1080\/00401706.1973.10489124","article-title":"Discrimination between the log-normal and the Weibull distributions","volume":"15","author":"Dumonceaux","year":"1973","journal-title":"Technometrics"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/6\/476\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:55:10Z","timestamp":1760032510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/6\/476"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,19]]},"references-count":34,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["axioms14060476"],"URL":"https:\/\/doi.org\/10.3390\/axioms14060476","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,19]]}}}