{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T16:57:48Z","timestamp":1780937868523,"version":"3.54.1"},"reference-count":88,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/100012908","name":"Indian Institute of Engineering Science and Technology, Shibpur","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012908","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Reliability Engineering &amp; System Safety"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.ress.2026.112782","type":"journal-article","created":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T23:56:57Z","timestamp":1777161417000},"page":"112782","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P1","title":["Ordering results involving k-out-of-n systems for a flexible Gompertz model with heterogeneity"],"prefix":"10.1016","volume":"275","author":[{"given":"Smaranika","family":"Bera","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruhul Ali","family":"Khan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dhrubasish","family":"Bhattacharyya","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Murari","family":"Mitra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.ress.2026.112782_b1","first-page":"513","article-title":"On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. FRS &c","volume":"115","author":"Gompertz","year":"1825","journal-title":"Philos Trans R Soc Lond"},{"issue":"28","key":"10.1016\/j.ress.2026.112782_b2","doi-asserted-by":"crossref","DOI":"10.1088\/1751-8113\/49\/28\/285002","article-title":"The distribution of path lengths of self avoiding walks on Erd\u0151s\u2013R\u00e9nyi networks","volume":"49","author":"Tishby","year":"2016","journal-title":"J Phys A"},{"issue":"3","key":"10.1016\/j.ress.2026.112782_b3","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.jss.2008.11.840","article-title":"Gompertz software reliability model: Estimation algorithm and empirical validation","volume":"82","author":"Ohishi","year":"2009","journal-title":"J Syst Softw"},{"issue":"5","key":"10.1016\/j.ress.2026.112782_b4","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1287\/mnsc.1110.1461","article-title":"Modeling purchasing behavior with sudden \u201cdeath\u201d: A flexible customer lifetime model","volume":"58","author":"Bemmaor","year":"2012","journal-title":"Manag Sci"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b5","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1078\/1125-7865-00034","article-title":"Application of the Gompertz equation for the study of xylem cell development","volume":"21","author":"Rossi","year":"2003","journal-title":"Dendrochronologia"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b6","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1017\/S1357729800008924","article-title":"Application of the Gompertz model to describe the fermentation characteristics of chemical components in forages","volume":"66","author":"Lavren\u010di\u010d","year":"1998","journal-title":"Anim Sci"},{"key":"10.1016\/j.ress.2026.112782_b7","first-page":"1","article-title":"A generalized Gompertz growth model with applications and related birth-death processes","author":"Asadi","year":"2020","journal-title":"Ric Mat"},{"issue":"1\u20132","key":"10.1016\/j.ress.2026.112782_b8","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.apm.2011.05.017","article-title":"The generalized Gompertz distribution","volume":"37","author":"El-Gohary","year":"2013","journal-title":"Appl Math Model"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b9","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1016\/j.jmaa.2015.02.003","article-title":"On magnitude orderings between smallest order statistics from heterogeneous beta distributions","volume":"426","author":"Torrado","year":"2015","journal-title":"J Math Anal Appl"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b10","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/s11009-017-9562-7","article-title":"Comparisons between largest order statistics from multiple-outlier models with dependence","volume":"20","author":"Navarro","year":"2018","journal-title":"Methodol Comput Appl Probab"},{"key":"10.1016\/j.ress.2026.112782_b11","first-page":"235","article-title":"A new class of bivariate Gompertz distributions and its mixture","volume":"2","author":"Al-Khedhairi","year":"2008","journal-title":"Int J Math Anal (Ruse)"},{"key":"10.1016\/j.ress.2026.112782_b12","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/S0169-7161(01)20005-4","article-title":"Ch. 3. bathtub-shaped failure rate life distributions","volume":"20","author":"Lai","year":"2001","journal-title":"Handbook of Statist"},{"key":"10.1016\/j.ress.2026.112782_b13","series-title":"The use of the Gamma Distribution in Estimating Regulated Output from Storage","author":"Alexander","year":"1961"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b14","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1111\/1467-842X.00072","article-title":"Theory & methods: Generalized exponential distributions","volume":"41","author":"Gupta","year":"1999","journal-title":"Aust N Z J Stat"},{"key":"10.1016\/j.ress.2026.112782_b15","volume":"vol. 115","author":"Bain","year":"1991"},{"key":"10.1016\/j.ress.2026.112782_b16","series-title":"Statistical methods for reliability data","author":"Meeker","year":"2014"},{"key":"10.1016\/j.ress.2026.112782_b17","series-title":"Stochastic orders","author":"Shaked","year":"2007"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b18","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1109\/TNET.2012.2192747","article-title":"A utility maximization framework for fair and efficient multicasting in multicarrier wireless cellular networks","volume":"21","author":"Liu","year":"2012","journal-title":"IEEE\/ACM Trans Netw"},{"issue":"5","key":"10.1016\/j.ress.2026.112782_b19","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1504\/IJEBR.2012.048776","article-title":"Homogenous goods markets: an empirical study of price dispersion on the internet","volume":"4","author":"Warin","year":"2012","journal-title":"Int J Econ Bus Res"},{"key":"10.1016\/j.ress.2026.112782_b20","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.apenergy.2014.05.064","article-title":"Degradation pattern prediction of a polymer electrolyte membrane fuel cell stack with series reliability structure via durability data of single cells","volume":"131","author":"Bae","year":"2014","journal-title":"Appl Energy"},{"key":"10.1016\/j.ress.2026.112782_b21","series-title":"A first course in order statistics","author":"Arnold","year":"2008"},{"key":"10.1016\/j.ress.2026.112782_b22","series-title":"Handbook of statistics. v. 16: Order statistics: theory and methods","author":"Balakrishnan","year":"1998"},{"issue":"4","key":"10.1016\/j.ress.2026.112782_b23","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1017\/S0269964813000156","article-title":"Ordering properties of order statistics from heterogeneous populations: a review with an emphasis on some recent developments","volume":"27","author":"Balakrishnan","year":"2013","journal-title":"Probab Engrg Inform Sci"},{"key":"10.1016\/j.ress.2026.112782_b24","volume":"vol. 297","author":"David","year":"2003"},{"key":"10.1016\/j.ress.2026.112782_b25","article-title":"Reliability analysis of a complex series-parallel performance sharing system with performance excess failure and storage units","author":"Gu","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b26","article-title":"Approximate approaches for reliability evaluation and redundancy allocation for large-scale multi-state series\u2013parallel systems","author":"Zhang","year":"2026","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b27","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.111033","article-title":"Preventive replacement policies of parallel\/series systems with dependent components under deviation costs","volume":"260","author":"Niu","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b28","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.111249","article-title":"Reliability analysis of a capacitated series-parallel multi-state system subject to performance sharing mechanism and transmission loss","volume":"263","author":"Zhang","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b29","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2024.110457","article-title":"An efficient reliability evaluation method for large-scale multi-performance multi-state series-parallel systems considering multi-dimensional approximation","volume":"252","author":"Hu","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b30","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2024.110116","article-title":"Joint optimization of maintenance and spares inventory policy for a series-parallel system considering dependent failure processes","volume":"247","author":"Qi","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b31","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109706","article-title":"A subset simulation analysis framework for rapid reliability evaluation of series-parallel cold standby systems","volume":"241","author":"Lin","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b32","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109604","article-title":"A DNN-based reliability evaluation method for multi-state series-parallel systems considering semi-Markov process","volume":"242","author":"Bo","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b33","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109780","article-title":"Reliability analysis and redundancy optimization of k-out-of-n systems with random variable k using continuous time Markov chain and Monte Carlo simulation","volume":"242","author":"Oszczypa\u0142a","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b34","first-page":"324","article-title":"Reliability assessment of consecutive k-out-of-n systems with two types of dependent components","volume":"238","author":"Ozkut","year":"2024","journal-title":"Proc Inst Mech Eng Part O: J Risk Reliab"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b35","first-page":"58","article-title":"An algorithmic reliability evaluation approach for a multi-state k-out-of-n: G system with nonidentical and large number of components","volume":"237","author":"Kilic","year":"2023","journal-title":"Proc Inst Mech Eng Part O: J Risk Reliab"},{"key":"10.1016\/j.ress.2026.112782_b36","article-title":"Optimal design of k-out-of-n: G system under load redistribution and stochastic mission duration","author":"Mannai","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b37","article-title":"Condition-based maintenance planning for K-out-of-N systems under partial observability","author":"Hu","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b38","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.111484","article-title":"Lifetime analysis of circular k-out-of-n: G balanced systems in a shock environment","volume":"265","author":"Baik","year":"2026","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b39","article-title":"A multi-agent reinforcement learning (MARL) framework for designing an optimal state-specific hybrid maintenance policy for a series k-out-of-n load-sharing system","author":"Zhao","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.112782_b40","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.111291","article-title":"Multi-state k-out-of-n: F network system performance evaluation by considering a balance dependence mechanism","author":"Gao","year":"2025","journal-title":"Reliab Eng Syst Saf"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b41","first-page":"1","article-title":"Modelling of extremal events in insurance and finance","volume":"39","author":"Embrechts","year":"1994","journal-title":"Z Oper Res"},{"issue":"5","key":"10.1016\/j.ress.2026.112782_b42","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1016\/j.orl.2004.09.010","article-title":"A note on expected rent in auction theory","volume":"33","author":"Li","year":"2005","journal-title":"Oper Res Lett"},{"issue":"4","key":"10.1016\/j.ress.2026.112782_b43","doi-asserted-by":"crossref","first-page":"1997","DOI":"10.1007\/s11587-022-00715-3","article-title":"Ordering results between extreme order statistics in models with dependence defined by Archimedean [survival] copulas","volume":"73","author":"Das","year":"2024","journal-title":"Ric di Mat"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b44","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1080\/03610926.2015.1099671","article-title":"Stochastic comparisons of series and parallel systems with independent heterogeneous lower-truncated Weibull components","volume":"45","author":"Fang","year":"2016","journal-title":"Comm Statist Theory Methods"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b45","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1080\/02331888.2025.2552185","article-title":"Ordering results for random maxima and minima from two dependent Kumaraswamy-generalized distributed samples","volume":"60","author":"Das","year":"2026","journal-title":"Statistics"},{"issue":"3","key":"10.1016\/j.ress.2026.112782_b46","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1080\/03461238.2020.1830845","article-title":"Ranking the extreme claim amounts in dependent individual risk models","volume":"2021","author":"Torrado","year":"2021","journal-title":"Scand Actuar J"},{"key":"10.1016\/j.ress.2026.112782_b47","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2024.110604","article-title":"Analyzing component failures in series-parallel systems with dependent components","volume":"197","author":"Torrado","year":"2024","journal-title":"Comput Ind Eng"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b48","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0167-7152(01)00139-0","article-title":"Stochastic comparisons of random minima and maxima from life distributions","volume":"55","author":"Bartoszewicz","year":"2001","journal-title":"Statist Probab Lett"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b49","doi-asserted-by":"crossref","first-page":"420","DOI":"10.2307\/3215381","article-title":"Stochastic comparisons of random minima and maxima","volume":"34","author":"Shaked","year":"1997","journal-title":"J Appl Probab"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b50","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/S0378-3758(97)00058-X","article-title":"Stochastic comparisons of parallel systems of heterogeneous exponential components","volume":"65","author":"Dykstra","year":"1997","journal-title":"J Statist Plann Inference"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b51","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1239\/jap\/1300198149","article-title":"On the skewness of order statistics in multiple-outlier models","volume":"48","author":"Kochar","year":"2011","journal-title":"J Appl Probab"},{"issue":"6","key":"10.1016\/j.ress.2026.112782_b52","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1016\/j.spl.2013.03.002","article-title":"On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components","volume":"83","author":"Misra","year":"2013","journal-title":"Statist Probab Lett"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b53","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1239\/jap\/1429282609","article-title":"Stochastic order relations among parallel systems from Weibull distributions","volume":"52","author":"Torrado","year":"2015","journal-title":"J Appl Probab"},{"issue":"3","key":"10.1016\/j.ress.2026.112782_b54","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.orl.2017.02.005","article-title":"Stochastic comparison of parallel systems with log-Lindley distributed components","volume":"45","author":"Chowdhury","year":"2017","journal-title":"Oper Res Lett"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b55","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1017\/jpr.2018.14","article-title":"On stochastic comparisons of k-out-of-n systems with Weibull components","volume":"55","author":"Balakrishnan","year":"2018","journal-title":"J Appl Probab"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b56","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1017\/jpr.2018.40","article-title":"Hazard rate ordering of the largest order statistics from geometric random variables","volume":"55","author":"Bara","year":"2018","journal-title":"J Appl Probab"},{"issue":"3","key":"10.1016\/j.ress.2026.112782_b57","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1080\/03610926.2017.1417433","article-title":"Ordering results for series and parallel systems comprising heterogeneous exponentiated Weibull components","volume":"48","author":"Barmalzan","year":"2019","journal-title":"Comm Statist Theory Methods"},{"issue":"6","key":"10.1016\/j.ress.2026.112782_b58","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1080\/03610926.2018.1429630","article-title":"Comparisons between parallel systems with exponentiated generalized gamma components","volume":"48","author":"Haidari","year":"2019","journal-title":"Comm Statist Theory Methods"},{"key":"10.1016\/j.ress.2026.112782_b59","doi-asserted-by":"crossref","DOI":"10.1016\/j.physa.2019.123124","article-title":"Stochastic comparisons of series, parallel and k-out-of-n systems with heterogeneous bathtub failure rate type components","volume":"540","author":"Bhattacharyya","year":"2020","journal-title":"Phys A"},{"key":"10.1016\/j.ress.2026.112782_b60","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2020.112965","article-title":"Stochastic comparisons of series and parallel systems with dependent heterogeneous extended exponential components under Archimedean copula","volume":"380","author":"Barmalzan","year":"2020","journal-title":"J Comput Appl Math"},{"key":"10.1016\/j.ress.2026.112782_b61","first-page":"1","article-title":"Stochastic comparisons of series and parallel systems with dependent Burr type XII components","author":"Barmalzan","year":"2020","journal-title":"Comm Statist Theory Methods"},{"key":"10.1016\/j.ress.2026.112782_b62","first-page":"1","article-title":"Stochastic comparisons of finite mixture models with generalized lehmann distributed components","author":"Sattari","year":"2021","journal-title":"Comm Statist Theory Methods"},{"key":"10.1016\/j.ress.2026.112782_b63","doi-asserted-by":"crossref","DOI":"10.1017\/jpr.2020.74","article-title":"Stochastic comparisons and aging properties of an extended gamma process","author":"Al Masry","year":"2021","journal-title":"J Appl Probab"},{"issue":"6","key":"10.1016\/j.ress.2026.112782_b64","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1080\/16843703.2021.1963033","article-title":"Comparing the reliability of coherent systems with heterogeneous, dependent and distribution-free components","volume":"18","author":"Torrado","year":"2021","journal-title":"Qual Technol Quant Manag"},{"key":"10.1016\/j.ress.2026.112782_b65","volume":"vol. 143","author":"Marshall","year":"1979"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b66","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1080\/02331888.2017.1353516","article-title":"Ordering properties of sample minimum from Kumaraswamy-G random variables","volume":"52","author":"Kundu","year":"2018","journal-title":"Statistics"},{"issue":"6","key":"10.1016\/j.ress.2026.112782_b67","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1080\/02331880310001598864","article-title":"Estimation of the parameters of the gompertz distribution under the first failure-censored sampling plan","volume":"37","author":"Wu","year":"2003","journal-title":"Statistics"},{"issue":"6","key":"10.1016\/j.ress.2026.112782_b68","doi-asserted-by":"crossref","first-page":"1376","DOI":"10.1080\/02331888.2016.1230859","article-title":"On extreme order statistics from heterogeneous Weibull variables","volume":"50","author":"Zhao","year":"2016","journal-title":"Statistics"},{"issue":"4","key":"10.1016\/j.ress.2026.112782_b69","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1007\/s11749-018-0581-7","article-title":"On stochastic comparisons of finite mixtures for some semiparametric families of distributions","volume":"27","author":"Hazra","year":"2018","journal-title":"Test"},{"issue":"3","key":"10.1016\/j.ress.2026.112782_b70","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1080\/02331888.2020.1750014","article-title":"Ordering results of extreme order statistics from heterogeneous Gompertz\u2013Makeham random variables","volume":"54","author":"Majumder","year":"2020","journal-title":"Statistics"},{"key":"10.1016\/j.ress.2026.112782_b71","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S026996482510017X","article-title":"Stochastic dominance results under multivariate chain majorization for extreme order statistics of a generalized Gompertz distribution","author":"Bera","year":"2026","journal-title":"Probab Engrg Inform Sci"},{"key":"10.1016\/j.ress.2026.112782_b72","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0269964826100199","article-title":"Ordering of extreme order statistics among q-Weibull random variables","author":"Mahmood K","year":"2026","journal-title":"Probab Engrg Inform Sci"},{"key":"10.1016\/j.ress.2026.112782_b73","doi-asserted-by":"crossref","DOI":"10.1186\/s13660-026-03453-4","article-title":"Preservation of hazard rate and relative average hazard rate orders in dependent series and parallel systems via Archimedean copulas","author":"Manshi","year":"2026","journal-title":"J Inequal Appl"},{"key":"10.1016\/j.ress.2026.112782_b74","article-title":"Dispersive and hazard rate orderings of parallel systems with exponential dependent components","author":"Alomani","year":"2025","journal-title":"Statist Probab Lett"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b75","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1186\/s13660-025-03290-x","article-title":"Dispersion and variation orders of extreme order statistics from dependent unit gamma gompertz random variables","volume":"2025","author":"Shekari","year":"2025","journal-title":"J Inequal Appl"},{"issue":"5","key":"10.1016\/j.ress.2026.112782_b76","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1080\/02331888.2025.2486283","article-title":"Stochastic comparisons of extremes with a generalization of Weibull distribution","volume":"59","author":"Al-jabbar","year":"2025","journal-title":"Statistics"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b77","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s00184-023-00905-5","article-title":"Comparison of extreme order statistics from two sets of heterogeneous dependent random variables under random shocks","volume":"87","author":"Amini-Seresht","year":"2024","journal-title":"Metrika"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b78","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1080\/02331888.2023.2177999","article-title":"Stochastic comparisons of second-order statistics from dependent and heterogenous modified proportional hazard rate observations","volume":"57","author":"Yan","year":"2023","journal-title":"Statistics"},{"issue":"1","key":"10.1016\/j.ress.2026.112782_b79","doi-asserted-by":"crossref","first-page":"7","DOI":"10.5209\/rev_REMA.2007.v20.n1.16528","article-title":"Permanents, order statistics, outliers, and robustness","volume":"20","author":"Balakrishnan","year":"2007","journal-title":"Rev Mat Complut"},{"issue":"3","key":"10.1016\/j.ress.2026.112782_b80","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1017\/S0269964801153088","article-title":"Stochastic properties of spacings in a single-outlier exponential model","volume":"15","author":"Khaledi","year":"2001","journal-title":"Probab Engrg Inform Sci"},{"issue":"2","key":"10.1016\/j.ress.2026.112782_b81","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1017\/S0269964811000313","article-title":"Stochastic comparisons of largest order statistics from multiple-outlier exponential models","volume":"26","author":"Zhao","year":"2012","journal-title":"Probab Engrg Inform Sci"},{"key":"10.1016\/j.ress.2026.112782_b82","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1007\/s11009-013-9377-0","article-title":"Comparisons of largest order statistics from multiple-outlier gamma models","volume":"17","author":"Zhao","year":"2015","journal-title":"Methodol Comput Appl Probab"},{"issue":"5","key":"10.1016\/j.ress.2026.112782_b83","doi-asserted-by":"crossref","first-page":"896","DOI":"10.1016\/j.jmva.2011.01.006","article-title":"Bounds for mixtures of order statistics from exponentials and applications","volume":"102","author":"P\u0103lt\u0103nea","year":"2011","journal-title":"J Multivariate Anal"},{"issue":"7","key":"10.1016\/j.ress.2026.112782_b84","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1016\/j.jspi.2007.08.001","article-title":"On the comparison in hazard rate ordering of fail-safe systems","volume":"138","author":"P\u0103lt\u0103nea","year":"2008","journal-title":"J Statist Plann Inference"},{"issue":"5","key":"10.1016\/j.ress.2026.112782_b85","doi-asserted-by":"crossref","first-page":"952","DOI":"10.1016\/j.jmva.2008.09.010","article-title":"Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables","volume":"100","author":"Zhao","year":"2009","journal-title":"J Multivariate Anal"},{"key":"10.1016\/j.ress.2026.112782_b86","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1051\/ps:2005020","article-title":"Comparison of order statistics in a random sequence to the same statistics with iid variables","volume":"10","author":"Bon","year":"2006","journal-title":"ESAIM Probab Stat"},{"key":"10.1016\/j.ress.2026.112782_b87","first-page":"1","article-title":"On stochastic comparisons of order statistics from heterogeneous exponential samples","author":"Yu","year":"2016","journal-title":"Probab Engrg Inform Sci"},{"key":"10.1016\/j.ress.2026.112782_b88","series-title":"Optimizing methods in statistics","first-page":"89","article-title":"Comparisons of order statistics and of spacings from heterogeneous distributions","author":"Pledger","year":"1971"}],"container-title":["Reliability Engineering &amp; System Safety"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0951832026005934?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0951832026005934?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T16:00:12Z","timestamp":1780934412000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0951832026005934"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":88,"alternative-id":["S0951832026005934"],"URL":"https:\/\/doi.org\/10.1016\/j.ress.2026.112782","relation":{},"ISSN":["0951-8320"],"issn-type":[{"value":"0951-8320","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Ordering results involving k-out-of-n systems for a flexible Gompertz model with heterogeneity","name":"articletitle","label":"Article Title"},{"value":"Reliability Engineering & System Safety","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ress.2026.112782","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"112782"}}