{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T04:17:14Z","timestamp":1778300234674,"version":"3.51.4"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T00:00:00Z","timestamp":1742947200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T00:00:00Z","timestamp":1742947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s00180-025-01612-7","type":"journal-article","created":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T22:38:41Z","timestamp":1743201521000},"page":"3781-3817","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Estimation of stress\u2013strength reliability for the generalized inverted exponential distribution based on improved adaptive Type-II progressive censoring"],"prefix":"10.1007","volume":"40","author":[{"given":"Chatany","family":"Swaroop","sequence":"first","affiliation":[]},{"given":"Subhankar","family":"Dutta","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2541-6267","authenticated-orcid":false,"given":"Shubham","family":"Saini","sequence":"additional","affiliation":[]},{"given":"Neeraj","family":"Tiwari","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,26]]},"reference":[{"issue":"11","key":"1612_CR1","doi-asserted-by":"publisher","first-page":"1301","DOI":"10.1080\/00949650802261095","volume":"79","author":"A Abouammoh","year":"2009","unstructured":"Abouammoh A, Alshingiti AM (2009) Reliability estimation of generalized inverted exponential distribution. J Stat Comput Simul 79(11):1301\u20131315","journal-title":"J Stat Comput Simul"},{"issue":"2","key":"1612_CR2","doi-asserted-by":"publisher","first-page":"239","DOI":"10.15672\/HJMS.2017.408","volume":"46","author":"N Akdam","year":"2017","unstructured":"Akdam N, K\u0131nac\u0131 \u0130, Saracoglu B (2017) Statistical inference of stress\u2013strength reliability for the exponential power (EP) distribution based on progressive type-II censored samples. Hacettepe J Math Stat 46(2):239\u2013253","journal-title":"Hacettepe J Math Stat"},{"issue":"3","key":"1612_CR3","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1080\/00949655.2013.824449","volume":"85","author":"M Basirat","year":"2015","unstructured":"Basirat M, Baratpour S, Ahmadi J (2015) Statistical inferences for stress\u2013strength in the proportional hazard models based on progressive Type-II censored samples. J Stat Comput Simul 85(3):431\u2013449","journal-title":"J Stat Comput Simul"},{"issue":"1","key":"1612_CR4","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/0886-7798(95)00047-X","volume":"11","author":"R Bhasin","year":"1996","unstructured":"Bhasin R, Grimstad E (1996) The use of stress\u2013strength relationships in the assessment of tunnel stability. Tunn Undergr Space Technol 11(1):93\u201398","journal-title":"Tunn Undergr Space Technol"},{"issue":"10","key":"1612_CR5","doi-asserted-by":"publisher","first-page":"4665","DOI":"10.1080\/03610918.2021.1966464","volume":"52","author":"\u00c7 \u00c7etinkaya","year":"2023","unstructured":"\u00c7etinkaya \u00c7 (2023) The stress\u2013strength reliability model with component strength under partially accelerated life test. Commun Stat Simul Comput 52(10):4665\u20134684","journal-title":"Commun Stat Simul Comput"},{"issue":"1","key":"1612_CR6","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1080\/10618600.1999.10474802","volume":"8","author":"M-H Chen","year":"1999","unstructured":"Chen M-H, Shao Q-M (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat 8(1):69\u201392","journal-title":"J Comput Graph Stat"},{"issue":"1","key":"1612_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"AP Dempster","year":"1977","unstructured":"Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Stat Soc Ser B (Methodol) 39(1):1\u201322","journal-title":"J Roy Stat Soc Ser B (Methodol)"},{"key":"1612_CR8","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/j.stamet.2013.07.007","volume":"18","author":"S Dey","year":"2014","unstructured":"Dey S, Pradhan B (2014) Generalized inverted exponential distribution under hybrid censoring. Stat Methodol 18:101\u2013114","journal-title":"Stat Methodol"},{"issue":"4","key":"1612_CR9","doi-asserted-by":"publisher","first-page":"2109","DOI":"10.1007\/s00180-023-01376-y","volume":"39","author":"S Dutta","year":"2024","unstructured":"Dutta S, Dey S, Kayal S (2024) Bayesian survival analysis of logistic exponential distribution for adaptive progressive Type-II censored data. Comput Stat 39(4):2109\u20132155","journal-title":"Comput Stat"},{"issue":"2","key":"1612_CR10","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1080\/16843703.2022.2027601","volume":"19","author":"S Dutta","year":"2022","unstructured":"Dutta S, Kayal S (2022) Estimation of parameters of the logistic exponential distribution under progressive Type-I hybrid censored sample. Quality Technol Quant Manag 19(2):234\u2013258","journal-title":"Quality Technol Quant Manag"},{"issue":"4","key":"1612_CR11","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1177\/09576509221142398","volume":"237","author":"S Dutta","year":"2023","unstructured":"Dutta S, Kayal S (2023) Inference of a competing risks model with partially observed failure causes under improved adaptive type-II progressive censoring. Proc Inst Mech Eng Part O J Risk Reliab 237(4):765\u2013780","journal-title":"Proc Inst Mech Eng Part O J Risk Reliab"},{"key":"1612_CR12","doi-asserted-by":"publisher","DOI":"10.1201\/9780429258411","volume-title":"Bayesian data analysis","author":"A Gelman","year":"1995","unstructured":"Gelman A, Carlin JB, Stern HS, Rubin DB (1995) Bayesian data analysis, 1st edn. Chapman and Hall\/CRC, Boca Raton","edition":"1"},{"issue":"1","key":"1612_CR13","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","volume":"57","author":"WK Hastings","year":"1970","unstructured":"Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97\u2013109","journal-title":"Biometrika"},{"issue":"6","key":"1612_CR14","doi-asserted-by":"publisher","first-page":"4671","DOI":"10.1080\/03610918.2015.1129408","volume":"46","author":"F Hemmati","year":"2017","unstructured":"Hemmati F, Khorram E (2017) On adaptive progressively Type-II censored competing risks data. Commun Stat Simul Comput 46(6):4671\u20134693","journal-title":"Commun Stat Simul Comput"},{"issue":"2","key":"1612_CR15","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1007\/s00500-022-07628-1","volume":"27","author":"J Jia","year":"2023","unstructured":"Jia J, Yan Z, Song H, Chen Y (2023) Reliability estimation in multicomponent stress\u2013strength model for generalized inverted exponential distribution. Soft Comput 27(2):903\u2013916","journal-title":"Soft Comput"},{"issue":"3","key":"1612_CR16","doi-asserted-by":"publisher","first-page":"1345","DOI":"10.1007\/s00180-020-00991-3","volume":"35","author":"JK Jose","year":"2020","unstructured":"Jose JK, Drisya M (2020) Time-dependent stress\u2013strength reliability models based on phase type distribution. Comput Stat 35(3):1345\u20131371","journal-title":"Comput Stat"},{"issue":"9","key":"1612_CR17","doi-asserted-by":"publisher","first-page":"7447","DOI":"10.1080\/03610918.2016.1241405","volume":"46","author":"T Kayal","year":"2017","unstructured":"Kayal T, Tripathi YM, Rastogi MK, Asgharzadeh A (2017) Inference for Burr XII distribution under Type I progressive hybrid censoring. Commun Stat Simul Comput 46(9):7447\u20137465","journal-title":"Commun Stat Simul Comput"},{"issue":"5","key":"1612_CR18","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1080\/03610926.2018.1554126","volume":"49","author":"A Kohansal","year":"2020","unstructured":"Kohansal A (2020) Bayesian and classical estimation of R= P (X$<$ Y) based on Burr type XII distribution under hybrid progressive censored samples. Commun Stat Theory Methods 49(5):1043\u20131081","journal-title":"Commun Stat Theory Methods"},{"issue":"6","key":"1612_CR19","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1080\/00949655.2011.647027","volume":"83","author":"H Krishna","year":"2013","unstructured":"Krishna H, Kumar K (2013) Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample. J Stat Comput Simul 83(6):1007\u20131019","journal-title":"J Stat Comput Simul"},{"issue":"7","key":"1612_CR20","doi-asserted-by":"publisher","first-page":"1754","DOI":"10.1016\/j.jspi.2009.12.028","volume":"140","author":"K Krishnamoorthy","year":"2010","unstructured":"Krishnamoorthy K, Lin Y (2010) Confidence limits for stress\u2013strength reliability involving Weibull models. J Stat Plan Inference 140(7):1754\u20131764","journal-title":"J Stat Plan Inference"},{"issue":"6","key":"1612_CR21","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1080\/00949655.2022.2122970","volume":"93","author":"A Kumari","year":"2023","unstructured":"Kumari A, Kumar S, Kumar K (2023) Inference for reliability in a multicomponent stress\u2013strength model from generalized inverted exponential lifetime distribution under progressive first failure censoring. J Stat Comput Simul 93(6):863\u2013887","journal-title":"J Stat Comput Simul"},{"issue":"10","key":"1612_CR22","doi-asserted-by":"publisher","first-page":"2509","DOI":"10.1016\/j.csda.2005.05.002","volume":"50","author":"D Kundu","year":"2006","unstructured":"Kundu D, Joarder A (2006) Analysis of Type-II progressively hybrid censored data. Comput Stat Data Anal 50(10):2509\u20132528","journal-title":"Comput Stat Data Anal"},{"issue":"2","key":"1612_CR23","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1109\/TEM.2016.2527684","volume":"63","author":"L Li","year":"2016","unstructured":"Li L, Liu M, Shen W, Cheng G (2016) A discrete stress\u2013strength interference theory-based dynamic supplier selection model for maintenance service outsourcing. IEEE Trans Eng Manage 63(2):189\u2013200","journal-title":"IEEE Trans Eng Manage"},{"issue":"2","key":"1612_CR24","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1111\/j.2517-6161.1982.tb01203.x","volume":"44","author":"TA Louis","year":"1982","unstructured":"Louis TA (1982) Finding the observed information matrix when using the EM algorithm. J R Stat Soc Ser B Stat Methodol 44(2):226\u2013233","journal-title":"J R Stat Soc Ser B Stat Methodol"},{"issue":"6","key":"1612_CR25","doi-asserted-by":"publisher","first-page":"2388","DOI":"10.1080\/03610918.2021.1908552","volume":"52","author":"J Ma","year":"2023","unstructured":"Ma J, Wang L, Tripathi YM, Rastogi MK (2023) Reliability inference for stress\u2013strength model based on inverted exponential Rayleigh distribution under progressive Type-II censored data. Commun Stat Simul Comput 52(6):2388\u20132407","journal-title":"Commun Stat Simul Comput"},{"issue":"247","key":"1612_CR26","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1080\/01621459.1949.10483310","volume":"44","author":"N Metropolis","year":"1949","unstructured":"Metropolis N, Ulam S (1949) The Monte Carlo method. J Am Stat Assoc 44(247):335\u2013341","journal-title":"J Am Stat Assoc"},{"issue":"4","key":"1612_CR27","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1080\/00401706.1995.10484376","volume":"37","author":"GS Mudholkar","year":"1995","unstructured":"Mudholkar GS, Srivastava DK, Freimer M (1995) The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics 37(4):436\u2013445","journal-title":"Technometrics"},{"issue":"9","key":"1612_CR28","doi-asserted-by":"publisher","first-page":"1664","DOI":"10.1080\/02664763.2023.2230536","volume":"51","author":"M Nassar","year":"2024","unstructured":"Nassar M, Elshahhat A (2024) Estimation procedures and optimal censoring schemes for an improved adaptive progressively type-II censored weibull distribution. J Appl Stat 51(9):1664\u20131688","journal-title":"J Appl Stat"},{"issue":"4","key":"1612_CR29","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1016\/S0167-9473(01)00091-3","volume":"39","author":"H Ng","year":"2002","unstructured":"Ng H, Chan P, Balakrishnan N (2002) Estimation of parameters from progressively censored data using EM algorithm. Comput Stat Data Anal 39(4):371\u2013386","journal-title":"Comput Stat Data Anal"},{"issue":"8","key":"1612_CR30","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1002\/nav.20371","volume":"56","author":"HKT Ng","year":"2009","unstructured":"Ng HKT, Kundu D, Chan PS (2009) Statistical analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme. Naval Res Logist (NRL) 56(8):687\u2013698","journal-title":"Naval Res Logist (NRL)"},{"issue":"6","key":"1612_CR31","doi-asserted-by":"publisher","first-page":"1412","DOI":"10.1108\/IJQRM-05-2021-0130","volume":"40","author":"H Panahi","year":"2022","unstructured":"Panahi H (2022) Reliability analysis for stress\u2013strength model from inverted exponentiated Rayleigh based on the hybrid censored sample. Int J Quality Reliab Manage 40(6):1412\u20131428","journal-title":"Int J Quality Reliab Manage"},{"issue":"1","key":"1612_CR32","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1115\/1.2842158","volume":"118","author":"S Quin","year":"1996","unstructured":"Quin S, Widera G (1996) Use of stress\u2013strength model in determination of safety factor for pressure vessel design. J Pressure Vessel Technol 118(1):27\u201332","journal-title":"J Pressure Vessel Technol"},{"key":"1612_CR33","volume-title":"R: a language and environment for statistical computing","author":"R Core Team","year":"2013","unstructured":"R Core Team (2013) R: a language and environment for statistical computing. Foundation for Statistical Computing, Vienna, Austria"},{"issue":"14","key":"1612_CR34","doi-asserted-by":"publisher","first-page":"3177","DOI":"10.1080\/00949655.2024.2374829","volume":"94","author":"S Saini","year":"2024","unstructured":"Saini S (2024) Estimation of multi-stress strength reliability under progressive first failure censoring using generalized inverted exponential distribution. J Stat Comput Simul 94(14):3177\u20133209","journal-title":"J Stat Comput Simul"},{"issue":"5","key":"1612_CR35","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1080\/00949655.2010.551772","volume":"82","author":"B Sara\u00e7o\u011flu","year":"2012","unstructured":"Sara\u00e7o\u011flu B, Kinaci I, Kundu D (2012) On estimation of R = P (Y$<$ X) for exponential distribution under progressive type-II censoring. J Stat Comput Simul 82(5):729\u2013744","journal-title":"J Stat Comput Simul"},{"issue":"393","key":"1612_CR36","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1080\/01621459.1986.10478240","volume":"81","author":"L Tierney","year":"1986","unstructured":"Tierney L, Kadane JB (1986) Accurate approximations for posterior moments and marginal densities. J Am Stat Assoc 81(393):82\u201386","journal-title":"J Am Stat Assoc"},{"issue":"2","key":"1612_CR37","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1080\/00949655.2013.822871","volume":"85","author":"SK Tomer","year":"2015","unstructured":"Tomer SK, Panwar M (2015) Estimation procedures for Maxwell distribution under type-I progressive hybrid censoring scheme. J Stat Comput Simul 85(2):339\u2013356","journal-title":"J Stat Comput Simul"},{"issue":"4","key":"1612_CR38","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1080\/15326349.2022.2162545","volume":"39","author":"L Wang","year":"2023","unstructured":"Wang L, Wu S-J, Dey S, Tripathi YM, Mao S (2023) Estimation of stress\u2013strength reliability for multicomponent system with a generalized inverted exponential distribution. Stoch Model 39(4):715\u2013740","journal-title":"Stoch Model"},{"issue":"1","key":"1612_CR39","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.compositesa.2008.10.001","volume":"40","author":"Z Xia","year":"2009","unstructured":"Xia Z, Yu J, Cheng L, Liu L, Wang W (2009) Study on the breaking strength of jute fibres using modified Weibull distribution. Compos A Appl Sci Manuf 40(1):54\u201359","journal-title":"Compos A Appl Sci Manuf"},{"key":"1612_CR40","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.apm.2021.01.050","volume":"95","author":"W Yan","year":"2021","unstructured":"Yan W, Li P, Yu Y (2021) Statistical inference for the reliability of Burr-XII distribution under improved adaptive Type-II progressive censoring. Appl Math Model 95:38\u201352","journal-title":"Appl Math Model"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-025-01612-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-025-01612-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-025-01612-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T08:13:27Z","timestamp":1757146407000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-025-01612-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,26]]},"references-count":40,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["1612"],"URL":"https:\/\/doi.org\/10.1007\/s00180-025-01612-7","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,26]]},"assertion":[{"value":"1 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 January 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 March 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}