{"id":"https://openalex.org/W4377007911","doi":"https://doi.org/10.1109/access.2023.3276904","title":"A New Flexible Four Parameter Bathtub Curve Failure Rate Model, and Its Application to Right-Censored Data","display_name":"A New Flexible Four Parameter Bathtub Curve Failure Rate Model, and Its Application to Right-Censored Data","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4377007911","doi":"https://doi.org/10.1109/access.2023.3276904"},"language":"en","primary_location":{"id":"doi:10.1109/access.2023.3276904","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2023.3276904","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/10005208/10126085.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/10005208/10126085.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042893321","display_name":"Laila A. Al\u2010Essa","orcid":null},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Laila A. Al-Essa","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-2788-8946","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043518836","display_name":"Mustapha Muhammad","orcid":"https://orcid.org/0000-0003-0329-5898"},"institutions":[{"id":"https://openalex.org/I4210128140","display_name":"Guangdong University of Petrochemical Technology","ror":"https://ror.org/030ffke25","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210128140"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mustapha Muhammad","raw_affiliation_strings":["Department of Mathematics, Guangdong University of Petrochemical Technology, Maoming, China"],"raw_orcid":"https://orcid.org/0000-0003-0329-5898","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guangdong University of Petrochemical Technology, Maoming, China","institution_ids":["https://openalex.org/I4210128140"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061653531","display_name":"M. H. Tahir","orcid":"https://orcid.org/0000-0002-2157-3997"},"institutions":[{"id":"https://openalex.org/I174731842","display_name":"Islamia University of Bahawalpur","ror":"https://ror.org/002rc4w13","country_code":"PK","type":"education","lineage":["https://openalex.org/I174731842"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"M. H. Tahir","raw_affiliation_strings":["Department of Statistics, The Islamia University of Bahawalpur (IUB), Bahawalpur, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, The Islamia University of Bahawalpur (IUB), Bahawalpur, Pakistan","institution_ids":["https://openalex.org/I174731842"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000505492","display_name":"Badamasi Abba","orcid":"https://orcid.org/0000-0001-6768-8346"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Badamasi Abba","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Hunan, China"],"raw_orcid":"https://orcid.org/0000-0001-6768-8346","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Hunan, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034547648","display_name":"Jinsen Xiao","orcid":"https://orcid.org/0000-0002-1276-6770"},"institutions":[{"id":"https://openalex.org/I4210128140","display_name":"Guangdong University of Petrochemical Technology","ror":"https://ror.org/030ffke25","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210128140"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinsen Xiao","raw_affiliation_strings":["Department of Mathematics, Guangdong University of Petrochemical Technology, Maoming, China"],"raw_orcid":"https://orcid.org/0000-0002-1276-6770","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guangdong University of Petrochemical Technology, Maoming, China","institution_ids":["https://openalex.org/I4210128140"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010653691","display_name":"Farrukh Jamal","orcid":"https://orcid.org/0000-0001-6192-9890"},"institutions":[{"id":"https://openalex.org/I174731842","display_name":"Islamia University of Bahawalpur","ror":"https://ror.org/002rc4w13","country_code":"PK","type":"education","lineage":["https://openalex.org/I174731842"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Farrukh Jamal","raw_affiliation_strings":["Department of Statistics, The Islamia University of Bahawalpur (IUB), Bahawalpur, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-6192-9890","affiliations":[{"raw_affiliation_string":"Department of Statistics, The Islamia University of Bahawalpur (IUB), Bahawalpur, Pakistan","institution_ids":["https://openalex.org/I174731842"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":5.5723,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.96871925,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"11","issue":null,"first_page":"50130","last_page":"50144"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/weibull-distribution","display_name":"Weibull distribution","score":0.7098444104194641},{"id":"https://openalex.org/keywords/bathtub","display_name":"Bathtub","score":0.6026335954666138},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5520563125610352},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5239477157592773},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5199012160301208},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.48711228370666504},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4747215509414673},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4526410698890686},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43237677216529846},{"id":"https://openalex.org/keywords/quantile","display_name":"Quantile","score":0.42423075437545776},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42235177755355835},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.41230645775794983},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3762284815311432},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3147655129432678}],"concepts":[{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.7098444104194641},{"id":"https://openalex.org/C2777728836","wikidata":"https://www.wikidata.org/wiki/Q152095","display_name":"Bathtub","level":2,"score":0.6026335954666138},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5520563125610352},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5239477157592773},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5199012160301208},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.48711228370666504},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4747215509414673},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4526410698890686},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43237677216529846},{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.42423075437545776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42235177755355835},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.41230645775794983},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3762284815311432},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3147655129432678},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2023.3276904","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2023.3276904","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/10005208/10126085.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:cbb30871a67a4dd4aeca2be3d0f6dfa8","is_oa":true,"landing_page_url":"https://doaj.org/article/cbb30871a67a4dd4aeca2be3d0f6dfa8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 11, Pp 50130-50144 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2023.3276904","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2023.3276904","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/10005208/10126085.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3143669702","display_name":null,"funder_award_id":"PNURSP2023R443","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"}],"funders":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4377007911.pdf","grobid_xml":"https://content.openalex.org/works/W4377007911.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W1478186840","https://openalex.org/W1599850012","https://openalex.org/W1964557639","https://openalex.org/W1966745815","https://openalex.org/W1968119812","https://openalex.org/W1986078173","https://openalex.org/W1986351075","https://openalex.org/W1991475878","https://openalex.org/W1998782763","https://openalex.org/W2000821665","https://openalex.org/W2021794795","https://openalex.org/W2023219679","https://openalex.org/W2038289147","https://openalex.org/W2073570371","https://openalex.org/W2079730059","https://openalex.org/W2086406817","https://openalex.org/W2090001193","https://openalex.org/W2100291152","https://openalex.org/W2130388500","https://openalex.org/W2135966495","https://openalex.org/W2148534890","https://openalex.org/W2154540401","https://openalex.org/W2170618033","https://openalex.org/W2171401706","https://openalex.org/W2184467236","https://openalex.org/W2499305340","https://openalex.org/W2754904044","https://openalex.org/W2775363893","https://openalex.org/W2797062063","https://openalex.org/W2888873674","https://openalex.org/W2903839378","https://openalex.org/W2919448320","https://openalex.org/W2939258995","https://openalex.org/W2947177886","https://openalex.org/W2963977107","https://openalex.org/W2966311197","https://openalex.org/W2973242080","https://openalex.org/W3002074776","https://openalex.org/W3044294480","https://openalex.org/W3080615193","https://openalex.org/W3083504727","https://openalex.org/W3098865414","https://openalex.org/W3123857276","https://openalex.org/W4220952461","https://openalex.org/W4221037784","https://openalex.org/W4231594839","https://openalex.org/W4232853770","https://openalex.org/W4242533288","https://openalex.org/W4246466113","https://openalex.org/W4253711439","https://openalex.org/W4283073729","https://openalex.org/W4293738259","https://openalex.org/W4312600699","https://openalex.org/W4313325407","https://openalex.org/W4317534982","https://openalex.org/W4319790644","https://openalex.org/W4319836540","https://openalex.org/W4376502702","https://openalex.org/W6686483067","https://openalex.org/W6762710610","https://openalex.org/W6766432192","https://openalex.org/W6852319747"],"related_works":["https://openalex.org/W2022038840","https://openalex.org/W2073570371","https://openalex.org/W2006458583","https://openalex.org/W1975325085","https://openalex.org/W2061488756","https://openalex.org/W2028006048","https://openalex.org/W1620508096","https://openalex.org/W2357734103","https://openalex.org/W1490217699","https://openalex.org/W4251880570"],"abstract_inverted_index":{"This":[0],"article":[1],"introduces":[2],"a":[3,43,53,65,74,185],"new":[4],"flexible":[5],"four":[6],"parameter":[7],"distribution":[8,16],"by":[9,64],"convolution":[10],"of":[11,28,47,73,101,140,171],"the":[12,18,32,71,94,102,127,132,138,141,164,168,172,180],"exponential":[13],"and":[14,61,85,90,97,105,109,130,151],"Weibull":[15],"using":[17],"odd":[19],"function":[20,96],"transformation,":[21],"which":[22],"offers":[23],"greater":[24],"flexibility":[25],"in":[26],"terms":[27],"fit,":[29],"its":[30,78,114],"called":[31],"modified":[33],"exponential-Weibull":[34],"(MEW).":[35],"The":[36,80,117,160],"MEW":[37,103,133,142,165],"model":[38,143,166,182],"is":[39,62,123],"designed":[40],"to":[41,77,112,125],"provide":[42],"more":[44,58],"accurate":[45],"description":[46,170],"failure":[48,59,174],"time":[49,175],"data":[50,146,176],"resulting":[51],"from":[52],"system":[54],"with":[55,148,154],"one":[56],"or":[57],"modes":[60],"characterized":[63],"hazard":[66],"rate":[67],"(HR)":[68],"that":[69,163,179],"takes":[70],"shape":[72],"bathtub":[75],"due":[76],"complexity.":[79],"moments":[81],"properties,":[82],"quantile":[83],"function,":[84],"residual":[86],"life":[87],"are":[88],"derived":[89],"discussed.":[91],"We":[92,136],"discussed":[93],"HR":[95,150],"several":[98],"distributional":[99],"properties":[100],"model,":[104],"applied":[106],"maximum":[107],"likelihood":[108],"Bayesian":[110],"techniques":[111],"estimate":[113],"unknown":[115],"parameters.":[116],"Hamiltonian":[118],"Monte":[119],"Carlo":[120],"(HMC)":[121],"algorithm":[122],"employed":[124],"simulate":[126],"posterior":[128],"distributions":[129],"verify":[131],"Bayes":[134],"estimators.":[135],"examined":[137],"behavior":[139],"on":[144],"two":[145,173],"sets":[147],"bathtub-shaped":[149,158],"compare":[152],"it":[153],"five":[155],"other":[156],"popular":[157],"methodologies.":[159],"results":[161],"indicate":[162],"provided":[167],"best":[169],"sets,":[177],"suggesting":[178],"proposed":[181],"could":[183],"be":[184],"viable":[186],"candidate":[187],"for":[188],"solving":[189],"various":[190],"real-life":[191],"problems.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":8}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
