{"id":"https://openalex.org/W3032943352","doi":"https://doi.org/10.3390/sym12060937","title":"Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data","display_name":"Statistical Inference of the Lifetime Performance Index with the Log-Logistic Distribution Based on Progressive First-Failure-Censored Data","publication_year":2020,"publication_date":"2020-06-03","ids":{"openalex":"https://openalex.org/W3032943352","doi":"https://doi.org/10.3390/sym12060937","mag":"3032943352"},"language":"en","primary_location":{"id":"doi:10.3390/sym12060937","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12060937","pdf_url":"https://www.mdpi.com/2073-8994/12/6/937/pdf?version=1592828208","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/6/937/pdf?version=1592828208","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100458718","display_name":"Ying Xie","orcid":"https://orcid.org/0000-0003-3223-1797"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ying Xie","raw_affiliation_strings":["Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053074333","display_name":"Wenhao Gui","orcid":"https://orcid.org/0000-0003-4318-1780"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenhao Gui","raw_affiliation_strings":["Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China"],"raw_orcid":"https://orcid.org/0000-0003-4318-1780","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053074333"],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.7219,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.82702859,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"6","first_page":"937","last_page":"937"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9991000294685364,"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/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.9937000274658203,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/censoring","display_name":"Censoring (clinical trials)","score":0.7859200239181519},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.6378502249717712},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6099035739898682},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.600538432598114},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5469551086425781},{"id":"https://openalex.org/keywords/bayes-theorem","display_name":"Bayes' theorem","score":0.47750967741012573},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4651860296726227},{"id":"https://openalex.org/keywords/confidence-interval","display_name":"Confidence interval","score":0.4606573283672333},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.43062594532966614},{"id":"https://openalex.org/keywords/posterior-probability","display_name":"Posterior probability","score":0.4300564229488373},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.370799720287323}],"concepts":[{"id":"https://openalex.org/C137668524","wikidata":"https://www.wikidata.org/wiki/Q189813","display_name":"Censoring (clinical trials)","level":2,"score":0.7859200239181519},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6378502249717712},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6099035739898682},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.600538432598114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5469551086425781},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.47750967741012573},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4651860296726227},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.4606573283672333},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.43062594532966614},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.4300564229488373},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.370799720287323}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12060937","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12060937","pdf_url":"https://www.mdpi.com/2073-8994/12/6/937/pdf?version=1592828208","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d4c754a77fd34f60b991da5522bce09a","is_oa":true,"landing_page_url":"https://doaj.org/article/d4c754a77fd34f60b991da5522bce09a","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":"Symmetry, Vol 12, Iss 6, p 937 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/6/937/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym12060937","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12060937","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12060937","pdf_url":"https://www.mdpi.com/2073-8994/12/6/937/pdf?version=1592828208","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W22107882","https://openalex.org/W598477298","https://openalex.org/W614512727","https://openalex.org/W1528708126","https://openalex.org/W1811135684","https://openalex.org/W1965250302","https://openalex.org/W1979476799","https://openalex.org/W2017596715","https://openalex.org/W2018690110","https://openalex.org/W2019747837","https://openalex.org/W2050960381","https://openalex.org/W2056753861","https://openalex.org/W2071057856","https://openalex.org/W2088038447","https://openalex.org/W2089408108","https://openalex.org/W2111545886","https://openalex.org/W2131491795","https://openalex.org/W2151038992","https://openalex.org/W2151411627","https://openalex.org/W2154890155","https://openalex.org/W2157202423","https://openalex.org/W2159443410","https://openalex.org/W2227010554","https://openalex.org/W2379261786","https://openalex.org/W2485957347","https://openalex.org/W2500905618","https://openalex.org/W2530236676","https://openalex.org/W2530990767","https://openalex.org/W2614647477","https://openalex.org/W2734196654","https://openalex.org/W2784092068","https://openalex.org/W2898670740","https://openalex.org/W2954744336","https://openalex.org/W2969934758","https://openalex.org/W4237296266","https://openalex.org/W4250828386","https://openalex.org/W6600925095","https://openalex.org/W6663007230"],"related_works":["https://openalex.org/W71678127","https://openalex.org/W2157655363","https://openalex.org/W4205763938","https://openalex.org/W2292189132","https://openalex.org/W4288092343","https://openalex.org/W2134332527","https://openalex.org/W4386114318","https://openalex.org/W2888496681","https://openalex.org/W2790979771","https://openalex.org/W2963009826"],"abstract_inverted_index":{"Estimating":[0],"the":[1,21,57,60,64,72,93,99,104,109,131],"accurate":[2],"evaluation":[3,28],"of":[4,56,59],"product":[5],"lifetime":[6,22,65],"performance":[7,23,66],"has":[8],"always":[9],"been":[10,136],"a":[11,30,43,118],"hot":[12],"topic":[13],"in":[14],"manufacturing":[15],"industry.":[16],"This":[17],"paper,":[18],"based":[19],"on":[20,26],"index,":[24],"focuses":[25],"its":[27],"when":[29],"lower":[31],"specification":[32],"limit":[33],"is":[34],"given.":[35],"The":[36],"progressive":[37],"first-failure-censored":[38],"data":[39,120],"we":[40,91,116],"discuss":[41],"have":[42,135],"common":[44],"log-logistic":[45,61],"distribution.":[46],"Both":[47],"Bayesian":[48],"and":[49,63,75,83,103],"non-Bayesian":[50],"method":[51],"are":[52,68],"studied.":[53,137],"Bayes":[54],"estimator":[55,96],"parameters":[58],"distribution":[62],"index":[67],"obtained":[69],"using":[70],"both":[71],"Lindley":[73],"approximation":[74],"Monte":[76],"Carlo":[77],"Markov":[78],"Chain":[79],"methods":[80],"under":[81],"symmetric":[82],"asymmetric":[84],"loss":[85],"functions.":[86],"As":[87],"for":[88,122,129],"interval":[89],"estimation,":[90],"apply":[92],"maximum":[94],"likelihood":[95],"to":[97,107],"construct":[98],"asymptotic":[100],"confidence":[101],"intervals":[102],"Metropolis\u2013Hastings":[105],"algorithm":[106],"establish":[108],"highest":[110],"posterior":[111],"density":[112],"credible":[113],"intervals.":[114],"Moreover,":[115],"analyze":[117],"real":[119],"set":[121],"demonstrative":[123],"purposes.":[124],"In":[125],"addition,":[126],"different":[127],"criteria":[128],"deciding":[130],"optimal":[132],"censoring":[133],"scheme":[134]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
