{"id":"https://openalex.org/W7127908575","doi":"https://doi.org/10.1007/s11424-026-4556-6","title":"Statistical Inference for Software Reliability Constrained by the Shape of the Mean Value Function","display_name":"Statistical Inference for Software Reliability Constrained by the Shape of the Mean Value Function","publication_year":2026,"publication_date":"2026-02-01","ids":{"openalex":"https://openalex.org/W7127908575","doi":"https://doi.org/10.1007/s11424-026-4556-6"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-026-4556-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-026-4556-6","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122010005","display_name":"Kangan Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I1304256225","display_name":"University of Wisconsin System","ror":"https://ror.org/03ydkyb10","country_code":"US","type":"education","lineage":["https://openalex.org/I1304256225"]},{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kangan Chen","raw_affiliation_strings":["Department of Industrial and System Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and System Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA","institution_ids":["https://openalex.org/I1304256225","https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125120802","display_name":"Jian Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jian Liu","raw_affiliation_strings":["Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ, 85721, USA"],"affiliations":[{"raw_affiliation_string":"Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ, 85721, USA","institution_ids":["https://openalex.org/I138006243"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101205533","display_name":"Qingpei Hu","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qingpei Hu","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China"],"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125207273","display_name":"Min Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Min Xie","raw_affiliation_strings":["Department of Industrial Engineering, City University of Hong Kong, Hong Kong, 999077, China"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, City University of Hong Kong, Hong Kong, 999077, China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101205533"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.37775061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"1","first_page":"334","last_page":"362"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12423","display_name":"Software Reliability and Analysis Research","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12423","display_name":"Software Reliability and Analysis Research","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10743","display_name":"Software Testing and Debugging Techniques","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.0010000000474974513,"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/estimator","display_name":"Estimator","score":0.8180000185966492},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.569100022315979},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.5257999897003174},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.46779999136924744},{"id":"https://openalex.org/keywords/software-quality","display_name":"Software quality","score":0.4636000096797943},{"id":"https://openalex.org/keywords/parametric-model","display_name":"Parametric model","score":0.41940000653266907},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.40529999136924744},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.36469998955726624}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8180000185966492},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.569100022315979},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.5257999897003174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47189998626708984},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.46779999136924744},{"id":"https://openalex.org/C117447612","wikidata":"https://www.wikidata.org/wiki/Q1412670","display_name":"Software quality","level":4,"score":0.4636000096797943},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4535999894142151},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.41940000653266907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4156999886035919},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.40529999136924744},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.352400004863739},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.35089999437332153},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.3465000092983246},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34200000762939453},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.32710000872612},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3086000084877014},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2806999981403351},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2628999948501587},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.2623000144958496},{"id":"https://openalex.org/C82214349","wikidata":"https://www.wikidata.org/wiki/Q657339","display_name":"Software metric","level":5,"score":0.2554999887943268},{"id":"https://openalex.org/C201729545","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability theory","level":3,"score":0.25369998812675476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11424-026-4556-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-026-4556-6","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W145568977","https://openalex.org/W200594380","https://openalex.org/W1569393825","https://openalex.org/W1891457878","https://openalex.org/W1972308890","https://openalex.org/W1973240875","https://openalex.org/W1975116882","https://openalex.org/W1977098624","https://openalex.org/W1980595883","https://openalex.org/W1982016747","https://openalex.org/W1985258194","https://openalex.org/W1990418076","https://openalex.org/W2003113187","https://openalex.org/W2016864600","https://openalex.org/W2022284665","https://openalex.org/W2028227373","https://openalex.org/W2029683878","https://openalex.org/W2051203581","https://openalex.org/W2057121649","https://openalex.org/W2060308631","https://openalex.org/W2076051662","https://openalex.org/W2078533963","https://openalex.org/W2082990111","https://openalex.org/W2091509464","https://openalex.org/W2099809181","https://openalex.org/W2108193906","https://openalex.org/W2117039703","https://openalex.org/W2126383955","https://openalex.org/W2143781653","https://openalex.org/W2165238463","https://openalex.org/W2178281776","https://openalex.org/W2241837990","https://openalex.org/W2295410397","https://openalex.org/W2314152483","https://openalex.org/W2330041398","https://openalex.org/W2566448884","https://openalex.org/W3127333363","https://openalex.org/W4293256909","https://openalex.org/W4308945320"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-02-07T06:15:42.627816","created_date":"2026-02-07T00:00:00"}