{"id":"https://openalex.org/W2116128007","doi":"https://doi.org/10.1109/isqed.2009.4810271","title":"Accurate closed-form parameterized block-based statistical timing analysis applying skew-normal distribution","display_name":"Accurate closed-form parameterized block-based statistical timing analysis applying skew-normal distribution","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2116128007","doi":"https://doi.org/10.1109/isqed.2009.4810271","mag":"2116128007"},"language":"en","primary_location":{"id":"doi:10.1109/isqed.2009.4810271","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isqed.2009.4810271","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 10th International Symposium on Quality of Electronic Design","raw_type":"proceedings-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/A5028504813","display_name":"Chun-Yu Chuang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210148468","display_name":"Industrial Technology Research Institute","ror":"https://ror.org/05szzwt63","country_code":"TW","type":"nonprofit","lineage":["https://openalex.org/I4210148468"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Chun-Yu Chuang","raw_affiliation_strings":["Industrial Technology and Research Institute, Taiwan","Industrial Technology Research Institute, Taiwan"],"affiliations":[{"raw_affiliation_string":"Industrial Technology and Research Institute, Taiwan","institution_ids":["https://openalex.org/I4210148468"]},{"raw_affiliation_string":"Industrial Technology Research Institute, Taiwan","institution_ids":["https://openalex.org/I4210148468"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023903936","display_name":"Wai-Kei Mak","orcid":"https://orcid.org/0000-0001-5593-4319"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wai-Kei Mak","raw_affiliation_strings":["Department of Computer Science, National Tsing Hua University, Taiwan","Department of Computer Science, National Tsing Hua University, , Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National Tsing Hua University, Taiwan","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"Department of Computer Science, National Tsing Hua University, , Taiwan","institution_ids":["https://openalex.org/I25846049"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028504813"],"corresponding_institution_ids":["https://openalex.org/I4210148468"],"apc_list":null,"apc_paid":null,"fwci":0.2991,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.63846682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"68","last_page":"73"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10363","display_name":"Low-power high-performance VLSI design","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/design-for-manufacturability","display_name":"Design for manufacturability","score":0.774377167224884},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.746554434299469},{"id":"https://openalex.org/keywords/process-variation","display_name":"Process variation","score":0.7330644130706787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5995689630508423},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5905364155769348},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5302215218544006},{"id":"https://openalex.org/keywords/static-timing-analysis","display_name":"Static timing analysis","score":0.5258241891860962},{"id":"https://openalex.org/keywords/very-large-scale-integration","display_name":"Very-large-scale integration","score":0.4978306293487549},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49175551533699036},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.45100489258766174},{"id":"https://openalex.org/keywords/normal-distribution","display_name":"Normal distribution","score":0.44856545329093933},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4357427656650543},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.43235430121421814},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2662283182144165},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19144853949546814},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1270994246006012}],"concepts":[{"id":"https://openalex.org/C62064638","wikidata":"https://www.wikidata.org/wiki/Q553878","display_name":"Design for manufacturability","level":2,"score":0.774377167224884},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.746554434299469},{"id":"https://openalex.org/C93389723","wikidata":"https://www.wikidata.org/wiki/Q7247313","display_name":"Process variation","level":3,"score":0.7330644130706787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5995689630508423},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5905364155769348},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5302215218544006},{"id":"https://openalex.org/C93682380","wikidata":"https://www.wikidata.org/wiki/Q2025226","display_name":"Static timing analysis","level":2,"score":0.5258241891860962},{"id":"https://openalex.org/C14580979","wikidata":"https://www.wikidata.org/wiki/Q876049","display_name":"Very-large-scale integration","level":2,"score":0.4978306293487549},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49175551533699036},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.45100489258766174},{"id":"https://openalex.org/C102094743","wikidata":"https://www.wikidata.org/wiki/Q133871","display_name":"Normal distribution","level":2,"score":0.44856545329093933},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4357427656650543},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.43235430121421814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2662283182144165},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19144853949546814},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1270994246006012},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isqed.2009.4810271","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isqed.2009.4810271","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 10th International Symposium on Quality of Electronic Design","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321040","display_name":"National Science Council","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1977055509","https://openalex.org/W2006447899","https://openalex.org/W2008066920","https://openalex.org/W2075245708","https://openalex.org/W2103323734","https://openalex.org/W2104785869","https://openalex.org/W2112662324","https://openalex.org/W2120860882","https://openalex.org/W2126564504","https://openalex.org/W2158750015","https://openalex.org/W2163262735","https://openalex.org/W2165740397","https://openalex.org/W2316835848","https://openalex.org/W3150180620","https://openalex.org/W4251870584","https://openalex.org/W6641789886","https://openalex.org/W6641884055","https://openalex.org/W6669570333","https://openalex.org/W6675376406","https://openalex.org/W6678664461"],"related_works":["https://openalex.org/W4251264894","https://openalex.org/W3192656014","https://openalex.org/W1569991298","https://openalex.org/W2160859600","https://openalex.org/W3092420867","https://openalex.org/W2115729972","https://openalex.org/W2042032654","https://openalex.org/W2158291854","https://openalex.org/W2123535323","https://openalex.org/W2165340891"],"abstract_inverted_index":{"Statistical":[0],"static":[1],"timing":[2,22,29,39,112,134],"analysis":[3],"(SSTA)":[4],"is":[5,36],"indispensable":[6],"for":[7,38,43],"nanometer":[8],"manufacturing":[9],"under":[10,45],"process":[11,14,46],"variability.":[12],"The":[13],"variations":[15],"cause":[16],"significant":[17],"uncertainty":[18],"in":[19,57,107],"VLSI":[20],"circuit":[21],"and":[23,28,41,64,79,96,109,136,142],"this":[24,101],"makes":[25],"yield":[26,139],"control":[27],"verification":[30],"a":[31,72],"very":[32],"difficult":[33],"challenge.":[34],"SSTA":[35,53],"suitable":[37],"estimation":[40],"design":[42],"manufacturability":[44],"variation.":[47],"However,":[48],"most":[49],"of":[50],"the":[51,89,115,127,133,138],"existing":[52],"techniques":[54],"have":[55,114],"difficulty":[56],"keeping":[58],"closed-form":[59],"expressions":[60],"after":[61,76],"max":[62,77],"operations":[63,66,78],"sum":[65,80],"on":[67],"variation":[68],"sources.":[69],"For":[70],"computing":[71],"converged":[73],"statistical":[74],"form":[75,95],"operations,":[81],"we":[82],"propose":[83],"an":[84],"analytical":[85],"approach":[86,131],"which":[87],"innovates":[88],"concept":[90],"given":[91],"by":[92],"first-order":[93],"canonical":[94],"skew-normal":[97,116],"distribution":[98,117],"to":[99,126],"solve":[100],"problem.":[102],"These":[103],"derived":[104],"results":[105,122],"are":[106],"closedform":[108],"precise":[110],"when":[111],"sources":[113],"or":[118],"normal":[119],"distribution.":[120],"Experimental":[121],"show":[123],"that,":[124],"compared":[125],"Monte-Carlo":[128],"simulation,":[129],"our":[130],"estimates":[132],"constraint":[135],"predicts":[137],"within":[140],"1.5%":[141],"0.2%":[143],"error,":[144],"respectively.":[145]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}