{"id":"https://openalex.org/W4200463526","doi":"https://doi.org/10.3390/math10010035","title":"Inference for the Process Performance Index of Products on the Basis of Power-Normal Distribution","display_name":"Inference for the Process Performance Index of Products on the Basis of Power-Normal Distribution","publication_year":2021,"publication_date":"2021-12-23","ids":{"openalex":"https://openalex.org/W4200463526","doi":"https://doi.org/10.3390/math10010035"},"language":"en","primary_location":{"id":"doi:10.3390/math10010035","doi":"https://doi.org/10.3390/math10010035","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math10010035","pdf_url":"https://www.mdpi.com/2227-7390/10/1/35/pdf?version=1640251530","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/10/1/35/pdf?version=1640251530","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100694504","display_name":"Jianping Zhu","orcid":"https://orcid.org/0000-0001-6057-8072","observed_orcids":["https://orcid.org/0000-0001-6057-8072"]},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianping Zhu","raw_affiliation_strings":["Data Mining Research Center, Xiamen University, Xiamen 361005, China","School of Management, Xiamen University, Xiamen 361005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Mining Research Center, Xiamen University, Xiamen 361005, China","institution_ids":["https://openalex.org/I191208505"]},{"raw_affiliation_string":"School of Management, Xiamen University, Xiamen 361005, China","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103175235","display_name":"Hua Xin","orcid":"https://orcid.org/0000-0001-6292-010X","observed_orcids":["https://orcid.org/0000-0001-6292-010X"]},"institutions":[{"id":"https://openalex.org/I921716337","display_name":"Northeast Petroleum University","ror":"https://ror.org/03net5943","country_code":"CN","type":"education","lineage":["https://openalex.org/I921716337"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hua Xin","raw_affiliation_strings":["School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China","institution_ids":["https://openalex.org/I921716337"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027391283","display_name":"Chenlu Zheng","orcid":"https://orcid.org/0000-0001-6024-1541","observed_orcids":["https://orcid.org/0000-0001-6024-1541"]},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chenlu Zheng","raw_affiliation_strings":["Data Mining Research Center, Xiamen University, Xiamen 361005, China","School of Management, Xiamen University, Xiamen 361005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Mining Research Center, Xiamen University, Xiamen 361005, China","institution_ids":["https://openalex.org/I191208505"]},{"raw_affiliation_string":"School of Management, Xiamen University, Xiamen 361005, China","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078659099","display_name":"Tzong\u2010Ru Tsai","orcid":"https://orcid.org/0000-0001-6548-7663","observed_orcids":["https://orcid.org/0000-0001-6548-7663"]},"institutions":[{"id":"https://openalex.org/I107470533","display_name":"Tamkang University","ror":"https://ror.org/04tft4718","country_code":"TW","type":"education","lineage":["https://openalex.org/I107470533"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Tzong-Ru Tsai","raw_affiliation_strings":["Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan"],"raw_orcid":"https://orcid.org/0000-0001-6548-7663","affiliations":[{"raw_affiliation_string":"Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan","institution_ids":["https://openalex.org/I107470533"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027391283","https://openalex.org/A5078659099"],"corresponding_institution_ids":["https://openalex.org/I107470533","https://openalex.org/I191208505"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1728},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1728},"fwci":0.458,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.71838901,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"10","issue":"1","first_page":"35","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.98580002784729,"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"}},"topics":[{"id":"https://openalex.org/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.98580002784729,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.013100000098347664,"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/T13500","display_name":"Probability and Statistical Research","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/process-performance-index","display_name":"process performance index","score":1.0},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"statistical inference","score":0.8080000281333923},{"id":"https://openalex.org/keywords/maximum-likelihood-estimation","display_name":"maximum likelihood estimation","score":0.9179999828338623},{"id":"https://openalex.org/keywords/fisher-information-matrix","display_name":"Fisher information matrix","score":0.9229999780654907},{"id":"https://openalex.org/keywords/confidence-intervals","display_name":"confidence intervals","score":0.8849999904632568},{"id":"https://openalex.org/keywords/parametric-bootstrap","display_name":"parametric bootstrap","score":0.8619999885559082}],"concepts":[{"id":"https://openalex.org/C122048520","wikidata":"https://www.wikidata.org/wiki/Q2913954","display_name":"Percentile","level":2,"score":0.626321017742157},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.5993568897247314},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.5257623791694641},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.515012264251709},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4895976185798645},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4800170958042145},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4674813151359558},{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.45182910561561584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42768755555152893},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4108128547668457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38268333673477173},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36141449213027954},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12167537212371826}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/math10010035","doi":"https://doi.org/10.3390/math10010035","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math10010035","pdf_url":"https://www.mdpi.com/2227-7390/10/1/35/pdf?version=1640251530","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:tkuir.lib.tku.edu.tw:987654321/121820","doi":null,"is_oa":false,"landing_page_url":"https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/121820","pdf_url":null,"source":{"id":"https://openalex.org/S4406922698","display_name":"Tamkang University Institutional Repository (TKUIR)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"pmh:oai:RePEc:gam:jmathe:v:10:y:2021:i:1:p:35-:d:709271","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/10/1/35/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:76dfbe2e6494401ebad2eef177a3b0ca","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/76dfbe2e6494401ebad2eef177a3b0ca","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,"listed_in":[],"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":"Mathematics, Vol 10, Iss 1, p 35 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math10010035","doi":"https://doi.org/10.3390/math10010035","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math10010035","pdf_url":"https://www.mdpi.com/2227-7390/10/1/35/pdf?version=1640251530","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200463526.pdf","grobid_xml":"https://content.openalex.org/works/W4200463526.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W94194614","https://openalex.org/W1270368887","https://openalex.org/W1576240871","https://openalex.org/W1963626520","https://openalex.org/W1965449643","https://openalex.org/W2000159326","https://openalex.org/W2030476958","https://openalex.org/W2039002947","https://openalex.org/W2050226735","https://openalex.org/W2051516459","https://openalex.org/W2088038447","https://openalex.org/W2094228883","https://openalex.org/W2112326444","https://openalex.org/W2118777047","https://openalex.org/W2154890155","https://openalex.org/W2573107880","https://openalex.org/W2733015537","https://openalex.org/W2806472663","https://openalex.org/W2904568489","https://openalex.org/W2905934482","https://openalex.org/W2954652639","https://openalex.org/W3106889297"],"related_works":["https://openalex.org/W2789613218","https://openalex.org/W3199147077","https://openalex.org/W4323662770","https://openalex.org/W7112140364","https://openalex.org/W2379852495","https://openalex.org/W6939770577","https://openalex.org/W7164862446","https://openalex.org/W2046652816","https://openalex.org/W3118695577","https://openalex.org/W4392852732"],"abstract_inverted_index":{"The":[0,17,62,103],"process":[1,150],"performance":[2,133],"index":[3],"(PPI)":[4],"can":[5],"be":[6],"a":[7],"simple":[8],"metric":[9],"to":[10,94,114,130],"connect":[11],"the":[12,20,27,38,46,58,68,76,85,89,96,100,120,132,135,141,145,148],"conforming":[13],"rate":[14],"of":[15,19,49,87,99,134,144],"products.":[16],"properties":[18],"PPI":[21,59,72],"have":[22],"been":[23],"well":[24],"studied":[25],"for":[26,57,67,119,153],"normal":[28],"distribution":[29],"and":[30,41,71,75,107,123],"other":[31],"widely":[32],"used":[33,152],"lifetime":[34],"distributions,":[35],"such":[36],"as":[37],"Weibull,":[39],"Gamma,":[40],"Pareto":[42],"distributions.":[43],"Assume":[44],"that":[45],"quality":[47],"characteristic":[48],"product":[50],"follows":[51],"power-normal":[52],"distribution.":[53],"Statistical":[54],"inference":[55],"procedures":[56],"are":[60,112,128],"established.":[61],"maximum":[63],"likelihood":[64],"estimation":[65],"method":[66],"model":[69,101,121],"parameters":[70,122],"is":[73,81,151],"investigated":[74],"exact":[77,90],"Fisher":[78,91],"information":[79,92],"matrix":[80,93],"derived.":[82],"We":[83],"discuss":[84],"drawbacks":[86],"using":[88],"obtain":[95,115],"confidence":[97,117],"interval":[98],"parameters.":[102],"parametric":[104],"bootstrap":[105,108],"percentile":[106,110],"bias-corrected":[109],"methods":[111],"proposed":[113,136],"approximate":[116],"intervals":[118],"PPI.":[124],"Monte":[125],"Carlo":[126],"simulations":[127],"conducted":[129],"evaluate":[131],"methods.":[137],"One":[138],"example":[139],"about":[140],"flow":[142],"width":[143],"resist":[146],"in":[147],"hard-bake":[149],"illustration.":[154]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2021-12-31T00:00:00"}