{"id":"https://openalex.org/W2077503091","doi":"https://doi.org/10.1109/tr.2011.2170259","title":"A Proposed Measure of Residual Life of Live Components of a Coherent System","display_name":"A Proposed Measure of Residual Life of Live Components of a Coherent System","publication_year":2011,"publication_date":"2011-10-14","ids":{"openalex":"https://openalex.org/W2077503091","doi":"https://doi.org/10.1109/tr.2011.2170259","mag":"2077503091"},"language":"en","primary_location":{"id":"doi:10.1109/tr.2011.2170259","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2011.2170259","pdf_url":null,"source":{"id":"https://openalex.org/S87725633","display_name":"IEEE Transactions on Reliability","issn_l":"0018-9529","issn":["0018-9529","1558-1721"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Reliability","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/A5039956503","display_name":"N. Balakrishnan","orcid":"https://orcid.org/0000-0001-5842-8892"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Narayanaswamy Balakrishnan","raw_affiliation_strings":["Department of Mathematics and Statistics, McMaster University, Hamilton, Canada","Dept. of Math. & Stat., McMaster Univ., Hamilton, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McMaster University, Hamilton, Canada","institution_ids":["https://openalex.org/I98251732"]},{"raw_affiliation_string":"Dept. of Math. & Stat., McMaster Univ., Hamilton, ON, Canada","institution_ids":["https://openalex.org/I98251732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006965209","display_name":"Majid Asadi","orcid":"https://orcid.org/0000-0002-9259-0524"},"institutions":[{"id":"https://openalex.org/I39268498","display_name":"University of Isfahan","ror":"https://ror.org/05h9t7759","country_code":"IR","type":"education","lineage":["https://openalex.org/I39268498"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Majid Asadi","raw_affiliation_strings":["Department of Statistics, University of Isfahan, Isfahan, Iran","Dept. of Stat., Univ. of Isfahan, Isfahan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Isfahan, Isfahan, Iran","institution_ids":["https://openalex.org/I39268498"]},{"raw_affiliation_string":"Dept. of Stat., Univ. of Isfahan, Isfahan, Iran","institution_ids":["https://openalex.org/I39268498"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3114,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.88950825,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"61","issue":"1","first_page":"41","last_page":"49"},"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":0.9983999729156494,"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":0.9921000003814697,"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/computer-science","display_name":"Computer science","score":0.39050671458244324},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3395001292228699}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39050671458244324},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3395001292228699}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tr.2011.2170259","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tr.2011.2170259","pdf_url":null,"source":{"id":"https://openalex.org/S87725633","display_name":"IEEE Transactions on Reliability","issn_l":"0018-9529","issn":["0018-9529","1558-1721"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Reliability","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1993711389","https://openalex.org/W2004567334","https://openalex.org/W2010026686","https://openalex.org/W2027855608","https://openalex.org/W2028376965","https://openalex.org/W2058588258","https://openalex.org/W2062712414","https://openalex.org/W2083215154","https://openalex.org/W2085988852","https://openalex.org/W2093380938","https://openalex.org/W2121230460","https://openalex.org/W2122188798","https://openalex.org/W2159469674","https://openalex.org/W4237073223","https://openalex.org/W4245777296"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"The":[0],"concept":[1],"of":[2,5,18,29,32,37,46,53,88,130,133,136,153],"the":[3,13,19,26,30,44,47,50,54,89,110,113,128,137,154],"signature":[4,51],"a":[6,33,60,82,122],"coherent":[7,34,83],"system":[8,35,55,84,114],"is":[9,56,115],"useful":[10],"to":[11,58,126],"study":[12],"stochastic":[14,149],"and":[15,150],"aging":[16,151],"properties":[17,152],"system.":[20],"Let":[21],"X1m,":[22],"X2:n,":[23],"\u22ef":[24,95],"Xn:ndenote":[25],"ordered":[27],"lifetimes":[28],"components":[31,135],"consisting":[36],"n":[38],"i.i.d":[39],"components.":[40],"If":[41],"T":[42],"denotes":[43],"lifetime":[45],"system,":[48,138],"then":[49],"vector":[52],"defined":[57],"be":[59],"probability":[61,129],"vectors":[62],"=":[63,72,75,92,105,142],"(s1,":[64,93],"s2,":[65,94],"\u22ef,":[66,107,146],"sn)":[67],"such":[68],"that":[69,112],"si=":[70],"P(T":[71],"Xi:n),":[73],"i":[74,143],"1,":[76],"2,":[77],"\u22ef,n.":[78],"Here":[79],"we":[80,120],"consider":[81],"with":[85],"sig-":[86],"nature":[87],"form":[90],"s":[91],"Si,":[96],"0":[97],"...":[98],",":[99],"0),":[100],"where":[101],"sk>;":[102],"0,":[103],"k":[104,141],"1,2,":[106],"i.":[108],"Under":[109],"condition":[111],"working":[116],"at":[117],"time":[118,123],"t,":[119],"propose":[121],"dependent":[124],"measure":[125,156],"calculate":[127],"residual":[131],"life":[132],"live":[134],"i.e.,":[139],"Xk:n,":[140],"+":[144],"1":[145],"n.":[147],"Several":[148],"proposed":[155],"are":[157],"explored.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
