Reliability Analysis for nnon-independent and Non-Identical Series Systems Using Masked Data

Transcription

1 Joua of Psa Sees Vo ISS: : wwwasaaa/oua eab ass fo o-iepee a o-iea Sees Sses Us Mase Daa Fa Za a Y- S Depae of ppe Maeas owese Poea Ues X'a 77 P a s@wpueu eee p 9; aepe Ju 7 9 S ase o e ase aa e eab of o-epee a o-ea sees sse subee o soues of faa sos s esae We e e paaee esaos as we as eab esaos b aop aes appoa so a uea suao eape s e o usae ow oe a uze e eo o ae e paa pobe Kewos:ase aa;o-epee sse;aes appoa;eab aass; so oe Iouo I eab aass esaos of opoes eabes ae ofe obae ou e aass of sse fe aa Ue ea usaes s sse fe aa oas e faue e ao w foao o e ea opoe aus e sse faue Howee soe ases e ea opoe esposbe fo e sse faue a o be efe ue o e os of faue aoss a es e osas e esue aue of soe opoe a so o Isea s assue a e opoe auses e sse faue beos o soe subse of e opoes w osee poea esposbe fo e faue I s ase e ause of faue s ase Vaous sues use ase aa o esae e uow paaees a sse M Saa [] osee e au eoo esaosme a aes esaos of epoea opoesa e pesee ME of uow paaees of Webu faue ae opoes fo e ases of wo-opoe a ee-opoe sees sses [] M Saa a e H E-assou usse e ase of paae sses of opeea epoea opoes [3] Mos auos assue a opoes a sse us be epee oe o

2 Fa Za a Y- S osu oes Howee soe ases s ffu o eee e epeee Moeoe ee ess soe epee a osae eao bewee us e ofe us s poa a eafu o suss e eab of o-epee sees sse us ase aa ee seea auos use so oe o esae e paaees o-epee sees sse Su as Gabs a Saa [5] a Saa [6] obae esaos of soe eab easues fo sees a paae sses w wo o-epee a o-ea opoes; wa E-Goa [7] a wa E-Goa a Saa [9] eue aes esaos fo e paaees ue a wo a ee o-epee a o-ea opoe sees sse Hop Wu a Guofe Za [] pesee a aesa appoa fo esa e uow paaees a o-epee a o-ea sees sse subee o soues of faa sos Howee ee s e e sasa aass of o-epee sse ue ase aa a pese I s pape we suss ow o use e ase aa of sses o aaze e sse a opoe eabes of o-epee a o-ea sees sse subee o soues of faa sos w was popose [] Suao sues ae aso oe oe o epa ow oe a uze e eoea esus obae eoo fuo Hop Wu a Guofe Za [] osue e aeaa oe of o-epee a o-ea sees sse e oe s esbe as foows: e sse osss of opoes oee sees ee ae epee soues of faa sos ee o e sse so fo e soue esos e opoe we e so fo soue esos a e opoes of e sse so fo soue ous a a ao e sau e sbuo fuo of U s e foow fo: P U ep{ } > ssu eoes e fee of opoe e U U o o e epeee of e sos e eab fuo of opoe s e foow fo: ; P > P U U > P U > U > P U > P U > ep{ [ ]}

3 eab aass fo o-epee a o-ea sees sses 3 wee > e sse fee sa a sasfes a e e e sua fuo of e sse s e b a ; P a > ep{ } > ssu a ea sses of e esbe pe ae pu o e fe esa e es s eae f a e sses ae fae e S eoe e se of opoes a possb ause e sse o fa a e s eoe e eaze se fo S e e obsee aa s s s I s ep of e ue ause of faue of sse we S { } wee S { } epeses e a opoes ae faue O e oe a e ue ause of faue s ase we S { } S e K eoe e e of e opoe aua aus e sse o fa s fo e sse e eoo fuo 3 of s s: P s P K P s K wee P s K s e as pobab a beoes f s Hee we suppose a e as pobab s epee w e ause of faue a s fo e fe s P S s K P S s K fo a s eefoe we e e spfe eoo fuo: θ aa [ P s ] [ P K ] s s wee θ eoes e uow paaees a aa eoes e obsee aa e be e obsee sse e o faue we S {} I eas a s e ube of e obseaos we {} S e be e obsee sse e o faue we e aus sse faue s ase a s eoes e ube of e obseaos we S S e eoo fuo s ase eues o s { } P K s S { P K P K }

4 Fa Za a Y- S 4 oe a a } ep{ U U U P K P > > < < Sa } ep{ K P e eoo fuo s ase beoes ] ] ] wee pp e boa epaso a be we as: wee a be we as: wee a!!!!!!!!! us e eoo fuo a be we as e foow fo: ] ; wee

5 eab aass fo o-epee a o-ea sees sses 5 a 3 aes aass I s seo we w use aesa appoa o esae e uow paaees a e eab fuos of opoes a sse e foow assupos w be osee ae epee w ea oe ae aa po sbuos w ow paaees a I eas a 3 e oss ue we e eo of uow paaees ae esae b ae a quaa a s e oss fuo s ; Us e assupo a e o po pobab es fuo pf of sa aes e foow fo: e e ow we ae ea o pese a eoe a es e o poseo pf of e e obsee aa eoe Ge e obsee aa a ue assupos a e o poseo pf of s aa wee ] ] Poof Us e aes eoe e o poseo of e e obsee aa s eae o e foow eao aa aa /

6 Fa Za a Y- S 6 wee Θ Θ Θ Θ aa ] ] ooa e aa poseo pf of e e obsee aa s aa ] aa ] wee } }/{ { Poof e poof of s ooa a be eae b ea e o poseo pf of e e obsee aa oe a aabes espee ea e oe of e aa poseo pf of ae e e foow fo: / µ / µ wee a Poof e poof of s ea a be eae as foows: e poseo oe of ae efe as e poseo epeao of a s µ µ Subsu e poseo pf of o ese fouas a a soe auus aaees oe a eas ea e poof eoe Ue e assupo - 3: e aes esaos of ae espee µ µ

7 eab aass fo o-epee a o-ea sees sses 7 e u poseo s assoae w e aes esaos ae π / aa / / aa / π Poof e poof of s eoe epes o e assupo 3 e aes esaos of a e assoae u poseo s ae efe espee as e poseo epeao a poseo aae of E aa µ E aa µ ae π aa Va aa µ µ π aa Va aa µ µ Subsu e oe of e poseo pf of oe a opee e poof of eoe e foow eoes e e aes esaos a e assoae u poseo s fo e aue of eab fuos of opoes a sse a a spefe sso e eoe 3 Ue e assupos -3: e aes esao fo e eab fuo of opoe s E aa / e u poseo s assoae w e aes esao s Ψ / [ / ] wee

8 Fa Za a Y- S 8 M w w w } \{ } { M w Poof Ue e assupo 3 e aes esao fo e aue of eab of opoe efe as e epeao of wee } / ] [ ep{ ; us aa E ] ] ] ] M M e u poseo s assoae w sa Ψ s efe as e poseo aae of ae ] [ ] [ aa E aa E Ψ Sa o aa E we a eas oba ] [ aa E us oe a eas opee e poof eoe 4 Ue e assupos -3: D e aes esao fo e eab fuo of sse s

9 eab aass fo o-epee a o-ea sees sses 9 a a a E aa / D e u poseo s assoae w e aes esao s a Ψ / [ / ] a a a wee a / / Poof e poof s sa o a of eoe 3 4 uea Suao We sow s seo ow oe a app e peous eoea esus obae s seo s eoe o pese uea esus base o a ae suao su We ae suao of a wo opoes oee sees sse I s assue e suao a a e po sbuos of ae a 5 espee I s assue s suao a sses wee pu o e fe es e as ee s 5% e e fee of ea sse a e se of opoes a a ause e sse faue wee obsee e suae aa ae pesee abe ase o e suao aa e abe e aes esaos of e paaees ae opue e spefe sso e s 5 we ose e eab Fue e peeae eo assoae w e esaos s opue e peeae eo assoae w e esao θ of θ s e b PE θ θ / θ % e obae esus ae pesee abe θ abe Suae sse fee aa

10 Fa Za a Y- S Sse Obseao S Sse Obseao S abe aes esaos w peeae eo Paaee 3 3 a ue aue Esao PE oweees:s wo s suppoe b e aoa aua See Fouao of a o a e aua See Fouao of Euao Depae of Saa Poe o 3JK65 EFEEES M Saa eab esao of opoes fo ase sse fe aa[j] eab Eee & Sse Safe M Saa Esao of sse opoes eabes us ase aa [J] ppe Maeas a opuao M Saa e H E-assou Esao of opoes eab a paae sse us ase sse fe aa[j] ppe Maeas a opuao Kuo ae You Ya aesa eab oe fo ase sse fee aa[j] Sass & Pobab ees F Gabs M Saa aesa esao of wo o-epee opoes epoea sees sse[j] ppe Maeas a opuao M Saa aesa esao eab eo[d] Gas Ues Isue of Maeas Gas Poa E-Goa aesa esao a e paaees wo o-epee opoe sees sse w epee e faue ae J pp Ma opu

11 eab aass fo o-epee a o-ea sees sses 8 E-Goa aes esao of paaees a ee o-epee opoe sees sse w e epee faue ae[j] pp Ma opu E-Goa M Saa Esao of e paaees a ee o-epee opoe sees sse subee o soues of sos [J] pp Ma opu6 5:9 4 Hop Wu Guofe Za aesa esao of e paaees o-epee a o-ea sees sse[j] ppe Maeas a opuao