• Tidak ada hasil yang ditemukan

In the present paper, in order to apply these problems, the best or most effectively, a particular model is introduced

N/A
N/A
Protected

Academic year: 2024

Membagikan "In the present paper, in order to apply these problems, the best or most effectively, a particular model is introduced"

Copied!
8
0
0

Teks penuh

(1)

7KH$SSOLFDWLRQRI5HGXQGDQW8QLWVDQG$OWHUQDWLYH 'HVLJQVWR5HOLDELOLW\2SWLPL]DWLRQ

0RKDPPDG0RKDPPDGL1DMDIDEDGLDQG60DQVRXUL

'HSDUWPHQWRI&RPSXWHU6FLHQFH3D\DPH1RRU8QLYHUVLW\318 32%R[7HKUDQ,UDQ

(PDLOPPQDMDIDEDGL#SQXDFLU

'HSDUWPHQWRI(QJOLVK/DJXQDJH7HDFKLJ 1DMDIDEDG%UDQFK,VODPLF$]DG8QLYHUVLW\1DMDIDEDG,UDQ

(PDLOVDUDPDQVRXUL#SKXLDXQDFLU

$%675$&7

Broadly speaking, one of the major criteria for an engineering system implementation is the reliability of that system. The reliability coefficient, owing to the increasing advancement of sciences and technology, intricateness of today’s engineering systems and thus, the impact of their unreliable behavior on various areas, on one side, and the tendency for the evaluation of this coefficient in the engineering systems and the need to improve it, on the other side, has gotten of a great significance. In order for making the best or most effective use of these systems, diverse methods are applied to acquire or produce highly reliable goods. Highly capable in optimizing the engineering systems, genetic algorithms are among the most commonly utilized methods. In the present paper, in order to apply these problems, the best or most effectively, a particular model is introduced.

.H\ZRUGV5HOLDELOLW\RSWLPL]DWLRQHYROXWLRQDU\DOJRULWKPDOWHUQDWLYHGHVLJQRSWLPL]DWLRQSUREOHP 0DWKHPDWLFV6XEMHFW&ODVVLILFDWLRQ

&RPSXWLQJ&ODVVLILFDWLRQ6\VWHP*

,1752'8&7,21

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

SURGXFWWRWKHPRVWLQWULFDWHV\VWHPVLQDQ\PRGHUQFRPPXQLW\'LVWXUEDQFHVDWYDULRXVOHYHOVZRXOG EHUHVXOWHGIURPWKHIDLOXUHRIWKHSURGXFWVDQGV\VWHPVOLNHO\WREHUHJDUGHGDVDVHULRXVWKUHDWWRWKH ISSN 0973-1377 (Print), ISSN 0973-7545 (Online)

Copyright © 2017 by International Journal of Applied Mathematics and Statistics

(2)

FRPPXQLW\DQGWKHHQYLURQPHQW,QFRQVHTXHQFHWKHSURGXFWVDQGV\VWHPVDUHGHVLUHGE\WKHXVHUV LHWKHSHRSOHRIWKHVRFLHW\LQWRWDOWREHUHOLDEOHVDWLVIDFWRU\DQGVDIH7KHUHIRUHWKHH[WHQWWRZKLFK DV\VWHPRYHULWVIXWXUHZRUNOLIHZRXOGEHUHOLDEOHDQGVDIHLVVXEVWDQWLDOO\TXHVWLRQHG

,QDEURDGVHQVHRQHRIWKHV\VWHPLPSOHPHQWDWLRQFULWHULDLVWKHUHOLDELOLW\'XHWRPRUHFRPSOH[LW\RI WKHV\VWHPVWKHLQIOXHQFHRIWKHLUXQUHOLDEOHEHKDYLRULQYDULHGDUHDVKDVJRWWHQPRUHVHULRXV6LPLODUO\

WKH WHQGHQF\ IRU WKH HYDOXDWLRQ RI WKH UHOLDELOLW\ FRHIILFLHQW RI WKH V\VWHPV DQG WKH QHHG IRU WKH LPSURYHPHQWRIWKLVFRHIILFLHQWKDYHEHHQUHPDUNDEO\UHJDUGHG&RQVHTXHQWO\WKHUHVHDUFKHUVDQG PDQDJHUV DWWHPSW WR XWLOL]H WKH V\VWHPV¶ UHOLDELOLW\ PRVW HIILFLHQWO\ HPSOR\LQJ GLIIHUHQW PHWKRGV H[SDQGHG WR D JUHDWHU H[WHQW ZLWK WKH DGYDQFHPHQW LQ VFLHQFHV DQG FRPSXWHU XVH VXFK DV 0RKDPPDGL DQG 0DQVRXUL :DQJ HW DO DQG $QWRQ\RYi HW DO 2QH RI WKH RSWLPL]DWLRQ PHWKRGV PRGHOHG RQ QDWXUH ZKLOH XWLOL]LQJ FRPSXWHU WRROV LV WKH JHQHWLF DOJRULWKPV

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

WRGRGHHSUHVHDUFKRQLWVGLIIHUHQWDVSHFW7KHUHIRUHWKHREMHFWLYHRIWKHSUHVHQWZRUNSDSHULVWR LQYHVWLJDWHWKHXVHRIUHGXQGDQWXQLWVDQGDOWHUQDWLYHGHVLJQVLQUHOLDELOLW\RSWLPL]DWLRQDQHJOHFWHG DUHDWRWKHEHVWRIUHVHDUFKHUVNQRZOHGJH

7RDFFRPSOLVKWKLVDLPDQGWRUHVSRQGWRDUHFHQWFDOOIRUUHVHDUFKWRGRWKLVSDSHUHPSOR\VJHQHWLF DOJRULWKPV WR RSWLPL]H D UHOLDELOLW\ SUREOHP ZKRVH REMHFWLYH IXQFWLRQ DQG UHVWULFWLRQV DUH IX]]\ ,W H[DPLQHVWKHUHOLDELOLW\VWUXFWXUHV1H[WWKHJHQHUDOWUHQGDQGXVHGJHQHWLFDOJRULWKPVRSHUDWRUVDUH PHQWLRQHG(YHQWXDOO\ZHDWWDLQWKHRSWLPXPVROXWLRQRIWKHREMHFWLYHIXQFWLRQ$GGLWLRQDOO\YLDPXOWLSOH IDLOXUHPRGHOVWKHRSWLPL]DWLRQPRGHORIUHOLDELOLW\LVLQYHVWLJDWHG

237,0,=$7,212)5(/,$%,/,7<

6XSSRVHWKDWWKHV\VWHPLQFOXGHVܰVXEV\VWHP5HODWHGWRHYHU\VXEV\VWHPWKHUHDUHYDULRXVRSWLRQV

RI GHVLJQ DOWHUQDWLYHV WKDW FDQ EH DSSOLHG E\ WKH V\VWHP GHVLJQHU WR VDWLVI\ WKH UHTXLUHPHQWV RI UHOLDELOLW\:HFRQVLGHUWKHIROORZLQJH[DPSOH

ƒš ܴሺ݉Ƕߙሻ ൌ ς ൫ͳ െ ൫ͳ െ ܴଵସ௜ୀଵ ሺߙሻ൯൯ሺͶǤͳሻ ݏǤ ݐǤܥሺ݉Ǥ ߙሻ ൌ σଵସ ܥ

௜ୀଵ ሺߙሻ ൈ ݉൑ͳ͵ͲሺͶǤʹሻ

ܹሺ݉Ǥ ߙሻ ൌ σଵସ ܹ

௜ୀଵ ሺߙሻ ൈ ݉൑ͳ͹ͲሺͶǤ͵ሻ

(3)

ͳ ൑݉൑ ݑሺͶǶͶሻ

ͳ ൑ߙ൑ ߚሺͶǶͷሻ

݉൒ Ͳܽ݊݀ߙ൒ Ͳܽݎ݁݅݊ݐ݁݃݁ݎǤ݅ ൌ ͳǤʹǤήήήǤ ܰሺͶǤ͸ሻ

,QZKLFKߙLVWKHVLJQIRUWKHGHVLJQDOWHUQDWLYHVDFFHVVLEOHWRWKH݅WKVXEV\VWHP݉VKRZVWKHHTXDO XQLWV XVHG LQ UHGXQGDQF\ IRU WKH݅WK VXEV\VWHPݑ LV WKH XSSHU ERXQG RI UHGXQGDQF\ IRU WKH݅WK VXEV\VWHPߚLVWKHXSSHUERXQGRIDOWHUQDWLYHGHVLJQIRUWKH݅WKVXEV\VWHP7KHSUREOHPWKDWUDLVH KHUHLVKRZWRGHFLGHZKLFKDOWHUQDWLYHWRFKRRVHDQGWKHQWRGHWHUPLQHKRZPDQ\XQQHFHVVDU\XQLWV DUHQHHGHGWREHXVHGLQRUGHUWRUHDFKWKHKLJKHVWUHOLDELOLW\ZKLOHWKHRYHUDOOV\VWHPFRVWDQGZHLJKW DUHNHSWLQWKHDOORZDEOHDPRXQWV

'HWHUPLQHZKLFKDOWHUQDWLYHWRVHOHFWDQGWKHQGHFLGHKRZPDQ\UHGXQGDQWXQLWVWRXVHLQRUGHUWR DFKLHYH WKH JUHDWHVW UHOLDELOLW\ ZKLOH NHHSLQJ WKH WRWDO V\VWHP FRVW DQG ZHLJKW ZLWKLQ WKH DOORZDEOH DPRXQWV'DWDDUHVKRZQLQ7DEOH

*(1(7,&$/*25,7+0$1'180(5,&$/(;$03/(

*HQHWLFDOJRULWKPVDUHDEUDQFKRIVRFLDORSWLPL]DWLRQWHFKQLTXHVLQZKLFKELRORJLFDOV\VWHPVDQGWKHLU

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

5HSUHVHQWDWLRQRI&KURPRVRPHDQG1XPHULFDO([DPSOH$JHQHLVGHILQHGDVDQRUGHUHGFRXSOH RIGHVLJQDOWHUQDWLYHVߙ௞௜DQGUHGXQGDQWXQLWV݉௞௜VKRZQDVIROORZV

࢑࢏ൌ ሺࢻ࢑࢏Ǥ ࢓࢑࢏

(4)

7DEOH5HGXQGDQW8QLWVDQG$OWHUQDWLYH'HVLJQ VXEV\VWHP 'HVLJQ$OWHUQDWLYH

L 5 5 5 5

ൌ ૝ࢌ࢕࢘࢏ ൌ ૚Ǥ ૜Ǥ ૟Ǥ ૢǤ ૚૛Ǥ ૚૝Ǥ ࢼൌ ૜ ࢌ࢕࢘ ࢏ ൌ ૛Ǥ ૝Ǥ ૞Ǥ ૠǤ ૡǤ ૚૙Ǥ ૚૚Ǥ ૚૜Ǥ ࢇ࢔ࢊ࢛ൌ ૞׊࢏

:KHUHWKHVXEVFULSW݇LVWKHLQGH[RIFKURPRVRPHWKHJHQHEHORQJVWRDQGWKHVXEVFULSW ݅VKRZWKH

VXEV\VWHP݅$FKURPRVRPHLVDQRUGHUHGOLVWRIVXFKJHQHVDVIROORZV ݒൌ ሾݒ௞ଵݒ௞ଶήήήݒ௞ଵସሿ 7KHUHSUHVHQWDWLRQFDQEHUHYLVHGDVIROORZV

ݒൌ ሾሺߙ௞ଵǤ ݉௞ଵሻሺߙ௞ଶǤ ݉௞ଶሻήήήሺߙ௞ଵସǤ ݉௞ଵସሻሿ

,QLWLDO3RSXODWLRQ7KHLQLWLDOSRSXODWLRQRIFKURPRVRPHVLVJHQHUDWHGUDQGRPO\DVIROORZV 3URFHGXUH,QLWLDOL]DWLRQ

EHJLQ

IRUN WR݌݋݌௦௜௭௘GR IRUL WRGR ߙ௞௜ UDQGRPࢼ

݉௞௜ UDQGRP࢛

HQGݒൌ ሾሺߙ௞ଵǤ ݉௞ଵሻሺߙ௞ଶǤ ݉௞ଶሻήήήሺߙ௞ଵସǤ ݉௞ଵସሻሿ

HQGHQG

:KHUHUDQGRPQXPPHDQVWRUHWXUQDUDQGRPLQWHJHUZLWKLQWKHUDQJHሾͳǤ ݊ݑ݉ሿ/HW݌݋݌௦௜௭௘ൌ ͶWKH

UDQGRPO\JHQHUDWHGFKURPRVRPHVDUHJLYHQDVIROORZV

ݒൌ ሾሺʹǤͳሻሺͳǤͳሻሺͶǤͳሻሺͳǤͶሻሺ͵ǤͶሻሺͶǤʹሻሺʹǤͳሻሺͳǤ͵ሻሺ͵ǤʹሻሺʹǤʹሻሺʹǤͳሻሺͳǤʹሻሺ͵ǤͶሻሺ͵ǤͶሻሿ ݒൌ ሾሺʹǤʹሻሺͳǤ͵ሻሺʹǤ͵ሻሺͳǤͳሻሺʹǤͷሻሺʹǤͳሻሺͳǤͳሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤʹሻሺͳǤʹሻሺͳǤʹሻሺͳǤʹሻሺͳǤͳሻሿ ݒൌ ሾሺͳǤ͵ሻሺʹǤ͵ሻሺ͵Ǥͳሻሺ͵ǤʹሻሺʹǤ͵ሻሺͳǤͳሻሺʹǤͳሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤͶሻሺͳǤʹሻሺͳǤʹሻሺ͵ǤͶሻሺʹǤͳሻሿ ݒൌ ሾሺ͵Ǥʹሻሺ͵Ǥͳሻሺ͵Ǥ͵ሻሺʹǤʹሻሺʹǤ͵ሻሺͶǤʹሻሺ͵Ǥʹሻሺ͵Ǥ͵ሻሺ͵Ǥ͵ሻሺ͵ǤͳሻሺʹǤͳሻሺͳǤ͵ሻሺ͵ǤʹሻሺͳǤʹሻሿ

&KURPRVRPH(YDOXDWLRQ

,IWKHJHQHWLFDOJRULWKPVDUHHPSOR\HGWRDODUJHVFDOHLQWHJHURSWLPL]DWLRQSUREOHPWKHUHZLOOEHD

VHULRXVSUREOHPRILOOHJDOSURGXFWLRQRIFKURPRVRPHVZKLFKGLVUXSWWKHV\VWHPFRQVWUDLQVWKHPVHOYHV 7KLVPDMRUFKDOOHQJHLVWKHRXWFRPHRIFKURPRVRPHVSURGXFHGQRWRQO\E\WKHJHQHWLFRSHUDWLRQVEXW DOVR E\ UDQGRP LQLWLDO RSHUDWLRQV )RU WKH SUHYHQWLRQ RI WKH XQGHVLUDEOH LPSDFW RI WKHVH LOOHJDO

(5)

FKURPRVRPHVRQWKHV\VWHPFRQVWUDLQVDVDVKRUWFXWZHFDQPHHWWKHPRXWDVHYHUHSXQLVKPHQW ZKLFKFDQFDXVHWKHHYROXWLRQDU\SURFHVVEHHUDVHGIURPLOOHJDOFKURPRVRPHV7KHH[LVWHQFHRIWKH SXQLVKPHQWFUHDWHVDQLQHIIHFWLYHDQGQDUURZHGVHDUFKVSDFHDQGFDXVHVGLIILFXOWLHVILQGLQJEHWWHU FDQGLGDWHVIRUWKHJOREDORSWLPXPZLWKDQ\VHOHFWLRQPHFKDQLVP$VDUHVXOWWKHGLVWDQFHRIWKHLOOHJDO FKURPRVRPHVIURPWKHSRVVLEOHRULJLQLVGHILQHGDVDVSHFLDOPHDVXUHIXQFWLRQWRVROYHWKLVSUREOHP

%\WKHLQWHUDFWLRQRIDFRQVWDQWDQGVHYHUHSXQLVKPHQWZLWKHDFKLOOHJDOFKURPRVRPHWKHUHIXVDORI LOOHJDOFKURPRVRPHVIURPWKHHYROXWLRQDU\SURFHGXUHDQGWKHJHQHWLFVHDUFKVHOHFWLRQRIWKHRSWLPXP DWWKHERXQGDU\LVSRVVLEOH,IWKHILWQHVVHYROXWLRQHQFRPSDVVHVWKHLQIRUPDWLRQRIWKHGHJUHHRI LQIHDVLELOLW\RIWKHVROXWLRQVWKHRSWLPXPIURPERWKWKHIHDVLEOHDQGLQIHDVLEOHDUHDZLOOEHDSSURDFKHG E\WKHJHQHWLFVHDUFKZKLFKLVEURDGHUDVLVVKRZQWKHEHOORZILJXUHDVWKHPHDVXUHRILQIHDVLELOLW\

GHJUHHIRUDQLOOHJDOFKURPRVRPH

݀௞௧ൌ ە۔

ۓͲܩሺ݉Ǥ ߙሻ ൑ ܾ ሺܩሺ݉Ǥ ߙሻ െ ܾ

ܾ ݋ݐ݄݁ݎݓ݅ݏ݁

:KHUHWKHLQGH[݇VKRZVWKH݇WKFKURPRVRPHDQGݐVKRZVWKHݐWKOLPLWDWLRQDQGܶLVWRWDOQXPEHURI OLPLWDWLRQV7KHQWKHILWQHVVIXQFWLRQGHILQHGDVIROORZV

݁ݒ݈ܽሺݒሻ ൌ ܴሺ݉Ǥ ߙሻ ൭ͳ െͳ

ܶ෍ ݀௞௧

௧ୀଵ

7KHSULPDU\FKURPRVRPHVILWQHVVYDOXHVDUH

݁ݒ݈ܽሺݒሻ ൌ ͲǤ͸ͷ͸ͷ͹ͺǤ݁ݒ݈ܽሺݒሻ ൌ ͲǤͷͳ͸ͺ͵ͻǤ݁ݒ݈ܽሺݒሻ ൌ ͲǤͷ͸ͳͳͳͻǤ݁ݒ݈ܽሺݒሻ ൌ ͲǤͷ͹͵͵͸ͻ

LQIHDVLEOHDUHD

IHDVLEOHDUHD

)LJXUH*HQHWLFVHDUFKGLUHFWLRQ

5HFRPELQDWLRQ

:HXVHWKHVDPHUHFRPELQDWLRQZKLFKLVWKHEHVWDOWHUDWLRQIRUWKHSUREOHPLWKDVEHHQUHFRJQL]HGWR

EHJUHDWHUWRWUDGLWLRQDOUHFRPELQDWLRQSODQVIRUWKHFRPELQDWRULDOSUREOHP7KHILUVWWKLQJWKDWDXQLIRUP

(6)

UHFRPELQDWLRQ FUHDWHV LV D UDQGRP FURVVRYHU PDVN DQG WKHQ H[FKDQJHV DVVRFLDWHG JHQHV DPRQJ SDWHQWV DFFRUGLQJ WR WKH PDVN $ FURVVRYHU PDVN LV VLPSO\ D ELQDU\ VWULQJ ZLWK WKH VDPH VL]H RI FKURPRVRPH7KHHTXDOLW\RIHDFKELWLQWKHPDVNHVWDEOLVKHVIRUHDFKFRUUHVSRQGLQJELWLQDQRIIVSULQJ IURPZKLFKSDUHQWLWZLOOUHFHLYHWKDWELW7KLVLVVKRZQLQWKHIROORZLQJILJXUH

$UDQGRPPDVN

PDVN

3DUHQWVXQGHUPDVN

ݒ ݒ௜ଵ ݒ௜ଶ ݒ௜ଷ ݒ௜ସ ݒ௜ହ ݒ௜଺ ݒ௜଻ ݒ௜଼

ݒ ݒ௞ଵ ݒ௞ଶ ݒ௞ଷ ݒ௞ସ ݒ௞ହ ݒ௞଺ ݒ௞଻ ݒ௞଼

([FKDQJHUHODWLYHJHQHV

݋ ݒ௜ଵ ݒ௜ଶ ݒ௞ଷ ݒ௜ସ ݒ௜ହ ݒ௞଺ ݒ௞଻ ݒ௜଼

݋ ݒ௞ଵ ݒ௞ଶ ݒ௜ଷ ݒ௞ସ ݒ௞ହ ݒ௜଺ ݒ௜଻ ݒ௞଼

)LJXUHGHPRQVWUDWLRQRIWKHXQLIRUPUHFRPELQDWLRQRSHUDWLRQ

/HWWKHSUREDELOLW\RIUHFRPELQDWLRQEH݌ൌ ͲǤ͵ͷDQGOHWWKHVHTXHQFHRIUDQGRPQXPEHUVEH

,IDUDQGRPQXPEHUݎLVOHVVWKDQ݌VHOHFWUHODWLYHFKURPRVRPHIRUUHFRPELQDWLRQ,WGHPRQVWUDWHV WKDWWKHFKURPRVRPHVݒDQGݒZHUHFKRVHQIRUUHFRPELQDWLRQOLNHSDUHQWV7KHUDQGRPO\SURGXFHG SRVLWLRQVDUHDQGWKHQZHKDYH

ݒൌ ሾሺʹǤʹሻሺͳǤ͵ሻሺʹǤ͵ሻሺͳǤͳሻሺʹǤͷሻሺʹǤͳሻሺͳǤͳሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤʹሻሺͳǤʹሻሺͳǤʹሻሺͳǤʹሻሺͳǤͳሻሿ ݒൌ ሾሺͳǤ͵ሻሺʹǤ͵ሻሺ͵Ǥͳሻሺ͵ǤʹሻሺʹǤ͵ሻሺͳǤͳሻሺʹǤͳሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤͶሻሺͳǤʹሻሺͳǤʹሻሺ͵ǤͶሻሺʹǤͳሻሿ 7KHFRQVHTXHQWRIIVSULQJE\UHSODFLQJUHODWLYHJHQHVRIWKHLUSDUHQWVZLOOEH

݋ൌ ሾሺʹǤʹሻሺͳǤ͵ሻሺʹǤ͵ሻሺ૜Ǥ ૛ሻሺʹǤͷሻሺʹǤͳሻሺ૛Ǥ ૚ሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤʹሻሺͳǤʹሻሺͳǤʹሻሺ૜Ǥ ૝ሻሺͳǤͳሻሿ

݋ൌ ሾሺͳǤ͵ሻሺʹǤ͵ሻሺ͵Ǥͳሻሺ૚Ǥ ૚ሻሺʹǤ͵ሻሺͳǤͳሻሺ૚Ǥ ૚ሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤͶሻሺͳǤʹሻሺͳǤʹሻሺ૚Ǥ ૛ሻሺʹǤͳሻሿ 7KHILWQHVVYDOXHVRIWKHRIIVSULQJDUH

݁ݒ݈ܽሺ݋ሻ ൌ ͲǤͶ͸ʹͻ͹Ͳ݁ݒ݈ܽሺ݋ሻ ൌ ͲǤ͸ͷͳ͵ͳͶ

0XWDWLRQ

7KH SHUIRUPDQFH RI UDQGRP SHUWXUEDWLRQ LV 0XWDWLRQ )RU D FKRVHQ JHQH ݒ௞௜ൌ ሺߙ௞௜Ǥ ݉௞௜ሻߙ௞௜ZLOOEHH[FKDQJHGE\DUDQGRPLQWHJHUZLWKLQሾͳǤ ߚሿDQG݉௞௜ZLOOEHH[FKDQJHGE\

DUDQGRPLQWHJHUZLWKLQሾͳǤ ݑ

(7)

$VVXPHWKHSUREDELOLW\RIPXWDWLRQEH’ൌ Ͳ ή ͳLWPHDQVWKDWE\VWDQGDUGͳͶ ൈ Ͷ ൈ Ͳ ή ͳ ൌ ͷ ή ͸ELWV ZHUHFUHDWHGDQGWKUHHRIWKHPZHUHVPDOOHUWKDQWKHELWQXPEHUWKHOLVWEHORZGHPRQVWUDWHV UHODWLYHFKURPRVRPHVDQGWKHELWSRVLWLRQZLWKLQHDFKFKURPRVRPH

%LW1XPEHU FKURPRVRPH SRVLWLRQ 5DQGRP1XPEHU

7KDWLVWRVD\WKHFKURPRVRPHVݒ Ǥ ݒDQGݒZHVHOHFWHGIRUPXWDWLRQ7KHFRQVHTXHQWRIIVSULQJZLOO

EH

݋ൌ ሾሺʹǤʹሻሺͳǤ͵ሻሺʹǤ͵ሻሺͳǤͳሻሺʹǤͷሻሺʹǤͳሻሺͳǤͳሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤʹሻሺͳǤʹሻሺͳǤʹሻሺͳǤʹሻሺͳǤͳሻሿ

݋ൌ ሾሺͳǤ͵ሻሺʹǤ͵ሻሺͳǤͷሻሺ͵ǤʹሻሺʹǤ͵ሻሺͳǤͳሻሺʹǤͳሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤͶሻሺͳǤʹሻሺͳǤʹሻሺ͵ǤͶሻሺʹǤͳሻሿ

݋ൌ ሾሺ͵ǤͶሻሺ͵ǤͳሻሺͶǤ͵ሻሺ͵ǤͳሻሺͳǤͳሻሺʹǤ͵ሻሺ͵ǤʹሻሺʹǤͳሻሺ͵Ǥ͵ሻሺʹǤʹሻሺ͵ǤͷሻሺͳǤͳሻሺ͵ǤͳሻሺͳǤʹሻሿ

7KHILWQHVVYDOXHVRIRIIVSULQJDUH

݁ݒ݈ܽሺ݋ሻ ൌ Ͳ ή ͷ͸͹ʹͳͷǤ݁ݒ݈ܽሺ݋ሻ ൌ Ͳ ή ͸ͳ͵ͻͷͷǤ݁ݒ݈ܽሺ݋ሻ ൌ Ͳ ή Ͷͻ͵ͺʹ͹

6HOHFWLRQ

7KHVHOHFWLRQVWUDWHJ\LVDGRSWHGIRUWKHGHWHUPLQLVWLFVHOHFWLRQHJZHDUUDQJHDOOSDUHQWVDQG

RIIVSULQJLQGHVFHQGLQJVRUWDQGFKRVHWKHILUVW݌݋݌̴ݏ݅ݖ݁FKURPRVRPHVDVWKHQHZSRSXODWLRQ

ݒൌ ሾሺ͵Ǥʹሻሺ͵Ǥͳሻሺ͵Ǥ͵ሻሺʹǤʹሻሺʹǤ͵ሻሺͶǤʹሻሺ͵Ǥʹሻሺ͵Ǥ͵ሻሺ͵Ǥ͵ሻሺ͵ǤͳሻሺʹǤͳሻሺͳǤ͵ሻሺ͵ǤʹሻሺͳǤʹሻሿሺݒሻ ݒൌ ሾሺʹǤʹሻሺͳǤ͵ሻሺʹǤ͵ሻሺͳǤͳሻሺʹǤͷሻሺʹǤͳሻሺͳǤͳሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤʹሻሺͳǤʹሻሺͳǤʹሻሺͳǤʹሻሺͳǤͳሻሿሺ݋ሻ ݒൌ ሾሺʹǤͳሻሺͳǤͳሻሺͶǤͳሻሺͳǤͶሻሺ͵ǤͶሻሺͶǤʹሻሺʹǤͳሻሺͳǤ͵ሻሺ͵ǤʹሻሺʹǤʹሻሺʹǤͳሻሺͳǤʹሻሺ͵ǤͶሻሺ͵ǤͶሻሿሺݒሻ ݒൌ ሾሺͳǤ͵ሻሺʹǤ͵ሻሺͳǤͷሻሺ͵ǤʹሻሺʹǤ͵ሻሺͳǤͳሻሺʹǤͳሻሺ͵ǤͳሻሺͶǤͳሻሺ͵ǤͶሻሺͳǤʹሻሺͳǤʹሻሺ͵ǤͶሻሺʹǤͳሻሿሺ݋ሻ 7KHILWQHVVYDOXHVRIQHZJHQHUDWLRQDUH

݁ݒ݈ܽሺݒሻ ൌ Ͳ ή ͹ͷ͵͵͸ͻǤ݁ݒ݈ܽሺݒሻ ൌ Ͳ ή ͷ͸͹ʹͳͷǤ݁ݒ݈ܽሺݒሻ ൌ Ͳ ή ͸ͷ͸ͷ͹ͺǤ݁ݒ݈ܽሺݒሻ ൌ Ͳ ή ͸ͳ͵ͻͷͷ )URPDUDQGRPUXQWKHEHVWFKURPRVRPHDWWKHUGJHQHUDWLRQLV

ݒכൌ ሾሺ͵Ǥ͵ሻሺͳǤʹሻሺͶǤ͵ሻሺ͵Ǥ͵ሻሺʹǤ͵ሻሺʹǤʹሻሺͳǤʹሻሺͳǤͶሻሺ͵ǤʹሻሺʹǤ͵ሻሺͳǤʹሻሺͳǤͶሻሺʹǤʹሻሺ͵Ǥʹሻሿ 7KHUHOLDELOLW\RIV\VWHPLV7KHVWDWLVWLFDOGDWDJDWKHUHGRYHUUXQVDUHDVWKHIROORZLQJ

7RWDO5XQV

)UHTXHQF\IRUJHWWLQJRSWLPD (DUOLHVWJHQHUDWLRQIRUJHWWLQJRSWLPD

/DWHVWJHQHUDWLRQIRUJHWWLQJRSWLPD

$YHUDJHJHQHUDWLRQIRUJHWWLQJRSWLPD

(8)

5()5(1&(6

$QWRQ\RYi$$QWRQ\3-RHOLDQWR(

Statistical Analysis as Approach to Reliability Testing of Thermal properties in Building Insulation,QWHUQDWLRQDO-RXUQDORI$SSOLHG0DWKHPDWLFVDQG6WDWLVWLFV 9ROXPH,VVXH1XPEHU

&RLW ' : Maximization of system reliability with a choice of redundancy strategies ,(((

7UDQVDFWLRQVSS±

&RLW':DQG/LX-System reliability optimization with k-out-of n subsystems,QWHUQDWLRQDO -RXUQDORI5HOLDELOLW\4XDOLW\DQG6DIHW\(QJLQHHULQJSS±

0RKDPPDGL 1DMDIDEDGL 0 DQG 0DQVRXUL 6 Optimization of Reliability Coefficient of Engineering Systems Using a Specific Model for Genetic Algorithms -RXUQDO RI (QJLQHHULQJ DQG

$SSOLHG6FLHQFHV

0RQWD]HU+DJKLJKL$$DQG6KD\LE0$5HOLDELOLW\&RPSXWDWLRQ8VLQJ/RJLVWLFDQG([WUHPH 9DOXH'LVWULEXWLRQV,QWHUQDWLRQDO-RXUQDORI6WDWLVWLFV (FRQRPLFV9ROXPH1XPEHU6

6LQJK6.6LQJK8<DGDY$6

Reliability Estimation for Inverse Lomax Distribution Under Type-II Censored Data Using Markov Chain Monte Carlo Method,,QWHUQDWLRQDO-RXUQDORI0DWKHPDWLFV DQG6WDWLVWLFV9ROXPH,VVXH1XPEHU

:DQJ/<X&:DQJ;;X-

Degradation Prediction and Reliability Evaluation based on Hilbert-Huang Transform and Time Series Grey Analysis,QWHUQDWLRQDO-RXUQDORI$SSOLHG0DWKHPDWLFV DQG6WDWLVWLFV9ROXPH,VVXH1XPEHU

Referensi

Dokumen terkait

DVK DQG VRIW VRLO FDQ IXUWKHU PLQLPL]H WKH VZHOOLQJ YDOXH RI WKH VRIW VRLO E\ WZR WLPHV FRPSDUHG WR RQO\ IO\ DVK DV WKH VWDELOL]LQJ DJHQW 7KH UHDVRQ LV WKDW FHPHQW FRQWDLQV