X R \ È! u ½ ª T R C ß Æ Æ ò Æ 33 10 Vol33, No10 2013 10 Sysems Engineering Theory & Pracice Oc, 2013 1000-6788(2013)10-2695-06 E92 TJ811 A!"#$%&(')(*+(,(-($(%/(0 1 2 1, 35476 2 (1 89<=?@AB, C 101121 2 EFGIJKMLNOPIQ, C 100072) STWVWXWYWWW\W]W^`Wacb, dwewfwg XWYWh`ic\WjWkWlW\`cmon pwq`rcsw jwu vwwwx, ywz -S {WW}W~ jww WW W]WƒW W W `W W cˆ` cšw WTWVWXWỲ cœwh`ic, Ž ŒWh`i j kl VŠ o XY\]^ yz š œo Ÿ h W W q`r jw]w^ -S {WW}W~ W WW W]Wƒ` XWYWWW\W]W^ Evaluaion of dependabiliy of uni based on sae evaluaion and predicion SEN Jun 1, ANG Yao-hui 2 (1 Army Aviaion Research Insiue, Beijing 101121, China 2 eparmen of Technical Suppor Engineering, Academy of Armored Force Engineering, Beijing 100072, China) Absrac For he need of dependabiliy evaluaion, we give full consideraion o he characerisics of reliabiliy and mainainabiliy Through -S evidence heory and fuzzy comprehension assessmen, we arrival a a conclusion of unreliabiliy based on he sae monioring and forecasing We combine wih unreliabiliy and he relaed mainenance daa o achieve he evaluaion of dependabiliy of uni Finally, he applicabiliy of he mehod was validaed by an example Keywords sae predicion and assessmen -S evidence heory fuzzy comprehension assessmen dependabiliy evaluaion 1 WẄ WªW«W W W W W WẄ W±W²W³WẂµW W W W¹WºWẄ W±W²W³W»W¼W½W¾W WÀÂÁWẂÃWÄWÅÂÆ,ÇWÈWÉ ½WÊ Ë W WẄ W±W²W³WẂÃWÄWÌWÍ Î «WÏWÐWÑWÒÔÓÕÑWÖW WẂ½WẄ WØWÙW³W»W¼, ÚWÛWÜ 1 2] ÝWÞ ẂÏWÐ Wß Ẅ W±W²W³W»W¼WẂÏWÐà`á Ñâ, Î «WãWäWßWåWæWçWè ÛWÜ WéWêWµW W W WẂëWìíWî 3] È íwïðñwò ówô Wõ íwïwðwñwòwẃ«wöw W WøWùWúWûWẄ W±W²üWý ÏWÐWþWéWêW W Wÿ ÛWÜ W W WøWẂÒWç 4] èwẅ W±W²WüWýWúWû WßWÊWê W± WêW øw º Wà Wê, W ÛWÜ àw½ 5] WÆ - Ẅ ùwêwê WÆ WØ ù W±W W±²»W¼ " # $,! % Ẅ W±W²W³W»W¼ ½ 'W WéWêWẂ W W¹WºWẄ W±W²W³W»¼, &, Ú éwêwẃëwìwüwýwïwðwñwò ówô éwêw W Wÿ ( ½ * +Wà 'W W W, -W / ºWẂẄ ( 4WÊWêW³ 5 6 7 8»W¼, ) 0 1 2 3 9 ß ±²³ / 4 Øï, - / ù 7 8 ±²³»¼½ 4?, < = @ ó B C E F G I J K W» V W AWÛ, L M NW O N P, Q R -S S Ẅ W T! þ G IWẂẄ W±W²W³W»W¼ Ò % ¹WºWÃWÄ \ Ñ Ẁä 9a b -S S Ẅ Y 1, ] ^ Y åw 4WÊWêW³ ó d e f òwæùw G Ḧ IW / Ý c, Ý ¹ºW»W¼ -S S Ẅ g M NW O N 9 ß /»W¼ g h i j T, * 4 Ê l, -WẂò Y k (Ú WẄ mwíw B G IWẂØWÙ È n ½WÒWâ ), Ý ó o p / W» V W G IWẂẄ 4WØWÙ W¹ºWúWû WØ, q Q R T! r i ÙW³ ¾W W³W Wù o pwẅ W±W²W³W»W¼W g h suwvyx 2011-09-05 zu{uw} ~uu uu uƒu w (9140A27020210JB3508) u uû Šu~ (1988 ),, ŒuuŽuu, u u u u, u u w ũ ušu uœuuuuÿuu, E-mail shen4232@126com
A å ± Ï Ï R É S ò Ã Ç Þ Ç r ø Y ò 2696 Ž Ÿ 33 2 ª ª«ª 21 Θ J ² ³ µ (frame of discernmen), 9 ] ¹» ¼ Ø 1 L A 2 Θ ½ Θ ½ º, 2 Θ "Wê ¾ L A üwý ñwò 6WÿW±, ½ G Ý m 2 Θ 0, 1], À Á m( ) = 0 ] m(a) = 1 (1) A Θ à  m(a) J µ "W Ø Wï Ã Θ L A (basic probabiliy assignmen), m(a)  J Ø A L A L Ø ò Ä ÅWþW 4 Ç È ÉWẂ Ê Ë Ì º «5 A A Æ ( h ) Í Î» ¼ WñWò 2 m 2 Θ 0, 1] J µ "W Ø Wï Ã Θ L A ñâò ÂÐJÂøÐÑÂñÂò #ÂþÂ, àwøwê ¾ WñWò Bel Ú ÃWØ º Bel(A) = B A m(b), A Θ (2) ± X ÎÐ4ÂÊÂêW³ÂñWò, Ò A, ÓÐÔÐÕÐÖ Ý Bel( ) = 0, Bel(Θ) = 1 empser Ø Ù Ú ± ½ ² ³ µ "W WñWò ï ³W½ ÛW Ø Bel 1, Bel 2,, Bel n Θ, m 1, m 2,, m n L A ï Ã Ø Wï à J à, Ü Bel 1 + Bel 2 + + Bel n Ý ] L A m, m(a) = K m 1 (A 1 )m 2 (A 2 ) m n (A n ), A Θ, A, A 1, A 2,, A n Θ (3) Þ Ø ó A 1, A 2,, A n Θ A 1 A 2 A n = K = = 1 WàW½ Ä Å Æ ß Þ R Ï Wà æ ç p è WñWò é ê ë ì í î ï ð ñ ±WÃòÑ Ó Ó 1 2, ] A X A 1, A 2,, A n Θ A 1 A 2 A n = A 1, A 2,, A n Θ A 1 A 2 A n à é p J 4 Ç S A Y Θ, m 1 (A 1 )m 2 (A 2 ) m n (A n ) m 1 (A 1 )m 2 (A 2 ) m n (A n ) µwø 4 Æ ß Þ R Æ Wñò Ç S ø ] 1 ó Ø b ] 1 (4), Ú h S Æ 4 à á â, ã ä m(a X ) = max{m(a i ), A i Θ} (5) ] Ø ô Ý ó ] m(a Y ) = max{m(a j ), A j Θ i j} (6) m(a X ) m(a Y ) 1 m(θ) < 2 (7) m(a X ) m(θ) o pw Wï à JW» õ Ú h r L A ÞÀ Á ó (7), ã ä A X g h 22 ö ø ù ú ±Wà û ü º P = {p 1, p 2,, p n }(n 2), ß $ è û üw ý 4 þ 2W JWþ Ä Å û üw ý, Y ÿ 2W, WßW» V û üw ý º n W = {w 1, w 2,, w n }, i=1 w i = 1» º C = {c 1, c 2,, c m } (m 2) é p Å T f p i F (C), i = 1, 2,, n (8) f(p i ) = (r i1, r i2,, r im ) F (C) (9)
T x» ± ¼ Ý s Ù G ô C ð s Ç z S 10 Šu~, uÿu 2697 f(p i ) ½W Wß 5 6 lw» º B WÆ Þr C T Ẃ» p i T Å J T Å G 0 ý º, Þ r ij Ó Ô G = (r ij ) n m = W û ü Ø o lw WßW» º p i,wãw» r 11 r 12 r 1m r 21 r 22 r 2m r n1 r n2 r nm C "WẂ» c j T 9 Å f o pw û ü º P B = W G = (w 1, w 2,, w n ) (r ij ) n m = (b 1, b 2,, b m ) (11) ÍWẂ» V û ü ÛWẂ» º 6 JW» V g h 3!"$#&%&' 31 ( ö ) * +, - / 0 1 2 3, 4 5 6 7 8 9 - < = 1 -? @ 1 7], A B < C (12) E F P m = R m () + 1 R m ()]P ( cm < d ) = 1 F m ()] + F m ()P ( cm < d ) (12) G - / 0 I J - 0 K L M N O @QP RQS - < = T - < = P m cm R m () F m () @ P R S @ P R S\K ] @ P - 0 K L M I J d V W X Y P ( cm < d ) V W X Y - < = T R f < = T - R m () ^ `, a ^ b c A B d e, g h F m () i ^ ` A B < = T 2 3 - Q/ 0Q1 2 3 - { 2 3 } ~ j\k l m n o p q r s u vqw, x y z b c o p } ~ S - < = T ( ) ƒ, A B ˆ R m () = 1 F m () (13) e e dr() F m () = f()d = d = R(s) R(e) (14) s s d G - R f - } Š R f L M T Œ - R f < = T s v e f() R(s) v s R(e) - } Š R f < = T e R Ž - R f - } Š R f < = T G\ C ƒ R(s) s R(e), b c v m - - } ŠQR f <Q= TQ+,Q2 3 2 3 } ~ SQ S z h ` b c v, j\k ^ e, š R(s) a s, b s ], R(e) a e, b e ], œ y z (14) < F m () = R(s) R(e) a s b e, b s a e ] (15) 2 n Ÿ 4 F m () ƒ, A B ª 32 @ P R S«KQ] @QPQ- Q0QK LQM IQJ? @ Q V W X Y P ( cm < d ) y z n A B - ± ƒ 32 ² ³ µ ¹ º - / 0 1 2 3 A B E F ˆ e ¼, +, ½ ¾ { Ç o p r s q r, o p r À 4 Á Â Ã Ä Å a ` o p q r, Æ / Ò È É Ê s Ë Ì ` x Í Î Ï\Ð ÑQiÏ\Ð, C } ~ +, n l m Í Î, a ` A B q r Ó Ô w v Í Î» Õ } ~ +, ½ ¾ 2 3 ¼, y z o p r s o p q r, Ö -S z h Ó Ô o p, 2 3 1 Ø 1 ÚÛ -S ÜÝÞßàáâãäåæ» ç 2 3 } ~ è } 2, j\o p ` F m () +, ƒ A B ˆ ì í < = T < = T 1) é ê É Ê È, ë z h g o p î ï `  ð Á  ( ò ó ñ ) ½ ¾ - ± ô õ ö ø ö ú û ø 2) y z A B, j\é Ê ù 6 n (10)
g j j C x ¼ ¼ < ó z Ù í z ó T 2698 ü&ý&þ&ÿ 33 2 3 } ~ } ~ è ô õ 2 ø 3) n o p z, ¼ ë (15) 6 +, 2 ó 2 ø 2 4) j\é Ê, y z (11) ƒ k C B 5) B G! 2 ö 2 ø"#$ 2 } ~ ó ` Â F m ()»% ó, F m () &, }? @ '( ò ó @ P R S\K ]Q@ P - n 0 K L M I J V W X Y, P ( cm < d )») ó - / 0 I J - / 0 1 2 3, y z (12) ƒ, * ð Æ F, - / 0 1 2 3 + 2 Ø R(s) -S (15) Fm() P( cm< d) (12) R(e) 2,-/01ãä23 4 4656768 ½9<= +Q,Q- Q/Q0 1Q2Q3 n d+ @? ÍQÎ, - R S 13h, YABC 300km,,= T - G<=FG - / 0 I J <= - - 30km/h 4 ` xe YA ` / 0 1 +, 2 3 xe 41 IJKLMN <@=@ <@=@ @@O A@P (m 1 )QSR@TQ Qr P (m 2 ) n @ (m 3 ) @V@W z QoQpQ6 @X (A)Q Ð X (B)Q ey (C)Q Ð () (E) ) î ï R f +, 2 3 <] T \ v s r o p, š l 6^ E 1 Ø 1 `ÜÝàÚabcdef / empser ƒ 9 A B C E Θ m 1 02 04 02 01 0 01 m 2 03 05 005 01 0 005 m 3 05 02 01 005 0 015 K, m 1 Q m 2 ƒ K 12 ˆ K 12 = 1 (01 + 001 + 002 + 012 + 002 + 004 + 006 + 01 + 002 + 003 + 005 + 0005)] 1 235 } ~ K 12 h z m 1 Q m 2 E 2 Ø 2 ijüýjklm m 1(A) m 1(B) m 1(C) m 1() m 1(E) m 1(Θ) 02 04 02 01 0 01 m 2(A) = 03 006 012 006 003 0 003 m 2(B) = 05 01 02 01 005 0 005 m 2(C) = 005 001 002 001 0005 0 0005 m 2() = 01 002 004 002 001 0 001 m 2(E) = 0 0 0 0 0 0 0 m 2(Θ) = 005 001 002 001 0005 0 0005 < m 12 (A) = K 12 (006 + 003 + 001) = 0235, m 12 (B) = K 12 (02 + 005 + 002) = 06345, m 12 (C) = K 12 (001 + 0005 + 001) = 005875, m 12 () = K 12 (001 + 001 + 0005) = 005875, m 12 (E) = K 12 0 = 0, m 12 (Θ) = 0005K 12 = 001175 g h, n ë z 1 } ~ z 2 s z 3 +,, } ~ E 3
P < Á ë j ' Ó G K { c ` Ó & K P l E È c à º E E ` ú P Õ í O A ^ 10 o pq, r suvwx yz{}~ yzƒs 2699 3 `ÜÝ jklm A B C E Θ m 12 0235 0635 0059 0059 0 0012 m 123 0383 0542 0038 0030 0 0004 E 3 <ˆ ç <= I J Œ <= z o p F, y zš, šœ Á ÂŽ Ó Ô o p,? š 1 = 015Q 2 = 005, y z (5) (7) < ó <= 2 n Ó Ô o p B(Ð X ) - ± +, } ~ +, 2 3 ó<= - Ÿ 4 y z ` Á o p q r, y z q r o p } Š R f o p Æ k o p q r Í Î Ï\ÐQÑ, m 8 9] G <= k RT qqr T C Rš q r, V W &,  4 ` A B P 6 @Q Qq rqè 2 3 - } Š R f l mœ š o p q r s, e R<= Ó Ô o p E(Ð ) 42 ¹Ÿ 2 3 } ~ R f y z Ó Ô o p, s o p Ð X, } Š R f e o p Ð x n é ê É Ê È <= < = T o p `  ð Á Â, A B E 4 Ø 4 áâ b dª«uv ± ²³ ± µ j\e 4 <ˆ<= R 0 045 045 06 06 08 08 095 095 10 < = T - { 08 095 < - 045 06 y z (15) < F m () = R(s) R(e) a s b e, b s a e ] = 08 06, 095 045] = 02, 05] S / 2 ø \ ¼ 01 ë C e 9¹ C, C = {02, 03, 04, 05} P = {p 1, p 2, p 3 }={º C R S $¼½ C¾ 2 ö ø ½ ¾ C R SÀ ½ ¾ - Q± CQR S,», º } @º, a - ± R S $¼½ Kà /@Å òqó ½9ƽ <» y z ÉÂ Ó î 7Ä, 6 îçq e î ƽà C¾ È ÇÉ ±È î, º cçqëê )Ì / 2 <=Í, - < = T +, 2 É Ê `, 2 ö Q 6^ n É Ê 2 ÎÏ E 5 Ø 5 ÐÑÒÓef ÔÕãÖ y ØÙ ÚÛ ÜÝ y Þß 02 03 04 05 àáâã 04 1 1 3 0 äåæçèé 03 0 3 2 0 àáêë 03 1 2 2 0 j\e 5 2 ð G ˆ 1/5 1/5 3/5 0 G = 0 3/5 2/5 0 = ú û ø 1/5 2/5 2/5 0 W = {w 1, w 2, w 3 } = {04, 03, 03}, j (11) < 02 02 06 0 0 06 04 0 02 02 06 0 0 06 04 0 02 04 04 0 n B = W G = (04, 03, 03) = (014, 038, 048, 0) 02 04 04 0 <ˆ<= - j\k max(014, 038, 048, 0) = 048, ` l < = T 43 ² ³ µ @ P R S \KQ] @QPQ- Q0 KQL M I J '( ó ` k V W X Y P ( cm < d ), y z - n, L M N O @ P R S E 6 Ø 6 ìíîïðñòó ²ô õô öô ô øô ùô úô ûô üô ýô M c(h) 55 29 48 05 28 25 43 15 18 20 04, F m () = 04 <=
G < È c! + 2700 ü&ý&þ&ÿ 33 y z 41 G - <ˆ - F ] @ P I J G\Çÿ 07(þ E E - / 0 I J ` xe ˆ <= xe? @ R S V W X Y 3h, œj\e 6 <ˆ 3h <= L M K? @ R S < ó<= k 3h), P ( cm < d ) = 07 y z (12) h P m = 1 F m ()] + F m ()P ( cm < d ) = (1 04) + 04 07 = 088 - G FG - / 0 I J 088 5 ó 2 3 - /Q0 1Q2 3 - / 0 1 2 3 l m k o p q r s, F ey, ô õ 2Q Q -QQ/Q0Q1Q2Q3 k -S z hq QsQ Q Q Q @+ Q ½ 9 @@<@=@ -QQ/Q0Q1Q2Q3 nqd@+ < C 1 $ + ô õ?, Ë + l Í Î u, n ˆ e ¼ Í Î ` Ñ b c 9 -QQ/Q0Q1Q2Q3 P -QQ/Q0Q1Q+Q,Q2Q3 2Q3 P -QQ/Q0 @+, ` 9QQ v ÁQ, Q 9Q 1 2 3 Y 1],,, r s PMS { å!"# ~ µ ƒ J] $%'&)(*, 2007, 26(8) 9 10 Shi J B, Yu Y L, an X K, e al Research on mission reliabiliy of comba uni complex ask based on PMSJ] Armamen Auomaion, 2007, 26(8) 9 10 J J 2] +,-, /0, 12 s34567ý89<=s{~s SySz? J] üý@abc, 2004, 16(12) 2761 2763 Yang Y, Li, heng L Failure daa and inferenial saisics preferenially based mission reliabiliy evaluaion mehodsj] Journal of Sysem Simulaion, 2004, 16(12) 2761 2763 3] E, FG, I "#, $%KLMNOPQRST? J] VWBC, 2006, 27(4) 721 725 Liu F, Guo B, hang T, e al A solving process for mission success probabiliy of complex weapon sysemj] Aca Armamenarii, 2006, 27(4) 721 725 4] FG, I, X, Y\]^`abMNOPcdefg J] KLWhijklm, 2005, 25(2) 94 100 Guo B, hang T, hang Q, e al Phased-mission availabiliy assessmen model for sysem given limied sparesj] Sysems Engineering Theory & Pracice, 2005, 25(2) 94 100 5] nox, pqr, si, J 'u)mnopcvywxde?yz C]// vy{}h~fij?k By ƒ jq, V Wˆ Š, 2009 359 362 6] ŒŽ f (fuzzy) B M] B Š, 2002 7], n, š, J œmnvyÿyz J] v' )VWhB C, 2010, 24(1) 1 8 hang Y, Wang C, hang S X, e al Research on equipmen mainenance decision based on missionj] Journal of Academy of Armored Force Engineering, 2010, 24(1) 1 8 8] v' )vy wÿ yz ] v' )VWhB, 2010 9] s vy wde kÿyz ] v' )VWhB, 2009 µs