Evaluation of dependability of unit based on state evaluation and prediction

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1 X R \ È! u ½ ª T R C ß Æ Æ ò Æ Vol33, No Sysems Engineering Theory & Pracice Oc, (2013) E92 TJ811 A!"#$%&(')(*+(,(-($(%/( , (1 89<=?@AB, C EFGIJKMLNOPIQ, C ) STWVWXWYWWW\W]W^`Wacb, dwewfwg XWYWhìc\WjWkWlW\`cmon pwq`rcsw jwu vwwwx, ywz -S {WW}W~ jww WW W]WƒW W W `W W cˆ` cšw WTWVWXWỲ cœwhìc, Ž ŒWhì 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 , China 2 eparmen of Technical Suppor Engineering, Academy of Armored Force Engineering, Beijing , 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 WÃ 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 * +WÃ 'W W W, -W / ºWẂẄ ( 4WÊWêW³ »W¼, ) 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 zu{uw} ~uu uu uƒu w (9140A JB3508) u uû Šu~ (1988 ),, ŒuuŽuu, u u u u, u u w ũ ušu uœuuuuÿuu, shen4232@126com

2 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 Â m(a) J µ "W Ø Wï Ã Θ L A (basic probabiliy assignmen), m(a) Â 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 Ã J à, Ü Bel 1 + Bel 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 Ã JW» õ Ú h r L A ÞÀ Á ó (7), ã ä A X g h 22 ö ø ù ú ±WÃ 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)

3 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 ) * +, - / , < = 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 RQS - < = T - < = P m cm R m () F m P R 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 Q/ 0Q { 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+,Q } ~ 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 P R Q0QK LQM Q V W X Y P ( cm < d ) y z n A B - ± ƒ 32 ² ³ µ ¹ º - / 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, 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 ` Â ð Á Â ( 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)

4 g j j C x ¼ ¼ < ó z Ù í z ó T 2698 ü&ý&þ&ÿ } ~ } ~ 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 P R S\K ]Q@ P - n 0 K L M I J V W X Y, P ( cm < d )») ó - / 0 I J - / , y z (12) ƒ, * ð Æ F, - / Ø R(s) -S (15) Fm() P( cm< d) (12) R(e) 2,-/01ãä ½9<= +Q,Q- Q/Q0 1Q2Q3 n ÍQÎ, - R S 13h, YABC 300km,,= T - G<=FG - / 0 I J <= km/h 4 ` xe YA ` / 0 1 +, 2 3 xe 41 IJKLMN <@=@ A@P (m 1 )QSR@TQ Qr P (m 2 ) (m 3 z (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 m m K, m 1 Q m 2 ƒ K 12 ˆ K 12 = 1 ( )] } ~ 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) m 2(A) = m 2(B) = m 2(C) = m 2() = m 2(E) = m 2(Θ) = < m 12 (A) = K 12 ( ) = 0235, m 12 (B) = K 12 ( ) = 06345, m 12 (C) = K 12 ( ) = , m 12 () = K 12 ( ) = , m 12 (E) = K 12 0 = 0, m 12 (Θ) = 0005K 12 = g h, n ë z 1 } ~ z 2 s z 3 +,, } ~ E 3

5 P < Á ë j ' Ó G K { c ` Ó & K P l E È c Ã º E E ` ú P Õ í O A ^ 10 o pq, r suvwx yz{}~ yzƒs `ÜÝ jklm A B C E Θ m m 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 &, Â 4 ` A B P Qq rqè } 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 ` Â ð Á Â, A B E 4 Ø 4 áâ b dª«uv ± ²³ ± µ j\e 4 <ˆ<= R < = T - { < y z (15) < F m () = R(s) R(e) a s b e, b s a e ] = 08 06, ] = 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 a - ± R S $¼½ KÃ /@Å òqó ½9Æ½ <» y z ÉÂ Ó î 7Ä, 6 îçq e î Æ½Ã 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 àáâã äåæçèé àáêë 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) < n B = W G = (04, 03, 03) = (014, 038, 048, 0) <ˆ<= - j\k max(014, 038, 048, 0) = 048, ` l < = T 43 ² ³ P R S Q0 KQL M I J '( ó ` k V W X Y P ( cm < d ), y z - n, L M N P R S E 6 Ø 6 ìíîïðñòó ²ô õô öô ô øô ùô úô ûô üô ýô M c(h) , F m () = 04 <=

6 G < È c! 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 <= R S V W X Y 3h, œj\e 6 <ˆ 3h <= L M 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) = G FG - / 0 I J ó /Q0 1Q2 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 ½ -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 ` 9QQ v ÁQ, Q 9Q 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) Yang Y, Li, heng L Failure daa and inferenial saisics preferenially based mission reliabiliy evaluaion mehodsj] Journal of Sysem Simulaion, 2004, 16(12) ] E, FG, I "#, $%KLMNOPQRST? J] VWBC, 2006, 27(4) Liu F, Guo B, hang T, e al A solving process for mission success probabiliy of complex weapon sysemj] Aca Armamenarii, 2006, 27(4) ] FG, I, X, Y\]^`abMNOPcdefg J] KLWhijklm, 2005, 25(2) 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) ] nox, pqr, si, J 'u)mnopcvywxde?yz C]// vy{}h~fij?k By ƒ jq, V Wˆ Š, ] ŒŽ f (fuzzy) B M] B Š, ], 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, ] s vy wde kÿyz ] v' )VWhB, 2009 µs