5 Ò Ä Vol. o. 5 03 ý 0 TORPEDO TECHOLOGY Oct. 03 生存分析理论在鱼雷贮存可靠性评估中的应用, n, º (. ø Ñã ¼ø,, 430033;. Àh 9388, þ, 540) : Á áò ƒ Ò, ã  o áž ƒ æ á Ò, áš turnbull o Ñp o, MATLAB l Œ ÿ ÿ, Š é áž eo æt, ÿ áš Ñ áò Ò l áž o, ý Œ o ºÀ : ; áž ; áš ; Ñp o ; turnbull o f É ú: TJ63; TB4.3 h u: A ú: 673-948(03)05-033-05 Applcaton of Survval Analyss Theory to Relablty Assessent of Torpedo Storage XIE Yong, YUA Bng-cheng, XIE Hu (. Departent of Weaponry Engneerng, aval Engneerng Unversty, Wuhan 430033, Chna;. 9388 th Unt, The People s Lberaton Ary of Chna, Zhanang 540,Chna) Abstract: In the case of storage falure te data havng the censorng characterstc, t s of sgnfcance to scentfcally and ratonally assess torpedo storage relablty. In ths study, on the bass of the censored data of torpedo storage te, the storage relablty of the torpedoes n a batch s assessed respectvely by usng the turnbull estaton ethod and the axu lkelhood estaton ethod n survval analyss theory, and the correspondng calculaton progra s coded by the software MATLAB. Calculaton results of an exaple show that the survval analyss theory s effectve for assessent of torpedo storage relablty n the case of storage falure te data censorng, and can obtan ore reasonable assessent. Keywords: torpedo; storage relablty; survval analyss; axu lkelhood estaton; turnbull estaton 0 ÑÁ Œ ê ¼[-], œ ê f Á ý Š, ƒ Õ Ñ Ú, Á e œ e Ñq, žk Á Á ê d ¼ [3] ¼q á[4], (q ) [5](q )s ¼, gk Œ, Ñ Š Ðf á [6], ë Ðf œ æ v, æ é «, p Á Ðf á áž ükýã áê (ýã á ) áž ýã áê Á å l, Ø áœœ, ýã{[7] áž { ~v 0--8; 03-0-05. (985-),, Á Ï, åæ ž o. 33 Torpedo Technology www.ylszz.cn
03 ý 0, : áš Á áž o ÿ 5 á, Á å ÿ á l å á ƒ, w å [8], w å [9] ýã áê áž Š žk : ) Š ¼ á á ; ) ãœå x Ñ Š å Ðl á l ê œ êøq þ, å x [0], é ¼ áž ƒ e ¼Á á é æ,, ¼ å, w ÐäÕ, Á á é ¼ Ð å å [] Á œ Ò, Á Œ Á œ, ž Œ Ðf ƒ w Á ÃäÕ, Š ê d å, ž Ñf, áò ƒ Ò, ƒ ž o  o ¼ áž áš f ýœî Š, Ò Š [], ä pžk f ã É, ž fø ã, Õž ø áš o ¼ áž žk å, Œ o ü Š é á Æ å, ê áš Š œ Ñp o ê á, Š œ Ñp o Š ¼ áž É áš é T, Œ Á áš 4 Æ, å Õ {, ž, Šê Ò ( ), Ÿ Ò ø Ò ž þ Æ Ÿ Ÿ Table Table of lfe data types å Ÿ ê Š q ê t t Ÿ Ò ž qê Ñf t, ê Á t ø Ò + t ø Ò ž qê êf t, ê Á t Ÿ Ò t Ò ž q Šê Á t, t t t ( ] ( lf ( t, ], lf ( 0, t ] ) éf Ò, ã, ž ä ê [3], á Š žk  o ¼ áž áš, é ê T ž Š á Œ (, =,,,, k T t t t n [4] ) ) è è p( t ) t Œ t ŒƒÒ D {[5] p( t ) ( ), = P T = t = D n () ) á = > = () S( t ) P( T t ) p( t ) t > t S( tœ ž ž, ) Á áž 3) λ ( t ) Á t Ò é Á Œ t Ò, œ Ã Ò [5], áò λ ( t ) = P( T = t T t ) = p( t ) S( t ) (3) p( t ) = S( t ) S( t ), k Õ [6] 4) ýãê (4) S( t) = ( t) t t n µ = E( T ) = S ( t ) ( t t ) (5) = ÒÄ Â Á á œ Á œ œ xð, ž œ áò Ÿ Ò ø Ò Ò v êÿ www.ylszz.cn 333
03 ý 0 Ò ø Ò þ Ò, áò, L R (6) (, ] : L ; R œ, L 0, œ, R 3 ÒÄ«ùÅ q Turnbull Á é á Æä, áš é Æ Š, ê d o Turnbull o ê Š é t Ñý Š [7], ì qá Œ, k å qá ê Ÿ Ò, p ¼Á æ d o ê Ÿ Ò å ( Æ ) [4], f ¼ áž Š Turnbull o é Æ o [8], Turnbull Á 974 ý ýœî [9-0], Turnbull o æ é á Æ á ž o { Ð, áò ( L, R ],,,, Turnbull = (7) o áž ( á ) ýã áê Õ ) 0 = t 0 < t < t < < t < t+ = +, L, R ) k I œ Á ( L, R ] ƒ ž œ Á t, I œ{ e L R ( t, (, ] I t, ( t, t âÿ ( L, R ] f 0 ºw (8) 3) Œ t Ò p ( t ) Øo { p 0 ( t ) ê / ýãš Œ [] t, Œ Øo p ( t ) ã 0 p0 ( t ) = I Ik (9) = k= 4) Ø á { S 0 ( t ), 5) S0 ( t ) = p0 ( tk ) (0) k = t { p ( t ), = () p ( t ) S ( t ) S ( t ) F t 6) t ( ) [-6] F ( t ) F ( t ) = ( I p ) Ik pk () = k= t ( t ), 7) Á Œ = k (3) ( t ) F ( tk ) = 8) 6) 7) F ( t ) ( t ), (4) d o á {[7], t < t S ( t ) = { F ( t ) ( t ) }, t t t t (4) 9) S { S {, Õ Á t,, s S œk S { Ð 5 8 0) ýã áê µ = S ( t ) ( t t ) (5) = 4 ÒÄ«ùÅ Ñp o ÿ þ n o, ä Áù {å é ê Šù, ( Ÿ Ò ø Ò Ò) œ o 4. ¼ áê Šù éf k ¼, í á ø g«ð, pž Šù Æ Š Ð á ž, Áø ž, žk Œ [8] êá áž Šù Ñp o, áž Šù F ( t) = e t (6) 334 Torpedo Technology www.ylszz.cn
03 ý 0, : áš Á áž o ÿ 5, λ Ò 4. p áò Ò, { n Ÿ Ò, éÿ p [9-3] n ø Ò, n n+ n L ( ) [ F L ] F R = = n + [ F ( R, λ) F ( L, λ) ] = n+ n+ n Ò, 3 = (, ) (, ) λ λ λ (6), L n n+ n L R ( λ ) e ( e ) = = n + L R ( e e ) = n+ n+ = é (8) œé, n n+ n R ln L( λ) λ L ln ( e ) = = n + L R ln ( e e ) = n+ n+ = + + ê (9) é λ ê, n n+ n dlnl ( λ ) R L R e = + + R dλ = = n + e R L R e L e L R = n+ n+ e e (7) (8) (9) (0) k (0) f 0, ž, ž œ λ Ñp o { Á áž R, œ λ ()ž éÿ ž áê 5 ~ θr = ln R λ () {å Ð 39, { áò Ò Õ {, Á, ( 6.3, ] œ Ñf 6.3, ( 0.8,.8 ] œ Á 0.8.8 kƒ ) Turnbull o Turnbullo, ÿ MATLAB l Œ ÿ, ž áž ÕÀ À ÕÂœ e áž á, á, áž Ÿ ÂË Ÿ Table Table of censored falure te data ÿÿ ÿÿ ÿÿ (6.3,] 4 (.3,3.4] 7 (5.8,] (0.8,.8] 5 (.0,.3] 8 (3.8,4.3] 3 (.3,3.4] 6 (.4,.8] 9 (.3,3.] 4 (.,3.7] 7 (.5,.7] 30 (.9,.3) 5 (5.,] 8 (6.3,] 3 (.3,.8] 6 (.6,.6] 9 (5.4,] 3 (5.8,] 7 (.6,.3] 0 (.,.9] 33 (.8,3.0] 8 (5.7,] (.7,3.0] 34 (.0,3.] 9 (4.0,4.3] (3.0,3.5] 35 (.3,3.3] 0 (6.0,] 3 (4.5,] 36 (.,.8] (6.0,] 4 (3.3,4.0] 37 (0,.] (6.3,] 5 (.8,3.8] 38 (.3,3.3] 3 (5.9,] 6 (.0,.] 39 (.0,.5] Fg. «ùå ä Curve of storage relablty versus storage te (5) ýã áê µ = 3.5 a ) Ñp o (7) (0), š, ÿ MATLAB l Œ ÿ, ž λ Ñp o { λ = 0.98, ýã á MTBF 5 Á áž R, () ÿ ž áê θ R Õ 3 Ÿ 3 ùå«table 3 Relablty storage lfe R 0.8 0.5 0.3 θ R.6 3.47 6.0 6 é áž o, Œ áò Œý å Œ, ƒ Ò, áš Š e áž, turnbull o ýã áê Ñp o ýã ê, Turnbull o wä, Ñp o www.ylszz.cn 335
03 ý 0, æ, ¼ æ, Ñ ¼ ø æ, ƒ Õ þl{ õ h: [] äw. ø š [M]. «ë : «ë ø Ñã, 00: 5-6. [], Û. ¼ ( Š )[M]. ä: ø Ñã, 005: -. [3] ä. q š [M]. ä: ø Ñã, 998: -. [4],,. ž o [J]. ã, 00, 3(6): 73-74. Zhong Qang-hu, Zhang Zh-hua, Dong L. The Evaluaton Method of Torpedo Loaded Relablty[J]. Shp Scence and Technology, 00, 36(6): 73-74. [5] äw, Ù. q Š [J]. Œ, 007, 3(): 03-04. Song Bao-we, Jang Jun. Analyss of Cobat Effectveness for Torpedo[J]. Fre Control and Coand Control, 007, 3 (): 03-04. [6]. Í lœ [J]. Í, 997(3): 9-0. [7] GJB53A-96. [S]. h: À ø Ù n, 996. [8]. ê á q [J]. Í, 0, 39(): 58-60. Wang Jng. The Research of Storage Indcator Syste for Mssle[J]. Structure& Envronent Engneerng, 0, 39 (): 58-60. [9] ú. áž o [J]. Ð, 009(): 5-6. [0].  ê áž Ê [J]. ø ã ã, 99, 7(): 4-44. Lu Meng-un. Feld Data Provde the Bass for Studyng Storage Relablty of Mssle[J]. Journal of aval Aeronautcal Engneerng Acadey, 99, 7(): 4-44. [] vn. Êf}á Æ [J]. ã, 00, 3(): 73-76 Fang Jun-we. Torpedo Inspecton Perod Forecast Based on Storage Te[J]. Shp Scence and Technology, 00, 3(): 73-76. []. á Š [M]. h: ã, 006. [3] ç. áš ž [M]. h: hñã, 005. [4] á. áš [M]. h: Àh Ñã, 003: 4-47. [5], n. áš [M]. : ã, 993: 7-. [6]. à Á á ÿ [D]. h: hw ø Ñã, 009: 6-0. [7] Ù. Turnbull o œ [D]. : Ñã, 007: -4. [8] Turnbull B W. onparaetrc Estaton of a Survvorshp Functon wth Doubly Censored Data[J]. Journal of the Aercan Statstcal Assocaton, 974(69): 69-73 [9] Turnbull B W. The Eprcal Dstrbuton Functon wth Arbtrarly Grouped, Censored and Turncated Data[J]. Journal of the Aercan Statstcal Assocaton, 976(38): 90-95. [0]. Êf áš æ Ò Æ [D]. þ : øñã, 0: 6-0. [] Klen J P, Moeschberger M L. Survval Analyss Technques for Censored and Truncated Data[M]. Sprnger-Verlag ew York, 997: 35-46. [] Zhang Zh-gang, Sun Jan-guo. Interval Censorng[J]. Statstcal Methods n Medcal Research, 00(9): 53-70. [3] Shen Pao-sheng. The onparaetrc Maxu Lkelhood Estator for Mddle-censored Data[J]. Journal of Statstcal Plannng and Inference, 0(4): 494-499. [4] L Ln-xong, Watkns T, Yu Q-qng. An EM Algorth for Soothng the Self-consstent Estator of Survval Functons wth Interval-censored Data[J]. Board of the Foundaton of the Scandnavan Journal of Statstcs, 997(4): 53-537. [5]. Ò Š [D]. : ú Ñã, 008: 4-8. [6] Sun Jan-guo. The Statstcal Analyss of Interval-censored Falure Te Data[M]. ew York: Sprnger, 00: 50-50. [7],,. Ò á o œ SAS æ [J]. À, 0, 9(): -3. Wang Y-sheng, Zhang Jn-xn, Luo Fu-tan. Estatng Survval Functons of Interval-censored Data wth SAS[J]. Chnese Journal of Hosptal Statstcs, 0, 9(): -3. [8] âþ. ž ø Ê [M]. : ø ã, 989: 93-95. [9],,. áš Á áž o ÿ [J]. Œêã, 004, 4(4): 33-335. Lu Jn-e, Wang Jan-png, zhang L. The Applcaton of Survval Analyss to Evaluaton of Aunton Storage Relablty[J]. Journal of Proectles, Rockets, Mssles and Gudance, 004, 4(4): 33-335. [30], Ð,,. Ò á ž o [J]. øã, 996, 7(4): 304-306 L Chang-fu, Xa Jan-zhong, Huang Yue-de, et al. Method of Assessent for the Relablty of Aunton Storage Consderng Censorng of Data[J]. ACTA Araentar, 996, 7(4): 304-306. [3] ç. áš ž [M]. ä :, 993: 43-48. («{ ±: ) 336 Torpedo Technology www.ylszz.cn
5 Ò Ä Vol. o. 5 03 ý 0 TORPEDO TECHOLOGY Oct. 03 { ~v 0--8; 03-0-05. (985-),, Á Ï, åæ ž o. 337 Torpedo Technology www.ylszz.cn