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Assessing Material Aging from Doubly Censored Data : Weibull Distribution vs. Poisson Process

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(1)Assessing Material Aging from Doubly Censored Data : Weibull Distribution vs. Poisson Process Gilles Celeux, Christian Lavergne, Yann Vernaz. To cite this version: Gilles Celeux, Christian Lavergne, Yann Vernaz. Assessing Material Aging from Doubly Censored Data : Weibull Distribution vs. Poisson Process. [Research Report] RR-3857, INRIA. 2000. �inria00072799�. HAL Id: inria-00072799 https://hal.inria.fr/inria-00072799 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Assessing material aging from doubly censored data: Weibull distribution vs. Poisson process Gilles Celeux, Christian Lavergne, Yann Vernaz. N ˚ 3857 Janvier 2000. ISSN 0249-6399. ISRN INRIA/RR--3857--FR+ENG. ` THEME 4. apport de recherche.

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(68) ’§‡.   !  

(69)  5    . kZmtuxcMzyo p{ƒ omt~vŸnm|kxc¡uxoE Ÿnumtc!p ` pysc³} sEcuBprc p ƒopƒ oq~ “E¥qi|_*un`“Qc¡‚²0ss ijz{ƒ zyc sBsšuUÀc - ƒ p ` ² c!ddsm} c czrpym|ijijundD“ oq}pyc!cprs c   prp z ` oEc!uDz{oqo“mtijclun“°wZo cƒÃVoc dp]cprijuc ƒ o dDijzoq„ #Us knƒ iti|p´py~c s  ƒ c wnm|ijoqpritsBuxz ¡ _ oŸnm|c#e .JzrpyijdDoqprc z*kxzri|ux“Ddm ¥x± o§~cMzJiju   c ƒ cMuxcoEu } &(*) oq“ijun“DpycMzyp   s ƒ p ` c  } ijzyp ƒ ijŸxknpritsBu ± dc oEud!m+?zyp } 1 dc ouo§~E+?c zyz p } 1 wZc ƒ c uBpro“c°s -   1o² c wnpri|ux“Do“ijun“  ‘x¡  + ‘Z¡ ‡Œ 1 ’¡ ‘qe + ‘Z¡t’§ 1 ‘   ’M‘ ’E’¡  +?Eše qeZ¡ Œ 1 ‡‹‘E‘x¡|’ + ‡x¡ ‹ 1 . 8.

(70). 4 #.  

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(72) ’M‹.  

(73)    

(74)  !#"%$'&()* +. _ oŸxmtc . dm1oEu } ± §o ~Ec zri|oEu ž cijŸxknm|mwxo ƒ oEd!c pyc ƒ cMzypri|dDopyc z   s ƒ ŸZsEp ` “ ƒ sEkZwxz€s   dopyc ƒ ijoqmjz¡ ²0cp ` s } 0² s } c m ‚ o ƒ oEd!c pyc ƒ Jzrpyijdopyi|sEu d!m  y+ ’reE‘E‘‘ 1  ‘Z’§¡ ŽŽ ‡ x ¡   +y’  ‡q‘E‘‘ 1  ‘Z‡n¡ ’EŽš’‹ ¡ Œ  ± o§~c zrijou  +y’ reE‘E‘‘ 1  ’E¡ ‡xB’ ŽUE¡ Œ  ‡  +y’  ‡q‘E‘‘ 1  ‘Z‡Eq¡  ‘Z’U¡ ‡Ž . _ oŸxmtclŽ.&(*) ƒ cMzrknm|prz   s ƒ p ` cp´¤7sD“ ƒ sEkxw } oproDzyc p¡ ²0s } } cm ‚ o ƒ odcprc ƒ JzrpyijdDoqpritsBu +?zyp } 1 7cUijouxc ²0s } cm1‘  ‹x¡ Œ‘E‘‘ +?‘x¡ ‹EE  1 ‡ ¡ ‡še ²0s cm]’  eÀ´Z‘x¡ ¡eE‘E‘‘‘E‘ ‘ +?+?‘x‘x¡ ¡ ŽšŒq‹eU‹ ‡ 1 1 ‡qeZ¡ ŒE ²0s } cm‡  ‡n‡n¡¡ e ŽŽ +?+?‘x‘x¡¡ eEŽU‘B’E’ Œ 11 ’E’¡ ‘ ²0s } cm1‹  ‡n‘x¡ ¡ ŽUŽšŽš‘B‘ ‡ +?+?‘x‘x¡ ¡ ŽšŽ‹B‡nŽ ’  1 1 ’M‘x¡ Ž ´ À  ‡n¡ ‹B‡  +?‘x¡ Žš‘EŒŒ 1 . . 898;:=<>?@A. }  ’ ’ Œ ’ Œ ’§Ž.

(75) ’ e.   !  

(76)  5    . _ o} Ÿnm|ƒ c-} Ž } ijz{wnm|o§~nz³p ` c ƒ c z{knm|przs   p ` c ‚ sijzrzrsEunÀ - ² d!s } c mtijun“Q¡ _*` c   sm|mtsš¤*ijun“2ds } c m|z¤7c ƒ c sEuxzri c c . 0 ²0s } cm‘). s 3xnc } cÃXcMp. ¡ 0 ²0s } cm ’ .      cÃVc p. ¡ 0 ²0s } cm‡ .  cÃVc p. ]¡ 0 ²0s } cm)‹ .      ou }

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(78) c #UknCc uBprmt~ ¥ ¤7c’|sE’eQux¡ m|k _*} ` c³sEwQzrcsEzr§itproitm|Ekxcc m|z~ `  s o§ƒ cdpys s¨} cŸZm c5‡ +?sEddDowxpyco ƒƒ ijc oq} mXcprÃVs0c B p ` p 1c ¤ nÀF` šijoq `mjkncijz p ` BMac ƒ i|+y“ ’ ` 1pJ ds‹ } Œqc eZm ¡¡  ($ ! ³ƒ zrzrc z{zri|¥ un“ o` “ijun“¨cxmjkx} zyi|ƒ c mt} ~  ¬` ƒ sBd ƒ m|c   p5oEu }  ¬ƒ ƒ i|“ ` } p-cMuxƒ zys ƒ c }ª} opro£ ijz-o } it©  knm|p-proEzr¯X¡«† u p `  i|ƒz ooEzrprzri|c z{mtzrc i|un“¤Jco“ijuno§“cijz1prsBsuxozyiz{z{ckxdc c p p ` oqijz°p1pw ` csEŸn  om|c itmjd k ƒ c prsEi|d dc zitÃXo ƒc ijzycMc uB ¬p°ƒ sEwQd sijuBo*pržz³scijŸxBkni|m|cm ¤} ij¡5zyp  ƒ ijŸxknmjoprz{itsBzri|ub ¡oqm† ul¤7zro§kx~  ` s o } sEkxŸnƒ m|~!  ƒrc ƒ uxzr} s ƒ c } `sEuBpycUp ¥ sBk ƒ cxwQc ƒ i|` dc uB} p{z z ` sš` ¤ª} p ` oqp uxsEuD` iju   ` s ƒ dDoqpyi|  c ± o§~cMzyijou!iju ƒ   c ƒ c uxcƒ oEu pijŸQz€ƒ csBdkxw sŸncƒm|c c³czuxoEocu pr}k ƒ pywoqs mbƒ sšp oUu ic}} dDc°dm|ošc s nz{ƒ i|zc³d!zrzrkxprc oEdÂuxŸnzrmtijm|cŸnij¯qmtcMcczym|prpyi i|sdDsUUs oitpyc s ¤Sdƒ z oqc¡ “Ep ± i|uxs kn“!psop m|z€`scl“Eo ~-dD- ¤ 1oqij² u#ij wQ3xsn ijc uEo} puvcs s ÃX  prcMsEc k uvp€ƒ s c   uZsEo uBsEp‚ kZƒ sEuEijŸxi|prz{knc zyprsBitusBuUu2kxw dƒijzsUc p c ij` z{oqoqzp m¡ kx} dc ƒ i| ƒ oqmcnwQƒ c ƒ ijd!cMuBprzz ` sš¤‰p ` oqpp ` i|z°¤€o§~#s   ds } cm|i|un“#o“ijun“voEwxwQc o ƒ zpys#ŸQc-d!s ƒ c ƒ cm|i|oEŸnm|c oEu žd!c s mtijcdzritc pl sEk k cEƒ ¡ uUkxdc ƒ ijoqmijuBcMzyprit“Boqpyi|sEuZz³prs#dopyc ƒ ijoqmjzsBuxzyi } c ƒ c } oz°“EsUs } ozuxc¤¡-† užp ` i|z zrcpr` pyc ijunu “ ¥dDp oq` pyc c ƒ m|ijc oquxmjzD“p ` oEz°u/s  ŸQc#sEuBsEp uZƒ sEzyi m } ` c ƒo§c } cDpy1s# ŸQ"c  } iÁÃV3c ƒ c  uB p¥ prp s0` c dƒ c oE¯qi|z-cDuxp `spc-zrokZux o` mt~nožzri|zm|i|sd  i|proqoq“Epri|ituxsB“vu/wQoEsEu z{} zyijŸnp m|` cc ¡ ‚ sEi|z{zrsEuUÀ - 1ƒ ²¥ ds } c mtijun“ ƒ ijz*oqmjzys ds ƒ cuZoqprk ƒ om } ¡ ` ` cMu#sEunm|~ ¥ mtc   poEu } ƒ it“ ` } p ³ ¢ š s J ¤. c   c | i  p | i ³ z | i D d Q w s r p E o E u ³ p y p v s q ¯  c M c. w | i ¨ u  d | i u p  o  p E o r z r z. c { z y z j i n u “  o  “ j i n u “ ¤ } } } ¾ ƒ ƒ ƒ ƒ ƒ ƒ oEc uxszrsƒ } c i|ux“pyoqsproµp ` o cz{c5oo§dšcoqi|cm|oExŸnwZmtc c ƒ ijdcMdc uBopri|ouZmXzlz{oµ` cMwQd!sUs cmts ~£  gBwQc sEzrpyc i|sEu w nsE¡ ‹ Ÿx¥ mtcM3Zd2c°¡ dDoqs pyc ƒijuxijoqzymjp{z o ¬uxƒ sBc d ¤7o c5 zri|+yd!’ ykneBm|o‘py‘c ‘ 1 o¤€Eu o} zD3ZoEm|dc!sEdDzrpoqprp c ` ƒ c0i|om|z{z od ¬ƒ sEc d   s o;ƒ p ` c#+F‡ p´{¤7‡sž‘‘E¨‘ 1 c ¡i|ŸxgBkxijuxmtmcl} i|p zr` p c ƒ i|ŸZƒ c knwxpyoi|sEƒ uxpritz pritsBou2p s c   uZmtzyc s   p³ƒ ijoEunu“µ} pri|ƒ dit“ cM` z p³ c uZ zys ƒ ’ c ‘}v‘ž} ooqu pr}o B   ‡q‘‘ ¥ i|p-ijz ƒ oqp ` c ƒ ijdDwZsBzrzri|Ÿxmtc0prs } ijzypri|ux“Eknijz ` p ` c d ou } uxsEunc0s   p ` c¨oEŸZsšEc#d!cMuBpyi|sEunc } dc p ` s } z*¤€oz€oEŸnmtc°prs } cprc pŸQsp ` p ` co“ijun“oEu } p ` cdDopyc ƒ ijoqmbcÃVc p¡ ”2› ¼U` » 8 ¸ ƒ½ ¸ V—M– }   ¨ƒcJ` p ` oEux  ¯²µ} o ƒ i|cÀ “Eu c a ¥ z -}o ƒ unc ƒ sƒ oE±u } ƒ ± ` c u§„yoEd  i|u ƒ ³itm|mj`oqiju   s ƒ ` i|uBp ƒ s ƒ } kxi|ux“ pkZ` zcprs³oqm|p pyc ijƒ zuZw oqpysBi|Ÿnc°mtcMdd­s o} u cm s  s gBcMcprmjwitsBu knm x¡ i|‡xz{¡ kxz{zritsBuxz oEu ¢³c u i c p sEmtsBu s i|prz cmjw¤ c u!p c oqpri|ux“ . . . . . . . . . . . ). . . . . "' ). *. ).

(79). ). . . . c^d8 cfe.

(80) ’§.  

(81)    

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(83) 1} ¥ oqp{’oÀ´‹UŒZi|¡ oDp ` c  ² omt“Es ƒ itp ` d + ¤*itp ` } i|z{kZzrzritsBu 1 ¥ ! 5  3 $  +    2&    ¾ c mtm|c ƒ } ¥ ­"¡ +y’  Œ 1 ¥ # 2ƒ !#&    " " %  $ #($ 5  ' 5%& )[ +?zycMsEu } c i|pyi|sEu 1 ¡]«i|mtc ~ ³c¤]s ¯Q¡ o§¤*m|c z{z ¥ Q¡ ¾ ¡ +r’ ŒB‡ 1    &

(84) 2    

(85)  )21  %  

(86)    ¡ «itm|c~ ¥ c ¤]s ƒ ¯X¡ oEuxun!3sš~ ¥ ¡! o u }  &‚7 ƒ snoE &(i| o2 ¢l ¡ !+r’   qe  1 ƒ  #/¥U'‚  1ƒ 5&    5%$13  "  ' #    ¡ J~ sEmtm|c z o i|z ¡ ²µ  dDknomtmju oq“ o`lu } ‚ ¡q¢³oEou mt}m ¥ csEm u } } c sBƒ ubZ¡ 9¡ l¡ +y’ Œ  1 5%"2(    /%& + zrc sBu } c } i|pyi|sEu 1'¡  ` owUÀ gUkxu ¥ 7 ¡ ¥ +r’ & B9Ž  1"   #un spr 'c-sE5u unsBu£i|u5  s &ƒ  d ¥ opyXi|¥‹xc-’ w šƒ À´i|‹s ‹Eƒ Œxz ¡   s ƒ žcijŸxknm|m } i|zrp ƒ ijŸxknpyi|sEuZz¡  ! 5   ˆ sBŸZc ƒ p ¥  ¡ ‚ ¡ ¥ +y’  qe 1  ) $   #& ¡€gUw ƒ ijun“c ƒ À c ƒ m|o“ ¥ c ¤ ]s ƒ ¯X¡  . . . . . . 898;:=<>?@A.

(87) ’.   !  

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(89) C B. AWB + `C = . 1 *  .   žc ` o§Ec  Y Y  C a + ? 1

(90) ’ *.  m|s“ 9 + L@: 1  = . B B .  C  + 1 =  .     . AWB Y ’ C +  * .

(91) 1 Y .!A)B * * *

(92)  C B ’ = C . + + * .

(93) 1 1    .    B + `C = . 1  .   . .!AWB . AWB  _*` i|z€m|c o } z€pys p ` cmtij¯qc mti ` sUs } c #UkxoqpritsBu  Y + B * . C + = . C  1 C = . C * .

(94) *

(95) 1 +1 ’ + . 1H  ‘ . AWB   u2p ` csp ` c ƒ*` oEu }  Y  ’ C a + ? 1

(96) B Y.  m|s“ 9 + L@: 1 = . B  C  C = . 1 * . m|s“ * .  +    *

(97) C  1  . AWY B ’  + . 1 . AWB Y * * *

(98)  *  B ’ = C .  + + * .

(99) 1 1   1.  C B + `C = . 1  .  m|s“  .  . AWY B . AWB Y  .. * * *

(100) * *  B ’ = C . + + * .

(101) 1 1  .   m|s“  .  C B + `C = . 1  .   m|s“  .  . . AWB . AWB  zyijun“D

(102) c #Ukxopyi|sEu ¥ i|p*mtcMo } z€prs p ` cm|ij¯qcm|i ` sUs }

(103) c #Ukxopyi|sEu  Y + B * . mtsE“ + * . 1 C + = . C  1 C = . C * .

(104) *

(105) 1 +F9Ž 1 ’ + . 1  ‘ . AWB #. !. . . . . . H. c^d8 cfe.

(106)  

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(108)  !#"%$'&()* +. ;#;ž "0 ,  l!' #

(109) q! "#$#%#'& (* !"+"# žc } cMunsprc * . I  * .  . I ¤ ` c ƒ c 0 L %+ * . I 1   s ƒ #­’ !!"& oEu }   ’ !"!  } c uxspycsEdDwnm|cprc } oqpro ¥ 0  $  . I $   s ƒ # ­’  !"!5 ou } %­’ !"!  } c unsEpycdi|z{zri|un“ } opro ¥ 0  + * . {zy“Bu +  . I 1 1   s ƒ # ‰’ "!!5 ou }  ‰’"!"  } cMunsprc°sEŸxzrc ƒ c }5} oprox¡ _*` cm|ij¯qcm|i ` sUs }   kxuxpyi|sEu   s ƒ p ` csBdDwnmtc pyc } oproijz 9. ¤*i|p `. + L . 1 . >. a + *

(110) 1K   * . Y  X. > . + * . I 1. B. . AWB I&A)B. cxw. C. *. ,. ’šŽ. .   s ƒ * 1‘ . oEu } %+ . 1 ¡ _*` c J² omt“Es ƒ itp ` dÂsEuxzri|zrprz7s   omtprc ƒ uxoqpri|un“Dp ` c«zyprc wvou } p ` c² zrpycMwb¡ a   kZ— ux ¸ 

(111) pritsB u . 7c uxspyijun“ p ` cž k  ƒ{ƒ cM

(112) uEp2a cMpys ƒ cMzypri|dDoq9 prc L¥ p ` ijzv

(113) zrpycMwSsEuxzri|zrp5s   } cprc ƒ di|unijun“p ` c +8 1K!+¬m|s“ +  1  1b ¤ ` cƒc Y X B m|s“ 9 + L . 1 . AWB I&B AWB  m|s“   +8 C ’ 1Bm|s“ *  . I  C *  . I     žc ` o§Ec  +

(114) a 1    E m|s“ +81 C m|s“ +8 1 B Y B X C.+8 C ’ 1 +?m|s“ + * . I 1

(115)  1 C ’  *

(116)  .I  . AWB I&A)B  F H     E m|s“ Y +81 C m|s“ +8 1 F + C ’ 1 B E +  C = . 1+ mtsE“ + * . I 1

(117) * . I  * . 1 = . +¬m|s“ + * . I 1

(118)

(119) * . I * . 1 F Y . AWB ’ B C 6+  C = . 1 + * . I

(120) * . I  * . 1 = .  + * . I

(121) * . I  * . 1 . . 898;:=<>?@A. . . AWB. !. . . $#. .

(122) ’MŒ.   !  

(123)  5    . ¤ ` cƒc.   + * . I

(124) * . I  * . 1     +* .I

(125) * .I  * . 1 . . + mtsE“ + * . I 1

(126) * . I  * . 1   + mtsE“ + * . I 1

(127) * . I * . 1. oEu }. . + *

(128) a 1' * * .

(129) a 1  + ?  * + *

(130) a 1 ' *  ’ VC   + * .

(131) a 1   sE“ + * 1 + *

(132) a 1 ' * t m ?  *.

(133) a 1 + ?  * *

(134) a *  m|s“ + 1 + 1(' ’ C +*.

(135) a 1  ?. .  . . V . *. cnw C *  .    — ¸

(136) 7 . 7cprc ƒ di|unc V dDošnijdi0/ i|un“  +8

(137) a 1 ¡ V ijzzysEm|kxpyi|sEu2s   c

(138) #UkxoqpritsBu  +8 V

(139) a 1  V «‘ . .  + V

(140) a V. 1. . †´p*m|c o } z€pysDp ` cc

(141) #Ukxopyi|sEu. . +8 V 1 .  .  + V

(142) a V. 1. +*.

(143) 1.   V C  D V Y V PB  V

(144)   . AWB. ’. B. Y.   .!AWB !. . 6+ `C = . 1   + * . I 

(145)

(146) * . I  * . 1 !. . + `C = . 1   + * . I 

(147) * . I  * . 1 . m|s“. . Y.   + * . I 

(148) * . I  * . 1. $#. .   + * . I 

(149)

(150) * . I * . 1 . #.    E mtsE“ + * . I 1

(151)  . AWB I&A)B Y XF  * .I

(152)       ’ B B *

(153) C     . I  +8 V 1  . AWB I&A)B   V . :mtsE“ +8 V 1 . .   C   V +V  V 1 B Y B X + 1  .!A)B I&WA B. = .. = .. . +Œ 1 . B BX. . . . . c^d8 cfe.

(154) ’.  

(155)    

(156)  !#"%$'&()* +. †´p*m|c o } z€pysDp ` cc

(157) #Ukxopyi|sEu ’ V  C  ’ B Y B X LE m|s“ + * . I 1

(158)   ’ V B Y B X     + * .V I 

(159)  1  +8 1  . AWB I&AWB   F  +8 1   . AWB I&AWB ˜ ¼

(160) ¼ – ¬— ¼ .gBsEm|kxpyi|sEuxz€s   dm c #BkZoqpyi|sEuZz'+?‡ 1JoEu } + ‹ 1Jo ƒ c"3xnc } wQsijuBprz€s   p ` c ² oqm|“s ƒ i|p ` dv¡ ‚7ƒ sUs   . ¾ ƒ sBd + Œ 1 ¥ 3xnc } wQsijuBp€s    ² c ƒ i   ~ Y ’ B     + `C = . 1  * . I

(161)

(162) * . I  * . = .   * . I

(163)

(164) * . I * . . AWB    }oEu ¤Jc ` o§Ec  ¬ƒ sEd } i ƒ c pom| knm|opyi|sEuxz . . . !.  ¬ƒ sEd¤ ` c ƒ c.  . * .I

(165) * .I. . B. . Y .!A)B. . * .I

(166) * .I. . *.. . . . . *. *..  . . . . *.. *.. . C.  . + * .

(167) *

(168) 1     ’ + . 1. . ’. . C. *

(169) = . 1 C = . C + .+ *

(170) 1 .. C + `C. . . .  #. 1H. . ‘. ¤ ` i| ` i|zc

(171) #UkxoqpritsBu +?‹x¡ ‡ 1'¡  ¾ ƒ sEd +8 1 ¥ 3xnc } wQsijuBp*s   J² c ƒ i   ~ ’  C  ’ B Y E + `C = . 1  +?mtsE“ + * . I 1

(172) * . I  * . 1 = .   +¬m|s“ + * . I 1

(173) * . I  * . 1   . AWB F Y ’ B.  D . AWB +  C = . 1  * . I mtsE“ + * . I 1

(174) * . I  * . = .   * . I m|s“ + * . I 1

(175)

(176) * . I  * .    oEu } ¤Jc ` o§Ec ¥ m|cpypri|ux“  + *

(177)  1  ou } kxzri|ux“ijuBpyc “ ƒ oqpyi|sEuvŸB~5wxo ƒ p{z¡  ’  V. * a B  *

(178)

(179) * * *   +¬m|s“ + . I 1 . I  . 1   + * .

(180) 1  ? mtsE“ + 1   , cxw C *  . I  ' * ’*

(181) V mtsE“ 

(182) P cxw + C  1('  + . 1 +  ? 1

(183) V C  mtsE“ +8 1  + ’*

(184) 1 . + ? 1

(185) m|s“ + 1Bcn*w + 1'  !. . . . . 898;:=<>?@A. . $.  #.

(186) ‡‘.   !  

(187)  5    . .   +¬m|s“ + * . I 1

(188)

(189) * . I  * . 1 . .   + * . I m|s“ + * . I 1

(190)

(191) * . I  * . 1 . . .  . . . . .  * a B * .I * C | m  s “ + 1  c x  w ’ C  + . 1        '* + ? 1

(192) mtsE“  P cxw+ C  1(' ’

(193) ’ C +*.

(194) 1   ? tm  sE“ +8 1 +r’ C ’ + * .

(195) 1 1  + 1

(196) m|s“ + 1Bcxw+ C 1'  ’*

(197) V * mtsE“ + * 1  * a B cnw  C * . I ' *       + . 1 ?   V  P  cxw + C 1'   | m  s “   

(198) *

(199) + .  1 + ? 1

(200)  m|s“ + 1 V cn*w + C 1'   + * .

(201) 1 + ? 1

(202) V   + *  .

(203) 1 + ? 1

(204) m|s“ + 1Bcx*w + C 1'  m|s“ + 1  V    * . m|s“ + * . 1         + *  .

(205) 1 + ? 1

(206) m|s“ + 1Bcn*w + C 1'  ?  * a B  C * .I ’ * * ’ C + * .

(207) 1  m|s“ + 1     cxw    ' * ?. . .   + * . I m|s“ + * . I 1

(208)

(209) * . I  * . 1. ’*

(210). . . . . + ? 1

(211) ³mtsE“   P cxw+ C  1('

(212) ’ C   + * .

(213) 1   + ? 1

(214)  ’ C  + *

(215) 1 m|s“ + 1  ³cxw*+ C   1('  ’  . . * *

(216)   mtsE“ 8+  1   C   .  mtsE“ + * . 1 ’ C + . + *

(217) 1 1 .    +  ? 1

(218) . +r’ C  + * .

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