Study of Real time Dynamic Preventive Maintenance Policy for Deteriorating Production Systems

Size: px

Start display at page:

Download "Study of Real time Dynamic Preventive Maintenance Policy for Deteriorating Production Systems"

Samson Hampton
5 years ago
Views:

1 Sudy of Rel e Dyc reveve Mece olcy for Deeror roduco Syses Sudy of Rel e Dyc reveve Mece olcy for Deeror roduco Syses Ch-T Che M-H Ch- 3 d Joh Yu 4 Assoce professor Depre of Idusrl Eeer d Mee T-H Isue of Techoloy Hschu 37 T ROC. e-l:ecche@h.edu.. Assoce professor Depre of Auoo Eeer T-H Isue of Techoloy Hschu 37 T ROC. e-l:ehl@e4.h.edu.. 3 Depre of Idusrl Eeer d Eeer Mee Nol Ts-Hu Uversy R.O.C. 4 rofessor Depre of Idusrl Eeer d Eeer Mee Nol Ts-Hu Uversy R.O.C. Absrc The purpose of hs rcle s o propose boh se d e depede preveve ece polcy for deeror syse. Us helh dex er he preers speced by sesors c eere he rel-e equpe oper se. I hs reserch dscree e Mrov ul-se deeror odel s doped o descrbe he se rso of equpe. The odel lso cludes () he deeror of oper ses d () he of rso probbles;(3) Bse o hsorcl d e c ese he odel preers ( fcor d l rso rx) d (4) ssue h ulple perfec cos h rs re vlble. For he prccl pplco of he odel he ece e s lso e o cosdero. The rel e opl ece polcy of ech oper se c be eered by he rule of he u expeced ol cos per u e for ech cycle dur fe e ervl. Alorh d copuer code re lso lsed for dusrl pplco. eyords: dyc preveve ece polcy fcor helh dex. Iroduco The dvced echoloy dusres requre hh precso d hhly sble equpe o vod he cos cused by flure occurrece. Equpe uoo d preveve ece us be execued o eep equpe h proper oper ses. I hs lys bee por opc for sudy spec he oper ses of equpe by sesors d deer he dyc preveve ece polces ccord o he rel-e codo by copuer lyz ceers. Exesve reves of vrous ece polces o deeror syse c be foud [ 3]. The frs Ierol Jourl of The Copuer he Iere d Mee Vol. 5# (Jury Aprl 7) pp - 4

2 Ch-T Che M-H Ch- d Joh Yu clss s o del h o se syse. Ths follos fro he fc h he co s e upo flure oly uder such o speco equpe cse. The e replcee polcy (.e. replcee upo flure or e) [4] d her exesos by clud l repr such s [5-] belo o such clss. The bloc replcee polcy (.e. replcee T for or upo flure) d he flure replcee polcy (.e. replcee upo flure) lso belo o such clss [-3]. The scheduled ece polces hrouh predc flure e ssclly lso belo o hs clss [cf.4 5]. The secod clss s o del h ul-se deeror syse provded h speco equpe(s). Ech se of he syse us be defed hrouh speco for exple ech d. The he opl ece co c be decded d for he syse by z he obecve fuco such s he expeced ol cos per lfe cycle he expeced ol cos per u e d ec. Hece s oly he secod clss o preveve ece polces. d Yeh [6] proposed corol-l replcee polcy uder couous speco so h replcee s e oplly heever he hreshold se s defed by speco or he coplee flure s observed. d Yeh [] proposed oher corol-l replcee polcy uder speco ech d so h he replcee es plces d heever he syse se x d ssfes x for hreshold se o deere he opl (d). Ch d Yu [78] proposed oher corol-l preveve ece polces uder couous d perodc speco respecvely by deer o hreshold ses < (<<<) so h he opl co s h repr (resp. replcee do-oh) s e heever he syse se s defed s x so h x< (resp. x : oherse). ood [9] proposed corol l rule h requres resoro of he syse heever he de exceeds cer level uder couous speco. Such ehods hve o ssue h he syse before y ece polcy ssfes couous-e Mrov ch. Also he hreshold se(s) hus obed d so he opl ece co e s se depede oly (.e. o e depede). Jrde ec. [] proposed opl dyc (.e. e-depede oo) replcee polcy for codo-bsed ece. lde ec. [] proposed oher dyc preveve ece polcy h es lo-e eve pl s bss for subseque dpo ccord o vlble foro o he shor er by roll-horzo pproch. Recely Che e l [4] proposed se depede preveve ece polcy for ul-se deeror syse hch s equpped h speco equpe(s) coeced o copuer ceer. Afer he syse be defed s se x d hrouh copuo by he copuer ceer fer speco (or esuree) v equpe(s) oe ece co h he u expeced ol cos sce d ll Nd (here N for fxed eer < < ) ll be chose fro he se A x of lerves lso h he help of he copuer ceer. I rel cse he expeced ol coss sce d ll Nd ll be e depede d so s he ece co chose d. Exeded he reserch of Che e l. [4] he purpose of hs pper s o propose boh se d e depede preveve ece polcy for deeror syse. Such dyc preveve ece polcy c be llusred flo chr Fure. I Ch d Yu [78] he percee of defecves o producs hch he syse produces s

3 Sudy of Rel e Dyc reveve Mece olcy for Deeror roduco Syses fc e s he syse helhy dex H her corol-l preveve ece polces co preve he produco syse fro producs defecves effecvely s he proposed oe here. Opl Mece co Equpe fcor fcor fcor p Rel-e Mece polcy Rel e se Helh Idex(H) se Geere rel- e rso probbly rx Dbse Fure The dr of he dyc preveve ece polcy. Syse Model d Alorh - Sybol descrpo: β dscou re M perod for M polcy c ( ) expeced cos for co d c ( ) SH o () expeced cos dur d due o l reprs or scrp ve syse se R replcee cos of equpe T ( ) e for co ; T ( ) d SH T T T ( ) replcee e deeco e po for h decso equpe e for syse ( ) ( ) expec cos per u e for co d se expec cos per u e for co d se u co of ( ) ( ) ( ).e. ; s ssfed by ( ( ) { ) } opl co uder u cos per u e ( ( ) ( () ) ` ) opl co uder u cos per u e ( ) ) ( () ` - reveve ece polcy Expeced ol cos due o u reprs or scrp ve syse se dur ( ) for co c be expressed s follos: Ierol Jourl of The Copuer he Iere d Mee Vol. 5# (Jury Aprl 7) pp - 4 3

4 Ch-T Che M-H Ch- d Joh Yu o() l rl f O( ) l () O( ) o f robbly deeced syse se for co ( )c be expressed s follos: ( ) rh h h ( ) ( ) -3 Alorh: () (he ) Sep : deere opl co ( ) ( ) () d ( { ) ( )}.e. r SH Frsly clcule he cos d e for : R c ( )( ) o() ( )( ) he T d T ( ) O( ) ( ) ( ) ( ) f f f ( ) ( ) f f f d ( ) ( ) ( )( ) ( ) ( { ) ( )} e ob h ( ) ( ) ( { ) ( )} ( )( ) ( )( ) r SH ; ( ) ( ) ( )( ) ( ) d ( ) ( ) ) ( Sep Gve he codo ( ) ) ( deere he opl ece co e for ( () ) Frsly clcule he cos d expded () ( ) d R o c () ( ) : ( ) o β [ T ] ( ) ( ) () β { ( ( ) )} ( ) O β [ T( )] ( ) T d T ( ) { ( ( ) )} { ( ) ( ( ) )} ( ) ( ) ( ) For coveece le rdo vrble ( ) ( ) he X 及 be: f f f f f f 4

5 Sudy of Rel e Dyc reveve Mece olcy for Deeror roduco Syses Ierol Jourl of The Copuer he Iere d Mee Vol. 5# (Jury Aprl 7) pp () () d () () he () () () () () E d e ob h () r H S ; () () () (Gve () he () ) ( ) ( s obed) Sep Gve he codo of () () ) ( deere he opl ece co () ) (. For coveecele () () () () () () () () () () () () () () () () I es h ve he codo he expeced cos d e due o u repr or scrp ve syse se dur re clculed respecvely. Secodly he expeced cos d e due o u repr or scrp ve syse se dur re clculed [ ] () () () [ ] () T O c o T o R f f f β β β d () () T d T f f f e rdo vrble 及 be: he X d he E

6 Ch-T Che M-H Ch- d Joh Yu 6 d e ob h r H S ; Sep ( 3 ) Gve he codo deere he opl ece co () ) (. e () () () () () () () () () () () () I es h ve he codo () he expeced cos d e due o u repr or scrp ve syse se dur re clculed respecvely. The he expeced cos d e due o u repr or scrp ve syse se dur re clculed () [ ] () [ ] T O c o T o R f f f β β β d T d T f f f For coveece le rdo vrble d be he X d The E d e ob h r S H ; For coveece le

7 Sudy of Rel e Dyc reveve Mece olcy for Deeror roduco Syses ( ) ( () ) ( () ) () () ( () ) () ( ) ( () ) ( () ) ( () ) () ( ) I es h ve he codo he expeced cos d e due o u repr or scrp ve syse se dur re clculed respecvely. Sep : e ob ( ) ( ) () S H The he opl ece perod uder he codo of he expeced cos d e due o u repr or scrp ve syse se (.e. ( ) ( ) { ( )} ) for () opl co ( A ( ) ( ) () ( ) s obed ) dur r ( ) ( ( ) ) () 3 M (3) The pror code us Mlb sofre s lsed Appedx for referece. 3. Coclud Rer Exeded he reserch of Che e l. [4] he purpose of hs pper s o propose boh se d e depede preveve ece polcy for deeror syse. Ths reserch s focused o he deeror syse. Us helh dex er he preers speced by sesors c eere he rel-e equpe oper se. I hs reserch dscree e Mrov ul-se deeror odel s doped o descrbe he se rso of equpe. The eso ehodoloes of he odel preers re lso provded hs pper. For he prccl pplco of he odel he ece e s lso e o cosdero. Accord o he rel-e equpe sus he rel e opl ece polcy of ech oper se c be eered by he rule of he u expeced ol cos per u e for ech cycle dur fe e ervl. Refereces [].. ersll d J. A. Voeler A survey of ece odels: he corol d survellce of deeror syses Nvl Reserch osc Qurerly 3 (976) [] C. Vlderz-Flores d R. M. Feld A survey of preveve ece odels for sochsclly deeror sle-u syse. Nvl Reserch osc Qurerly 36 (989) [3] Y. S. Sherf d M.. Sh Opl ece odels for syse subec o flure: survey Nvl Reserch osc Qurerly 8 (98) [4] R. Brlo d. Huer Opl reveve Mece olces Operos Reserch 8 (96) 9-. [5] T. A. Mzzuch d R. Soyer A Byes perspecve o soe replcee srees Relbly Eeer d Ierol Jourl of The Copuer he Iere d Mee Vol. 5# (Jury Aprl 7) pp - 4 7

8 Ch-T Che M-H Ch- d Joh Yu Syse Sfey 5 (996) [6] S. H. Sheu R. H. Yeh Y. B. d M. G. Ju A Byes perspecve o e replcee h l repr Relbly Eeer d Syse Sfey 65 (999) [7] R. Cleroux. S. Dubuc d C. Tlqu The e replcee proble h l repr d rdo repr coss Opero Reserch 7 (979) [8] I. B d. J Iprovee deeroro opl replcee h l repr. IEEE Trsco o Relbly 43 (994) [9] M. Che M d R. M. Feld Opl ece polces h l repr odel. Europe Jourl of Operol Reserch 98 (997) [] J.. Jh d S. H. Sheu Opporuy-bsed e replcee polcy h l repr Relbly Eeer d Syse Sfey 64 (999) [] M. Ber M d B. Epse Coprso of e bloc d flure replcee polces IEEE Trscos o Relbly 7 (978) 5-9. [] C. T. d R. H. Yeh Opl Mece-olces For Deeroro Syses Uder Vrous Mece Srees IEEE Trscos o Relbly 43 (994) [3] H.. Bloc N. A. ber d T. H. Svs Repr replce polces Jourl of Appled robbly 3 (993) [4] R. V. Cfeld Cos opzo of perodc preveve ece IEEE Trscos o Relbly 35() (986) [5] D. Chudrhur d. C. Shu reveve ece ervls for opl relbly of deeror syse IEEE Trscos o Relbly 4(4) (977) [6] C. T. d R. H. Yeh Coprso of sequel d couous speco srees for deeror syses Advces Appled robbly 6 (994) [7] J. H. Ch d J. Yu Opl ece polcy for Mrov syse uder perodc speco Relbly Eeer d Syse Sfey 7 () [8] J. H. Ch d J. Yu Opl ece polcy for produco syse subec o e d shocs Jourl of Quly Mece Eeer 6(3) () -6. [9] A.. ood Opl Mece olces for Cosly Moored Syse Nvl Reserch oscs 35 (998) [] A. D. S. Jrde D. Bevc d V. Ms V. Opl Replcee olcy d he Srucure of Sofre for Codo-bsed Mece Jourl of Quly Mece Eeer 3 (997) 9-9. [] V. Ms d A.. S. Jrde Copuo of Opl olces Replcee Models Jourl of Mhecs Appled Busess & Idusry 3 (99) [] R. E. lde R. Deer d ACJM. S A dyc polcy for roup ece cves Europe Jourl of Opero Reserch 99 (997) [3] R. S. Guo A. Che S.. Tse I.. Fo A. Yu C.. ee C. H. u S. S. J. Hu Y. C. ee S. Ch d M E. ee A rel-e equpe oor d ful deeco syse. Secoducor Mufcur Techoloy orshop (998) pp. -. [4] C. T. Che Y.. Che d J. Yu O dyc preveve ece polcy for syse uder speco. Relbly Eeer d Syse Sfey 8 (3)

9 Sudy of Rel e Dyc reveve Mece olcy for Deeror roduco Syses Appedx ror code us Mlb sofre Ese fcor: Cod do cler ll; scd; ME; scd. % ve l rso probbly rx [ ; ; ; ; ; ;.78.99;.]; ; % ve ece co cos C[ ]'; % ve co rs rx R[ ; ; ; ; ; ]; % ve co e T[ ]'; % ve reulr se cos o[ ]'; lobl O O(:7)o(:7); O(8:3)R(:)o; O(4:8)R(:)o; O(9:)R(3:)o; O(3:5)R(4:)o; O(6:7)R(5:)o; O(8)R(6:)o; % dscou re lobl be be.96; lobl cos_sr Ierol Jourl of The Copuer he Iere d Mee Vol. 5# (Jury Aprl 7) pp - 4 9

10 Ch-T Che M-H Ch- d Joh Yu lobl perod_sr lobl UC_sr % ve fcor lobl _preer _preer.5; lobl p p; sple. scd; (::); for :9 (::)((::-)_preer); ed % eere 5 sple phs for u:5 se; sple_ph(use); for :9 sple_ph(u)rs(rd(sple_ph(u-):-)); f sple_ph(u)8 for :9 sple_ph(u)8; ed bre ed ed ed % clcule lehs of 5 sple phs leh zeros(5); for u : 5 for : 9 leh(u) leh(u) ; f sple_ph(u) 8 bre ed ed ed ME. sple; for : 9999 s / ; (::); for : x(leh) (::) ((::-)s); ed ed

11 Sudy of Rel e Dyc reveve Mece olcy for Deeror roduco Syses zeros(9999); for : 9999 for u : 5 for : leh(u)- () () lo((sple_ph(u)sple_ph(u))); ed ed ed [soreddex]sor(); Esdex(9999)/ Exple for M polcy : Cod do cler ll; scd; % ve d for : (_preer); ed dyc;. fuco rx (s); rx; for : 7 fd( (:) x( (:))); f 8 7; ed su ;Rsu ; for : su su(); ed for : 8 Rsu Rsu(); ed for : f su> rx() ()( - (Rsu/su)s); ed f rx() < rx() ; bre ed ed Ierol Jourl of The Copuer he Iere d Mee Vol. 5# (Jury Aprl 7) pp - 4

12 Ch-T Che M-H Ch- d Joh Yu ed for : 8 rx() ()( s); f rx() > rx() ; bre ed ed dyc. M(::); for : p Q(::)RM(::); M(::)(M(::)_preer); ed for : p cos_srzeros(8); perod_srzeros(8); UC_srzeros(8); lbel[ 9]; ; hle > dyc_ero; -; ed A(:)UC_sr;B(:)lbel;D(:)UC; ed for : 8 _sr()(fd(a(:p)(a(:p)))); co_sr()b(_sr()); ed _sr_sr- co_sr dyc_ero. epzeros(9); epzeros(9); for : 7 for : 8 ep()ep()(m()cos_sr()); ep()ep()(m()perod_sr()); ed ECos()C()O()beep()T(); Eerod()T()ep(); ed for 8 : 3 for : 8 ep()ep()(q()cos_sr());

13 ep()ep()(q()perod_sr()); ed ECos()C()O()beep()T(); Eerod()T()ep(); ed for 4 : 8 for : 8 ep()ep()(q()cos_sr()); ep()ep()(q()perod_sr()); ed ECos()C()O()beep()T(); Eerod()T()ep(); ed for 9 : for : 8 ep()ep()(q(3)cos_sr()); ep()ep()(q(3)perod_sr()); ed ECos()C()O()beep()T(); Eerod()T()ep(); ed for 3 : 5 for : 8 ep()ep()(q(4)cos_sr()); ep()ep()(q(4)perod_sr()); ed ECos()C()O()beep()T(); Eerod()T()ep(); ed for 6 : 7 for : 8 ep()ep()(q(5)cos_sr()); ep()ep()(q(5)perod_sr()); ed ECos()C()O()beep()T(); Eerod()T()ep(); ed for : 8 ep(8)ep(8)(q(6)cos_sr()); ep(8)ep(8)(q(6)perod_sr()); ed ECos(8)C(8)O(8)beep(8)T(8); Eerod(8)T(8)ep(8); for : 8 ep(9)ep(9)(()cos_sr()); Sudy of Rel e Dyc reveve Mece olcy for Deeror roduco Syses Ierol Jourl of The Copuer he Iere d Mee Vol. 5# (Jury Aprl 7) pp - 4 3

14 Ch-T Che M-H Ch- d Joh Yu ep(9)ep(9)(()perod_sr()); ed ECos(9)C(9)o()beep(9)T(9); Eerod(9)T(9)ep(9); UCECos./Eerod; UC_sr()UC(); UC_sr()([UC() UC(8)]); UC_sr(3)([UC(3) UC(9) UC(4)]); UC_sr(4)([UC(4) UC() UC(5) UC(9)]); UC_sr(5)([UC(5) UC() UC(6) UC() UC(3)]); UC_sr(6)([UC(6) UC() UC(7) UC() UC(4) UC(6)]); UC_sr(7)([UC(7) UC(3) UC(8) UC() UC(5) UC(7) UC(8)]); UC_sr(8)UC(9); for : 7 for : 8 f UC_sr()UC() lbel(); ed ed ed for : 7 cos_sr()ecos(lbel()); perod_sr()eerod(lbel()); ed 4

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY [Mjuh, : Jury, 0] ISSN: -96 Scefc Jourl Impc Fcr: 9 ISRA, Impc Fcr: IJESRT INTERNATIONAL JOURNAL OF ENINEERIN SCIENCES & RESEARCH TECHNOLOY HAMILTONIAN LACEABILITY IN MIDDLE RAPHS Mjuh*, MurlR, B Shmukh