An N-Component Series Repairable System with Repairman Doing Other Work and Priority in Repair

Transcription

1 Mor ppl Novmbr 8 N-Compo r Rparabl m h Rparma Dog Ohr ork a ror Rpar Jag Yag E-mal: jag_ag7@6om Xau Mg a uo hg ollag arb Normal Uvr Yaq ua Taoao ag uppor b h Fouao or h aural o b prov o Cha 5 uppor b h la roj o b Euao O No7 bra I h papr u h rlabl o a N-u r rparabl m h h rparma og ohr ork a pror rpar I h m aum ha h orkg m rbuo o h ompo a h arrval rval m rbuo o h uomr hh ar ou o h m ar boh poal a h ompo m gv pror rpar I alo aum ha h rpar m rbuo o h ompo a h rv m rbuo o h uomr ar boh gral ouou rbuo r rpar ompo ar a goo a Ur h aumpo ug a upplmar varabl hqu a Lapla raorm hqu om mpora rlabl uh a h m avalabl h l probabl o h rparma a h ra o rv or uomr ar rv Our problm o rm hhr or o gv h pror o ompo rparg uh ha h b o h m mamz Kor: Rlabl upplmar hqu ralz Markov pro Irouo I orr o mprov h r o h m h uprvor ala arrag h rparma rv or h uomr ou o m Ur h oo a aumpo ha h orkg m rbuo ar poal a h rpar m rbuo a h m rbuo o h rparma og ohr ork ar boh gral ouou rbuo b ug upplmar hqu a vor Markov pro h rlabl hav b oba a h b o h mol u u B 994 pp4-9 Lar h umbr o h uomr ha b rou LIU RB a TN Y 5 pp aum ha h orkg m a h arrval rval m hav poal rbuo hl ohr o b gral ouou rbuo B ug h upplmar varabl mho h vor Markov pro a h ool o h Lapla raorm om rlabl o h m hav b rv a h b o h m u U LM U JB a TIN RL 7 pp47-5 hav b rou h aumpo ha ah u ha o p o alur Th hav oba h rlabl o h m Zhag YL a ag J6pp7895 rou h pror u a rorag ol ab rparabl m 6

2 Vol No 6 Mor ppl hl ala mamzg h r o m ha rparma rvg or uomr ou o m h rpar ork o h ompo mab la or h rparma og ohr ork Th purpo o h papr o appl h pror rpar mol o a -ompo r rparabl m h h rparma og ohr ork No ma aum ha h u ar rpar a goo a a h u hav pror rpar Furhrmor aum ha h orkg m o h ompo a h arrval rval m uomr ar boh poall rbu a ohr grall rbu Mol u a -ompo r rparabl m h rparma og ohr ork a pror rpar b makg h ollog aumpo: umpo Iall h ompo ar all a ork oubl har hl h rparma l umpo h o ompo o rparg h ohr ll op orkg a o go rog Th m alg o umpo I a ol h h ompo ar all orkg a h uomr o arrv h rparma l I a ol h h ompo ar all orkg h uomr ll b lkl o arrval Th uomr o arrv h o ompo rpar or h rparma rvg or o uomr a aohr uomr ag or rv h o uomr ag or rv a o ompo go rog h uomr ll lav h ompo rpar mmal hl h uomr rv ll b ag or rv Th uomr ll b rv ar h rpar ovr a h rv bor val L X a Y b rpvl h orkg m a h rpar m o h ompo aum ha h rbuo o X a Y ar rpvl F p g p hr > > L b h rv m o h uomr aum ha h rbuo o h p L V b h m b rparma ar l a h arrval o h r uomr a b h arrval o h r uomr a h o o aum ha h rbuo ov V p hr > umpo 4 um ha X Y Th m aal L { } { } a V ar p b a oha pro hararz b h ollog muuall luv v: : ompo ar all orkg a h rparma l { } : Th ompo rpar { } { } : ompo ar all orkg h rparma rvg or h uomr : ompo ar all orkg h rparma rvg or o uomr a h ahr ag or rv { 4} : h ompo rpar h uomr ag or rv Th { } a oha pro h a pa Ω { 4 } { } a h o alur a F { 4 } org o h mol aumpo { } Th o orkg a o a Markov pro ovr a b o a gralz Markov pro b roug a upplmar varabl L X b h rpar m o h ompo u a m L Y b h rv m o h uomr u Th{ X Y } ou a gralz Markov pro 64

3 Mor ppl Novmbr 8 65 Th a margal probabl o h m a m ar b 4 4 Y X Y Y X org o h mol aumpo a h upplmar varabl hqu a oba h ollog ral quao or h m B raghorar probabl argum or ampl hav o hr Lg o zro a g I h am a hav Th bouar oo ar Th al oo ar 4 Th m ral quao ug Lapla raorm ar oba a ollo: 4

4 Vol No 6 Mor ppl Toghr h h borrl oo a h al oo h m o quao a b olv o l: [ ] hr 4 Rlabl 4 m avalabl a m ra o ourr o alur B h o h m avalabl a gv b h m orkg a m N k k Th Lapla-raorm o hr aorg o a hu hr Ug Taubra horm h a a avalabl or h lmg avalabl o h m gv b lm lm L b h ra o ourr o alur or h alur rqu o h m a m

5 Mor ppl Novmbr 8 67 M org o Lam [6] hav Th Lapla raorm o gv b Ug Taubra horm h a a alur rqu o h m gv b lm lm 4 4 Th l m probabl o h rparma Clarl h rparma ll b l a ol h ompo ar all orkg a o uomr arrval Thu h l m probabl o h rparma a m gv b I Th Lapla raorm o I I Ug Taubra horm h a a alur rqu o h m gv b I I I lm lm 5 4 Th ra o ourr o h rparma rvg or uomr L N b h umbr o h uomr rv urg a gv m ] h aorg Lam[6] hav D N hr D h ra o ourr o h rparma rvg or uomr or h rvg rqu o h rparma a m org o Lam [6] hav D Th Lapla raorm o D gv b D Ug Taubra horm h a a umbr o h uomr rv b h rparma pr u m gv b lm lm D D N 6 5 Th m b aal I h o our objv o rm hhr or o gv h pror o ompo rparg uh ha h b o h m mamz L b h orkg rar pr u m o h m b h avrag o

6 Vol No 6 Mor ppl ah m o h m a b h avrag rar o rvg or o uomr Ba o h aumpo h a a avrag rar pr u m o h m 7 D I orr o olv h our problm ar o rou om oluo a aumpo ha LIUR b TNYg hu &LUO Chua 5 hav u I h papr l b h orkg rar pr u m o h m b h avrag o ah m alur o h m a b h avrag rar o rvg or o uomr Clarl or o m h a ll b rpvl am o h a hl h ll b r rom bau h lu h o prou b ag rpar o h quao ll b hag o D Th a a avrag rar pr u m o h m Lam [] hhr or o h ompo gv h pror rparg ll p o h rul o h quao : h ompo ll b gv pror rpar h h rul o quao pov umbr hl h ompo ll o b gv pror rpar h h rul o quao gav I h a h b o h m ll b mamz Rr u B 994 a mol o -u r rparabl m h a rparma og ohr ork[j] Joural o hjazhuag Rala Iu LIU RB TN Y &LUO CY 5 N - u r rparabl m h a rparma og ohr ork [J] Joural o Naural o logjag Uvr U LM U JB & TIN RL 7 r rparabl m h o p o alur a a rparma og ohr ork [J] Joural o Yaha Uvr 47-5 Zhag YL & ag J 7 a rorag ol ab rparabl m h pror u[j] Europa Joural o Opraoal Rarh MEN XY LIU Y CEN J LIU LC YIN RL & YUN L 6 Rlabl aal o arm ab rparabl o o ompo h ouou lm h a pror [J] Joural o Yaha Uvr 5-56 h D 985 a mho or alulag h ma alur umbr o a rparabl m urg ][J] a Mahmaa pplara a 8-68