Journal of Engineering, Computers & Applied Sciences (JEC&AS) ISSN No: Volume 2, No.5, May 2013

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1 Joul of Egiig, Comuts & lid Sis JEC&S ISSN No: Volum, No.5, My 3 Costutio of Mid Smlig ls Idd Though MD & QL with Coditiol Rtitiv Gou Smlig l s ttibut l Usig Wightd oisso Distibutio R. Smth Kum, ssistt ofsso, Dtmt of Sttistis, Govmt ts Collg, Coimbto- 648, Tmil Ndu, Idi. R. Kiuthik, ssistt ofsso i Sttistis, Klig Kuidhi Istitut of Thology, Coimbto, Idi R. Rdhkish, ssoit ofsso, Dtmt of Sttistis, SG Collg of ts d Si, Coimbto, Idi BSTRCT This sts th odu fo th ostutio d sltio of mid smlig l with MD s qulity stdd d oditiol titiv gou smlig l s ttibut l usig wightd oisso distibutio s bs li distibutio. Th ls ostutd idd though MD d QL d lso omd. Tbls ostutd fo th sy sltio of th ls. Kywods d hss: Mimum llowbl t dftiv, tbl qulity lvl, Otig htisti, Tgt itt. MS Subt Clssifitio Numb: imy: 63 Sody: 6D5. Itodutio Mid smlig ls osist of two stgs of th difft tu. Duig th fist stg th giv lot is osidd s sml fom th stiv odutio oss d itio by vibls is usd to hk oss qulity. If oss qulity is udgd to b suffiitly good, th lot is td. Othwis th sod stg of th smlig l is td d lot qulity is hkd ditly by ms of ttibut smlig l. Th two tys of mid smlig ls lld iddt d ddt ls. If th fist stg sml sults ot utilid i th sod stg, th th l is sid to b iddt othwis ddt. Th iil dvtg of mid smlig l ov u ttibut smlig ls is dutio i sml si fo simil mout of ottio. It is th usul ti tht whil sltig smlig istio l, to fi th otig htisti OC uv i od with th dsid dg of disimitio. Th smlig l is i tu fid though suitbly hos mts. Th ty mts usd i th t smlig littu tbl qulity lvl QL, idiff qulity lvl IQL, limitig qulity lvl LQL d mimum llowbl t dftiv MD. Svl uthos hv ovidd odus to dsig th smlig ls idd though ths mts fo vious t smlig ls. Th ot of MD ws itodud by My 967 d futh studid by Soud 975 is th qulity lvl osodig to th ifltio oit o th OC uv. Th dg of shss of istio bout this qulity lvl is msud though t, th oit t whih th tgt to th OC uv t th ifltio oit uts th ootio dftiv is. O of th dsid otis of OC uv is tht th ds of should b slow fo lss vlus of d fst fo gt vlus of. If w st s th qulity stdd, th bov oty of th OC uv is obtid si osods to th ifltio oit of th OC uv d h d / d = fo = d / d < fo < d / d > fo > Th mid smlig l hs b dsigd ud two ss of sigifit itst. I th fist s sml si is fid d oit o th OC uv is giv. I th sod s ls dsigd wh two oits o th OC uv giv. Th odu fo dsigig th mid smlig ls to stisfy th bov mtiod oditios ws Blu O Rsh Jouls

2 Joul of Egiig, Comuts & lid Sis JEC&S ISSN No: Volum, No.5, My 3 ovidd by Shillig 967. Usig Shillig s odu, Dvul 3 hs ostutd tbls fo mid smlig ls iddt s hvig vious smlig ls s ttibut ls. Shm 965 hs itodud titiv gou smlig l i whih sml is dw d th umb of dftivs is outd. odig to fid itio, th lot is ith td, td o th sml is omltly disgdd d o hs to bgi with w sml i od to st lot. This is otiud util th fid itio idits us to ith t o t th lot. Submi 99 hs dvlod titiv gou smlig l ivolvig miimum sum of isks. Soud d Rmsmy 984, 986 hv md otibutios to RGS ls. Smth Kum t.l d Rdhkish t.l hv md otibutios to mid smlig l fo iddt s. Smth Kum 7 hs ostutd mid smlig l with vious smlig ls s ttibut ls usig oisso distibutio s bs li distibutio. Th wightd oisso distibutio lys imott ol i th t smlig, mily i th ostutio of smlig ls. Eh outom umb of dftivs is sifi but b ssigd with difft wights bsd o its imot o usg. I usig wightd oisso distibutio with wights X α, α = th g of th distibutio utild to,, 3 fom,, This distibutio b viwd s tutd oisso distibutio tutd t =. It will b mo usful to th idustis whih otts o sod s qulity lots d lso to th idustis whih hs tlst o dftiv i th moity of th muftuig lots. Ev though th mod thologis im t o dftiv/ dfts but tilly it is vy diffiult to mk th lot s o dftiv lot. I this ott, th litio of wightd oisso distibutio i th ostutio of smlig ls is vy lvt d it hs my ftus /dvtgs lso. Rdhkish Ro977 suggstd wightd Biomil distibutio b usd i dsigig smlig ls. Sudswi studid th ostutio of smlig ls usig wightd oisso distibutio s bs li distibutio. Moh iy 8, Smth Kum t.l, Rdhkish d Moh iy 8, 8 b hv ostutd th smlig ls usig wightd oisso distibutio s bs li distibutio. I this, mid smlig l iddt s with oditiol titiv gou smlig l s ttibut l is ostutd usig wightd oisso distibutio s bs li distibutio. Th ls idd though MD d QL ostutd stly by fiig th vlus of, d β '. Th mid ls idd though MD d QL lso omd.. Glossy Of Symbols Th symbols usd i this s follows: : submittd qulity of lot o oss : obbility of t fo giv qulity : mimum llowbl t dftiv t : th oit t whih th ifltio tgt of th OC uv uts th is. : th submittd qulity lvl suh tht =.95. h : ltiv slo t : sml si fo th vibl smlig l : sml si fo th ttibut smlig l : fist ttibuts t umb : sod ttibuts t umb d : umb of dftivs i th sml β : obbility of t fo lot qulity β ' : obbility of t ssigd to fist stg fo t dftiv β '' : obbility of t ssigd to sod stg fo t dftiv k : vibl fto suh tht lot is td if X = U-k 3. Otig odu Of Mid Smlig l Hvig Coditiol Rtitiv Gou Smlig l s ttibut l Shillig 967 hs giv th followig odu fo th iddt mid smlig l with u sifitio limit U d stdd dvitio σ.. Dtmi th mts of th mid smlig l,, k,, d.. Tk dom sml of si fom th lot. 3. If sml vg X = U- k, t th lot 4. If th sml vg X > = U- k, go to st i i Tk oth sml of si ii Cout th umb of dftivs d i th sml iii If d, t th lot. If d >, t th lot. If < d, utili th ifomtio of th t dig i sussiv lots i.., th ut lot is td if th dig i sussiv lots sult shows d i th sml, othwis t th lot. Th OC futio of th mid smlig l, suggstd by Shillig 967 fo sigl smlig Blu O Rsh Jouls 3

3 Joul of Egiig, Comuts & lid Sis JEC&S ISSN No: Volum, No.5, My 3 Blu O Rsh Jouls 4 l is... ; Equtio b ssd s β = β '+ - β ' β ''. By tkig th oditiol titiv gou smlig l s ttibut l, qutio b witt s....!!!! 4. Costutio Of Mid Smlig l Hvig Coditiol Rtitiv Gou Smlig l s ttibut l Usig Wightd oisso Distibutio Th dtild odu dotd i this fo th ostutio of mid smlig l hvig oditiol titiv gou smlig s ttibut l usig wightd oisso distibutio idd though MD is giv blow: ssum tht th mid l is iddt Did th sml si fo vibl smlig l to b usd. Clult th t limit fo th vibl smlig l s / ' { [ U }], wh is stdd oml vit osodig to t suh tht t = du t u Slit th obbility of t β s β ' d β ''suh tht β = β ' + - β ' β ''. Fi th vlu of β ' Dtmi β '', th obbility of t ssigd to th ttibut l ssoitd with th sod stg sml s β ''= β - β '/ - β '. Dtmi th oit sod stg sml of fom th ltio β '' =!!!! Usig th bov odu, tbls hv b ostutd to filitt sy sltio of mid smlig l usig oditiol titiv gou smlig l s ttibut ls idd though MD. 4. Costutio Of Tbls Th OC futio of wightd oisso distibutio fo sigl smlig l is giv by, ;, ; =,, 3 Th obbility of t fo oditiol titiv gou smlig l ud wightd oisso distibutio wh α = is usd i this fo dtmiig th sod stg obbilitis d is giv by 4.. ' =!!!! Usig th qutio 4 th ifltio oit is obtid by usig d d d 3 3 d d. Th ltiv slo of th OC uv h is giv by, h = d d t =. Th ifltio tgt of th OC uv uts th is t t = + /h. Th vlus of, h, t d R= t / lultd fo th sifid β ' =.4 usig C ogm d std i Tbl. 4. Sltio Of Th l Tbl is usd to ostut th ls wh MD d tgt itt t giv. Fo y giv vlus of, t d o fid th tio R = t /. Cosodig to th vlu of fid th vlu i Tbl ud th olum R whih is qul to o ust gt th th sifid tio, th osodig vlu of is otd. Fom this d vlus o dtmi th vlu of usig = /. Eml : Giv = 5, =.9, t =.7 d β ' =.4. Fid th tio R= t / = Usig Tbl, osodig to = 5 slt th vlu of R qul to o ust gt th this tio. Th vlu

4 Joul of Egiig, Comuts & lid Sis JEC&S ISSN No: Volum, No.5, My 3 of R is.899 whih is ssoitd with =5, =9 d = / = 5. 88/.9 = 58. Th mid smlig l with oditiol titiv gou smlig l s ttibut l is =58, = 5 d =9 th OC uv is std i Figu. 5. Sltio Of Mid Smlig l Hvig Coditiol Rtitiv Gou Smlig l s ttibut l Iddd Thoughh ql Th gl odu giv i stio 4 is usd fo dsigigg th mid smlig l hvig oditiol titiv gou smlig l s ttibut l iddd though QL. Fo th sifid vlus of β =.95 d β ' =.4, th vlus lultd fo difft vlus of d usig C ogm d std i Tbl. Tbl : Comiso of ls 5. SELECTION OF THE LN Tbl is usd to ostut th ls wh QL,, vlus giv. Fo y sifid vlus of, d o dtmi vlu usig = /. Eml : Giv =.7, = 4, = 5 d β '=.4. Usig Tbl, fid = / =.56/.7=3. Fo fid β '=.4, th mid smlig l with oditiol titiv gou smlig l s ttibut l is = 3, = 4 d =5. 6. Comiso Of ls Idd Though MD & QL I this stio th mid smlig l with oditiol titiv gou smlig l s ttibut l idd though MD is omd with th mid smlig l with oditiol titiv gou smlig l s ttibut l idd though QL by fiig th mts, d β '. Fo th sifid vlus of d t with th ssumtio β ' =.4 o fid th vlus of d idd though MD s i stio 4. By fiig th vlus of, d, fid th vlu of by qutig = β =.95. Usig β ' =.4,, d o fid th vlu of usig = / fom Tbl. Fo difft ombitios of, d t, th vlus of, idd though MD d, idd though QL lultd d std i Tbl. 7. Colusio I this th odu fo ostutig mid smlig ls with oditiol titiv gou smlig l ttibut l iddd though MD d QL with wightd oisso distibutio s th bsli distibutio std. Suitbl tbls lso ovidd fo th sy sltio of th ls fo th gis who wokig o th floo of th ssmbly. It is oludd fom th study tht th sod sml si quid fo mid smlig l with oditiol titiv gou smlig l s ttibut l idd though MD is lss th tht of th sod stg sml si of th mid smlig l with oditiol titiv gou smlig l s ttibut l iddd though QL, ustifid by Smth Kum 8. Ths ls dfiitly hl th odus, bus of th lss sml si whih ditly sult i lss smlig ost d iditly dus th totl ost of th odut. Th difft smlig ls lso b ostutd by hgig th fist stg obbilitis ββ ' d β ' d b omd fo thi ffiiy. Rfs [] S. Dvul, Cti Studis Rltig to Mid Smlig ls d Rlibility bsd Blu O Rsh Jouls 5

5 Joul of Egiig, Comuts & lid Sis JEC&S ISSN No: Volum, No.5, My 3 Smlig ls, h.d., Dissttio, Dtmt of Sttistis, Bhthi Uivsity, Coimbto, Tmil Ndu, Idi,3. [].L.My, ot o sum of oisso obbilitis d litio, Idustil Qulity Cotol, Vol.9, No.5,.-5,967. [3] L. Moh iy, Costutio d Sltio of t Smlig ls bsd o Wightd oisso Distibutio, h.d., Dissttio, Dtmt of Sttistis, Bhthi Uivsity, Coimbto, Tmil Ndu, Idi,8. [4] C. Rdhkish Ro, tul ml of wightd biomil distibutio, Th mi Sttistii, Vol.3, No.,977. [5] R. Rdhkish d L. Moh iy, Sltio of sigl smlig l usig oditiol wightd oisso distibutio, Ittiol Joul of Sttistis d Systms, Vol.3, No.,. 9-98,8. [6] R. Rdhkish d L. Moh iy, Comiso of CRGS ls usig oisso d wightd oisso distibutio, obstt Foum, Vol., No.,.5-6,8b. [7] R. Rdhkish, R. Smth Kum, d M. Mlthi, Sltio of mid smlig l with TNT-, ; l s ttibut l idd though MD d MOQ, Ittiol Joul of Sttistis d systm, Vol.5, No.4, ,. [8] R. Smth Kum, Costutio d Sltio of Mid Vibls-ttibuts Smlig ls - h.d., Dissttio, Dtmt of Sttistis, Bhthi Uivsity, Coimbto, Tmil Ndu, Idi,7. [9] R. Smth Kum, R. Kiuthik d R. Rdhkish, Comiso of mid smlig l idd though MD d LQL with sigl smlig l s ttibut l usig wightd oisso distibutio, Joul of sttistis si, Vol.3, No., ,. [] R. Smth Kum, R. Viykum d R. Rdhkish, Sltio of mid smlig ls with titiv gou smlig l s ttibut l idd though MD d QL usig itvd dom fft oisso distibutio, Globl oul of Mgmt si d thology, Vol., No. 4,. [] E.G. Shillig, Gl Mthod fo Dtmiig th Otig Chtistis of Mid Vibls - ttibuts smlig ls Sigl sid sifitios, S.D.kow, h.d., Dissttio- Rutgs- Th Stt Uivsity, Nw Buswik, Nw Jsy,967. [] R. E. Shm, Dsig d vlutio of titiv gou smlig l, Thomtis, Vol.7, No.,.-,965. [3] V. Soud d M. M. Rmsmy, Dsigig titiv gou smlig l idd by QL d LQL, IQR Tstio, Vol.9, No.,.9-4,984. [4] V. Soud d M. M. Rmsmy, odus d tbls fo ostutio d sltio of titiv gou smlig l, Th QR oul, Vol.3, No.3,.4-,986. [5] V. Soud, Mimum llowbl t dftiv MD sigl smlig istio by ttibut l, Joul of Qulity Thology, Vol.7, No.4,.73-8,975. [6] K. Submi, Studis o Dsigig ttibut t Smlig ls with Emhsis o Chi Smlig ls, h.d Thsis, Bhthi Uivsity, Coimbto, Tmil Ndu, Idi,99. [7] Sudswi, Dsigig of Smlig l usig Wightd oisso distibutio. M.hil., Dissttio, Dtmt of Sttistis, SG Collg of ts d Si, Coimbto,. Blu O Rsh Jouls 6