Matched Quick Switching Variable Sampling System with Quick Switching Attribute Sampling System
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1 Natur and Sn 9;7( g v, t al, Samlng Systm Mathd Quk Swthng Varabl Samlng Systm wth Quk Swthng Attrbut Samlng Systm Srramahandran G.V, Palanvl.M Dartmnt of Mathmats, Dr.Mahalngam Collg of Engnrng and Thnology, Pollah, Taml Nadu, 643, Inda Dartmnt of Statsts, Govrnmnt Arts Collg, Udumalt. Taml Nadu 646, Inda gvsrramahandran@yahoo.om, alanvlm@yahoo.om Abstrat: Ths ar rsnts a mthodology for fndng a Quk Swthng Sngl Samlng varabls nston systm mathng a gvn Quk Swthng attrbut samlng nston systm. Hr mathng mls th sam Atan Qualty Lvl (AQL (.95,.95 and Lmtng Qualty Lvl (LQL (.,. of th Oratng Charatrst (OC urvs for both th systms. [Natur and Sn 9;7(:33-39]. (ISSN: Ky words: Oratng Charatrst Curv, Atan Samlng, Atan Qualty Lvl and Lmtng Qualty Lvl. Introduton Hamakr (979 has gvn a mthod of onstrutng sngl samlng varabls nston lans suh that th OC urv of a gvn sngl samlng attrbuts nston lan and th OC of th varabls lan hav th sam ndffrn qualty lvl ( and th sam rlatv slo (h of th OC urv at. Bndr (975 has gvn a tabl for sngl samlng varabls nston lans mathd at th onts (.95,.95 and (.,. wth attrbuts nston lans gvn n Tabl II-A of MIL-STD- 5D (963. Bndr (975 ahvs ths mathng by mans of an tratv omutr rogram nvolvng non ntral t-dstrbuton. Rombosk (969 has studd a nw systm, omrsng of normal and tghtnd lans, alld Quk swthng systm (n;, [(n, and (n, ar normal and tghtnd sngl samlng lans rstvly wth > ] roosd by Dodg (967. Taylor (996 nvstgatd how to valuat and slt Quk Swthng Systms. Soundarajan.V and Palanvl.M (997 and Soundarajan.V and Palanvl.M ( has nvstgatd on Quk Swthng Varabls Sml Samlng (QSVSS Systms.. Oratng Produr St : From a lot, tak a random saml of sz n and ount th numbr of dftvs, d If at th lot and rat th st for th nxt lot. If d > rjt th lot and go to st. St : From th nxt lot, tak a random saml of sz n and ount th numbr of dftvs, d If at th lot and go to st rat th st for th nxt lot. If d > rjt th lot and rat th st. Basd on ths rodur, a quk swthng sngl samlng varabls nston systm an b oratd as follows: St : Draw a saml of sz n from th lot, nst and rord th masurmnt of th qualty haratrst for ah unt of th saml. Comut th saml man x If x + kn U (whr U s th ur sfaton lmt at th lot and rat st othrws, rjt th lot and follow st. St : Draw a saml of sz n from th nxt lot, nst and rord th masurmnt of th qualty htt:// 33
2 Natur and Sn 9;7( g v, t al, Samlng Systm haratrst for ah unt of th saml. Comut th saml man x, If x + kt U at th lot and go to st othrws, rjt th lot and rat st. 3. Prlmnars Aordng to Rombosk (969 th OC funton of Quk Swthng Sngl Samlng Attrbuts Systm (n;, s gvn by ( ( + By assumng th Posson modl, on obtan P ( P ( x( n( n! x( n( n! and P (.95 & P (. ( a a For a quk swthng sngl samlng varabls nston systm QSVSS n ; k N k [ ( n k and ( n k ar th normal and, N tghtnd sngl samlng lans rstvly, wth k > k ] wth known standard dvaton (, T N, T (, T th fraton non-onformng n a gvn lot wll b PF(-v ( μ u wth v (3 and th OC funton of th systm has bn gvn by Z u kt Pa ( (4 Z u k N + ZU kt whr PZ ( k φ( w, Z k φ( w u N U T wth w ( v k n and w ( v k n N T and L(.95 & L(. ( n ; k N, kt (5 4. Mathd QSS Varabl Systm wth Attrbut Systm Th rodur for obtanng a Quk swthng Varabl Samlng Inston Systm mathng a gvn attrbuts systm QSS (n;, of Soundarajan.V and Arumanayagam S.D. (99 s as follows: For th QSS (n;, wth.4,.5, α.5 and β., from Tabl th followng.5 valus ar dtrmnd n.4 and 3. Th narst valu of 3.57 n th tabl s 3.585, whh has assoatd wth t valu of Th saml sz s thn dtrmnd by n.4 n Th attrbuts systm s dsgnatd as QSS (86, 3, From quaton ( ( / ( ( / + ( For th abov systm / / n n Thrfor (.95 Smlarly ( n /!.659 / (6 ( n /!.9653 htt:// 34
3 Natur and Sn 9;7( g v, t al, Samlng Systm ( ( d ( / / + ( / If ( β. thn φ( w.699 and φ(w.379 [From (8 & (9] / / n n ( n ( n /!.699 /!.379 (7 w ( v kt n.48 and w ( v k n.33 N If.4 v..5 v.64 (9 Thrfor (. Thus th OC urv of th QSS (86, 3, asss through (.95,.95 and (.,.. To obtan Quk swthng samlng varabl systm w onsdr th OC funton ϕ( w ( ϕ ( w + ϕ ( w.95 Through ( and ( on an gt n 3, k.73 and k.68 N From th gvn Quk swthng samlng attrbut nston systm ( 86;3, on an obtan th QSVSS as , v.64 n k N k T v T whr w ( v kn n and w ( v kt n If (.95 thn ϕ( w.659 and ϕ(w [ From (6 & (7] w ( v kt n.4and w v k N n.8 (8 ( ( ϕ( w ϕ ( w + ϕ ( w. w ( v k n and w ( v k n N T Thus th quk swthng varabl samlng systm (3:.73,.68 s suh that th OC urv asss through (, and (.,.. Th quvaln of th OC urvs s llustratd n Tabl 3. Though n rat th saml sz n would hav to b roundd to 3, th OC urv for th Quk swthng varabl samlng systm has bn omutd wth th fratonal valu n n ordr to bttr dmonstrat th losnss of th agrmnt of th OC urvs. On an magn th savng of th varabl systm wth attrbuts systm whn th saml sz 3 s omard wth 86. htt:// 35
4 Natur and Sn 9;7( g v, t al, Samlng Systm 5. Slton of varabl Systms Mathng Quk Swthng Attrbut Systm Indxd by AQL and LQL Tabl rovds mathd varabls systm to that of attrbuts systms ndxd by AQL and LQL. For xaml, for gvn., α.5.5 and β., th OR valu s 4.666, th narst valu of n th Tabl 3.9 s 4.69, whh has Tabl : Valus of for QSS assoatd wth th attrbut systm n9, 3 and on an obtan th orrsondng mathd Quk swthng samlng varabl systm from Tabl as n 6,. 763, and k T k N.93. Tabl rovds th valu of n and ( α.5, β.., togthr wth ( α.5, β. for n htt:// 36
5 Natur and Sn 9;7( g v, t al, Samlng Systm Tabl.Quk Swthng Varabl Samlng Systm Mathd wth Quk Swthng Attrbut Samlng Systm n Attrbut QSS n Varabl QSS k N k T Tabl 3. Valus of [, L (] for Quk Swthng Attrbut Samlng Systm and th quvalnt varabl systm of th roosd mthod L( of attrbuts QSS L( of Varabls QSS htt:// 37
6 Natur and Sn 9;7( g v, t al, Samlng Systm..8 L(.6 Attrbuts Varabls Fgur. OC urvs - Attrbuts QSS vs. Varabls QSS 6. Conlusons Th mthodology usd n ths ar ould b adotd for othr dvlod samlng systm to math wth othr samlng systm. In th sho floor, w ould aly both th gvn attrbut quk swthng systms as wll as varabl quk swth systms. From th Tabl and Tabl 3, on an onlud that th varabl quk swthng samlng systm s bttr on. Aknowldgmnt Th authors ar gratful to th Managmnt of Dr.Mahalngam Collg of Engnrng & Thnology for th nouragmnt and suort n raraton of ths rsarh ar. Corrsondn to: Srramahandran G.V Snor Lturr n Mathmats Dr.Mahalngam Collg of Engnrng and Thnology Pollah-64 3 Taml Nadu Inda Cllular hon: ; Emal: gvsrramahandran@yahoo.om htt:// 38
7 Natur and Sn 9;7( g v, t al, Samlng Systm Rfrn [] Bndr A.J. Sngl Samlng by Varabls to Control th Fraton Dftv. Journal of Qualty Thnology. 975; 7(5: [] Dodg H.F. A Nw Dual Systm of Atan Samlng. Thnal rort No.6, Th Statsts ntr, Rutgrs Th Stat Unvrsty. Nw Brunswk, NJ. 967 [3] Hamakr H.C. Atan Samlng for Prnt Dftv by Varabl and Attrbuts. Journal of Qualty Thnology. 979; (3: [4] MIL-STD-5D. Mltary Standard Samlng Produrs and Tabls for Inston by Attrbuts. US Govrnmnt Prntng Prss, Washngton D.C. 963 [5] Rombosk L.D. An Invstgaton of Quk Swthng Atan Samlng Systm. Dotoral Dssrtaton Rutgrs- Th Stat Unvrsty, Nw Brunswk, Nw Jrsy. 969 [6] Soundarajan V., Arumanayagam S.D. Construton and Slton of Modfd Quk Swthng Systm. Journal of Ald Statsts. 99; 7(: 83-4 [7] Soundarajan V., Palanvl M. Quk Swthng Varabls Sngl Samlng (QSVSS Systm ndxd by AQL and LQL Atan Crtron Tghtnng. Journal of Ald Statsts Sn.997;6(: [8] Soundarajan V., Palanvl M. Quk Swthng Varabls Sngl Samlng (QSVSS Systm ndxd by AQL and AOQL. Journal of Ald Statsts. ; 7(7: [9] Taylor W.A. Quk Swthng Systms. Journal of Qualty Thnology.996; 8(4: //9 htt:// 39
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