TOPIK 9 PETA KENDALI KHUSUS. LD, Semester II 2003/04 1. PETA KENDALI UNTUK PENGUKURAN INDIVIDUAL

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1 TI 3 PENGENDALIAN KUALITAS STATISTIK TOPIK 9 PETA KENDALI KHUSUS LD, Seeer II 003/04 Hl. TI 3 PENGENDALIAN KUALITAS STATISTIK. PETA KENDALI UNTUK PENGUKURAN INDIVIDUAL =. Siuai: Diguakaya ipeki & pegukura ooai, eiap ui produk diaalii; Tigka produki aga redah, da idak eugkika dilakuka aplig dega >; Pegukura berulag pada proe aka berbeda karea fakor kealaha lab aau aalii, eperi pada proe kiia. Cooh: Pegedalia vikoia ca, dega daa aplig bb. Bach Σ Vikoia 33,75 33,05 34,00 33,8 33,46 34,0 33,68 33,7 33,49 33,0 33,6 33,00 33,54 33, 33,84 50,85 MR - 0,70 0,95 0,9 0,35 0,56 0,34 0,4 0, 0,9 0,4 0,6 0,54 0,4 0,7 6,73 5 i = i = = 4 MR i = i MR = = 4 PETA KENDALI 50,85 5 GT = MR = 0,48 BKAMR = D4MR = ( 3,67 )(0,48 ) =,57 BKBMR = D3MR = (0 )(0,48 ) = 0 PETA KENDALI : GT = = 33,5 = 33,5 6, 73 = 0,48 4 MR : MR 0,48 BKA /BKB = ± 3 = 33,5 ± 3 d,8 BKA = 34,80 da BKB = 3,4 Uuk = : D3 = 0 D4 = 3,67 d =,8 LD, Seeer II 003/04 Hl.

2 TI 3 PENGENDALIAN KUALITAS STATISTIK a. Pea Kedali Movig Rage b. Pea Kedali uuk Pegukura Idividual LD, Seeer II 003/04 Hl. 3 TI 3 PENGENDALIAN KUALITAS STATISTIK Pea Kedali uuk Pegukura Idividual Ierpreai haru hai-hai, karea erjadi korelai aar daa ovig average. a. Pea Kedali Movig Rage b. Pea Kedali uuk Pegukura Idividual LD, Seeer II 003/04 Hl. 4

3 TI 3 PENGENDALIAN KUALITAS STATISTIK. SHORT RUN PRODUCTION LD, Seeer II 003/04 Hl. 5 TI 3 PENGENDALIAN KUALITAS STATISTIK Pea Kedali p uuk hor-ru ru producio LD, Seeer II 003/04 Hl. 6

4 3. CUMULATIVE SUM (CUSUM) CONTROL CHART TI 3 PENGENDALIAN KUALITAS STATISTIK Kelebiha : Megguaka iforai yag erkadug dala obervai ebeluya. Dapa edeeki pergeera kecil. Julah kuulaif pada apel ke- : ( ) S = i µ o i= diaa i = raa apel ke - i & µ o = arge raa - proe Baa Kedali (V-Mak) : Jika = bear pergeera yag igi dideeki, pergeera relaif raa - proe : β Jarak peadu V - ak : d = l δ α Jika probabilia Error Tipe II, β, dipilih aga kecil, aka : d = l( α ) δ Sudu lega V -ak : a- θ =, diaa k k = fakor kala yag erepreeaika ui kala verikal pada pea Rekoedai : k aara σ da σ Average Ru Legh : ARL = p p = probabilia bahwa au iik aka jauh di luar baa kedali Uuk 3σ pada pea kedali Shewhar, di aa proe dala kedali, p = 0,06. δ = σ LD, Seeer II 003/04 Hl CUMULATIVE SUM (CUSUM) CONTROL CHART TI 3 PENGENDALIAN KUALITAS STATISTIK Cooh: Uuk pegedalia pereae kaduga kaliu dala oba dilakuka pegeceka erhadap 5 ubgrup dega =5. Targe raa-raa yag diigika adalah 6,5% dega deviai adar 0,%. Diigika pea kedali yag dapa eoior pergeera 0, dari raa- proe. Diauika igka error ipe I = 0,05. 0, DATA HASIL SAMPLING δ = = = =,4 σ σ / 0, / 5 Subgrup LD, Seeer II 003/04 Raa- Subgrup 5,5 6,0 6,6 6,8 7,5 5,9 7,0 5,4 6,4 6,3 6,9 7,8 6, 6,8 6,6 Deviai dari Targe -,0-0,5 0, 0,3,0-0,6 0,5 -, -0, -0, 0,4,3-0,3 0,3 0, Cuu (S i ) -,0 -,5 -,4 -, -0, -0,7-0, -,3 -,4 -,6 -, 0, -0, 0, 0, d = l( α ) = l δ (,4) Uuk k = 0,5, aka 0, θ = a- = a- k ( 0,05) ( 0,5) = 5, 74 = a 0,4 =,8 ( ) o Hl. 8

5 TI 3 PENGENDALIAN KUALITAS STATISTIK 4. MOVING AVERAGE CONTROL CHART Efekif uuk edeeki pergeera proe Uuk = Forulai Uu : Uuk ar-up period (<w) x + x x = M = w = lebar MA σ Var( x ) = Var( M ) = w CL = x = M UCL / LCL = x ± 3 + x x w w+ σ σ Var( xi ) = = w w+ 443 w σ w w+ σ w w x = x = M =, =,,..., w CL = x = M σ UCL / LCL = x ± 3, berubah _ euai _ LD, Seeer II 003/04 Hl. 9 TI 3 PENGENDALIAN KUALITAS STATISTIK CONTOH SOAL (=5, w = 6) Sa. No Saple Average x Movig Average, M Corol Lii LCL UCL x = 503 CL = = = 5,5 0 0 R( dikeahui) = 0,40 R 0,40 ˆ σ = = = 0,7 d,36 = 3( < w) : σ UCL / LCL = x ± 3 = 5,5 ± 3 UCL = 5,83 LCL = 5,07 0,7 (5)(3) LD, Seeer II 003/04 Hl. 0

6 TI 3 PENGENDALIAN KUALITAS STATISTIK 5. GEOMETRIC MOVING AVERAGE CONTROL CHART G = r x + ( r) G G = r x + ( r) G G = r x + r( r) x + ( r) G G = r x + r( r) x + r( r G0 = x = M σ r Var( G ) = r ) x { ( r) } G 0 Caaa: Uuk ar-up period, aalog dega Movig Average Corol Char Uuk yag bear, (-r) 0 σ r σ G = Var( G ) = r r UCL / LCL = x ± 3σ ( r) σ ˆ σ = R d Uuk kecil: r UCL / LCL = x ± 3σ ( r) [ ( r) ] LD, Seeer II 003/04 Hl. TI 3 PENGENDALIAN KUALITAS STATISTIK CONTOH SOAL ( = 5, w = 6, r = 0,) 503 x = = 5,5 0 R( dikeahui) = 0,40 R 0,40 ˆ σ = = = 0,7 d 0,36 G : G = ( r)( x) + ( r) G G0 = x = 5,5 G = (0,)(5,0) + ( 0,)(5,5) = 5, 0 UCL / LCL = 5,5 ± 3(0,7) UCL LCL = = 5,96 5,04 0, ( 0,)5 ()() [ ( 0,) ] LD, Seeer II 003/04 Hl.

7 TI 3 PENGENDALIAN KUALITAS STATISTIK 6. TREND CHART (REGRESSION CONTROL CHART) Uuk proe yag egguaka ool wear aau die wear; Raa-raa proe awal & akhir dieuka dega baa peifikai; Aui: rage baa peifikai > rage variabilia proe (Idek Kapabilia Proe >) C = a + b(i) LD, Seeer II 003/04 Hl. 3 TI 3 PENGENDALIAN KUALITAS STATISTIK Forula: C = fied value of he aple average for aple uber i; a = iik iereki pada C dega gari ubu verikal; b = lope dari C; i = oor ubgrup aau apel; g = julah ubgrup. a = b = x i g g x g i i ( i ( ( x i) x i)( i) i) i) UCL / LCL = ( a ± A R) + b( i) LD, Seeer II 003/04 Hl. 4

8 TI 3 PENGENDALIAN KUALITAS STATISTIK Saple CONTOH SOAL: No. Over he coure of achiig he di aeer of eel hub, ool wear ake place o a gradual bai. Saple of ize 4 were radoly eleced, ad he ea ad rage of he hub diaeer were foud. The followig able how he aple ea ad he rage R for 5 uch aple. Fid he ceer lie ad corol lii of a red char for he aple average. If he pecificaio lii ae ha he hub diaeer u be fro 34 o 78, whe hould he ool be chaged? Raa- (i) x ( x)( i ) , ,47.6 (i) ,55 R LD, Seeer II 003/04 i x ( x)( i ) i R Hl. 5 TI 3 PENGENDALIAN KUALITAS STATISTIK (.386,4)(5.55) (9.47,6)(35) a = = 40,97 5(5.55) (35) 5(.947,6) (.386,4)(35) b = =,4 5(5.55) (35) C = 40,97 +,4( i) R = 96 / 5 =,84 = 4, A = 0,79 PETA KENDALI UCL LCL= ( a+ A R) + b( i) / UCL/ LCL= [ 40,97± (0,79)(,84) ] UCL= 49,6035+ (,4)( i) UCL= 3,34 (,4)( i) BATAS-BATAS KENDALI + (,4)( i) LD, Seeer II 003/04 Hl. 6

9 TI 3 PENGENDALIAN KUALITAS STATISTIK 7. MULTIVARIATE CONTROL CHART Korelai : Idepede Korelai : A. Area kedali egiepa (joi corol), Pea kedali dibagu ecara idepede B. Area kedali elip, Pea kedali dibagu ecara iula; uuk variabel yag berkorelai Prob. (error ipe I) : Prob. raa- apel dala area elip α = (-α) p (dala kedali) = - α LD, Seeer II 003/04 Hl. 7 TI 3 PENGENDALIAN KUALITAS STATISTIK Hoellig T Corol Char T [ ( x x) + ( x x) ( x x)( x ) ] = x ( ) dof = (julah karakeriik kualia), da - (dof variai apel). Jika T > T α,, (-), aka palig idak ada au karakeriik kualia yag berada di luar baa kedali. Hubuga diribui T da F: ( ) ( p) α, p,( ) = p Fα, p, p = dof ueraor, -p = dof deoiaor diribui F. Uuk lebih dari karakeriik: T T = ( )' S ( ) p p p + p UCL = F p + α, p,( p+ ) = julah ubgrup (apel) = ukura ubgrup p = julah karakeriik yag dikedalika LD, Seeer II 003/04 Hl. 8

10 TI 3 PENGENDALIAN KUALITAS STATISTIK Vekor raa-raa apel dari i karakeriik : j = M j j pj, j =,,...,( o.apel ) Nilai raa-raa obervai uuk karakeriik ke-i dari apel ke-j: x k = ijk ij = i =,,..., p, j =,,..., k = o. obervai, k =,,, Variai apel dari karakeriik ke-i dari apel ke-j: i =,,..., p = ( ) ij ijk ij, ( ) j =,,..., k = Kovariai aara karakeriik ke-i & ke-h dari apel ke-j: ihj = ( ijk ij )( hjk hj ( ) k = j =,,..., ), i h LD, Seeer II 003/04 Hl. 9 TI 3 PENGENDALIAN KUALITAS STATISTIK Vekor raa-raa oial dari eiap karakeriik uuk apel: i = j= ij, i =,,..., p Elee arik variai-kovariai S: i ih = = j= j= ij ihj, i =,,..., p, i h Cooh Pea Kedali Hoellig T Marik variaikovariai S: LD, Seeer II 003/04 S = K K K p p M 3 p p Hl. 0

11 TI 3 PENGENDALIAN KUALITAS STATISTIK Daa for he bivariae proce characeriic of igle-rad break facor ad weigh of exile fiber LD, Seeer II 003/04 Hl. TI Perhiuga 3 PENGENDALIAN baa-baa KUALITAS kedali STATISTIK bivaria LD, Seeer II 003/04 T = ( [ ( x x) + ( x x) ( x x)( x ) ] x ) Hl.

12 TI 3 PENGENDALIAN KUALITAS STATISTIK Pea Kedali Hoellig T LD, Seeer II 003/04 T = ( )' S ( ) p p p + p UCL = F p + α, p,( p+ ) Hl. 3