VARIABLES CONTROL CHARTS

Ir. Budi Nurtama, M.Agr.

PS. SUPERVISOR JAMINAN MUTU PANGANPS. SUPERVISOR JAMINAN MUTU PANGANDEP. ILMU DAN TEKNOLOGI PANGANDEP. ILMU DAN TEKNOLOGI PANGAN

FATETA - IPBFATETA - IPB

Data Tabulasi Charts s R, ,x ,x ~

Subgrup (i)Pengukuran Perhitungan

x1i x2i . . . xnk Ri si

1 x11 x21 . . . xn1 R1 s1

2 x12 x22 . . . xn2 R2 s2

3 x13 x23 . . . xn3 R3 s3

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k x1k x2k . . . xnk Rk sk

ix

1x

3x

2x

kx

ix~

1x~

3x~2x~

kx~

x x~~ R s

k

ii

k

ii

k

k

ii

s k

s R k

R

x , ... , x , x median x x k

x

11

211

11

1)~~~(~~

Rumus Perhitungan Centerline

s A x

n

cs x

R A x n

dR x (Range)

: Limits Control

n μ σ μ Limits Control

x

34

22

3Baku Simpangan Dengan2

3 WilayahDengan1

Estimasi

33

.

.

σ

Chart x

R D LCLR D UCL

R d

d R

d

d R Limits Control

σ μ Limits Control RR

34

2

3

2

3

dan

313Estimasi

3

R Chart

s B LCLs B UCL

s c

c s

c

c s Limit Control

σ μ Limit Control ss

34

4

24

4

24

dan

131

13Estimasi

3

s Chart

Centerline UCL LCL

R Chart

Charts R x

Chart x x

R

R A x 2 R A x 2

R D4 R D3

CONTOH KASUS

Dari berbagai batch yang dihasilkan automatic

filling machine pada periode tanggal 8 – 12 Mei,

setiap harinya diambil 4 kemasan produk per batch

untuk diukur volumenya.

Tgl Batch x1 x2 x3 x4 x-bar R

8 Mei 1 288 294 278 294 288.5 16

  2 277 296 277 277 281.8 19

  3 302 287 300 288 294.3 15

  4 295 278 286 280 284.8 17

  5 276 296 304 296 293.0 28

9 Mei 1 295 300 282 295 293.0 18

  2 281 298 292 294 291.3 17

  3 300 300 299 302 300.3 3

  4 296 297 295 296 296.0 2

  5 288 282 291 300 290.3 18

10 Mei 1 283 300 296 278 289.3 22

  2 295 303 299 299 299.0 8

  3 279 282 288 282 282.8 9

  4 300 284 300 300 296.0 16

11 Mei 1 274 294 274 295 284.3 21

  2 283 295 299 303 295.0 20

  3 299 296 293 296 296.0 6

  4 304 299 288 314 301.3 26

12 Mei 1 298 307 284 298 296.8 23

  2 296 298 297 285 294.0 13

Untuk n = 4 : A2 = 0.729 D4 = 2.282 D3 = 0

Centerline = 292.36 15.85

UCL = 303.91 36.16

LCL = 280.82 0.00

TEST 5. 2 out of 3 points more than 2 standard deviations from center

line (on one side of CL). Test Failed at points: 15

Produk VolumeCharts R x

Batch

Sam

ple

Mean

2019181716151413121110987654321

305

300

295

290

285

280

__X=292.36

UCL=303.91

LCL=280.82

Batch

Sam

ple

Range

2019181716151413121110987654321

40

30

20

10

0

_R=15.85

UCL=36.16

LCL=0

5

Centerline UCL LCL

s Chart

Charts s x

Chart x x

s

s A x 3 s A x 3

s B4 s B3

Tgl Batch x1 x2 x3 x4 x-bar s

8 Mei 1 288 294 278 294 288.5 7.5

  2 277 296 277 277 281.8 9.5

  3 302 287 300 288 294.3 7.8

  4 295 278 286 280 284.8 7.6

  5 276 296 304 296 293.0 11.9

9 Mei 1 295 300 282 295 293.0 7.7

  2 281 298 292 294 291.3 7.3

  3 300 300 299 302 300.3 1.3

  4 296 297 295 296 296.0 0.8

  5 288 282 291 300 290.3 7.5

10 Mei 1 283 300 296 278 289.3 10.4

  2 295 303 299 299 299.0 3.3

  3 279 282 288 282 282.8 3.8

  4 300 284 300 300 296.0 8.0

11 Mei 1 274 294 274 295 284.3 11.8

  2 283 295 299 303 295.0 8.6

  3 299 296 293 296 296.0 2.4

  4 304 299 288 314 301.3 10.8

12 Mei 1 298 307 284 298 296.8 9.5

  2 296 298 297 285 294.0 6.1

Untuk n = 4 : A3 = 1.628 B4 = 2.266 B3 = 0

Centerline = 292.36 7.2

UCL = 304.07 16.29

LCL = 280.44 0.00

Produk VolumeCharts s x

Batch

Sam

ple

Mean

2019181716151413121110987654321

305

300

295

290

285

280

__X=292.36

UCL=304.07

LCL=280.66

Batch

Sam

ple

StD

ev

2019181716151413121110987654321

16

12

8

4

0

_S=7.19

UCL=16.29

LCL=0

5

TEST 5. 2 out of 3 points more than 2 standard deviations from center line (on one side of CL). Test Failed at points: 15

Centerline UCL LCL

Charts R x ~

x~~

R~

R A x ~~~5 R A x ~~~

5

R D ~6 R D ~

5

Chart x~

Chart R

Tgl Batch x1 x2 x3 x4 Median R

8 Mei 1 288 294 278 294 291.0 16

  2 277 296 277 277 277.0 19

  3 302 287 300 288 294.0 15

  4 295 278 286 280 283.0 17

  5 276 296 304 296 296.0 28

9 Mei 1 295 300 282 295 295.0 18

  2 281 298 292 294 293.0 17

  3 300 300 299 302 300.0 3

  4 296 297 295 296 296.0 2

  5 288 282 291 300 289.5 18

10 Mei 1 283 300 296 278 289.5 22

  2 295 303 299 299 299.0 8

  3 279 282 288 282 282.0 9

  4 300 284 300 300 300.0 16

11 Mei 1 274 294 274 295 284.0 21

  2 283 295 299 303 297.0 20

  3 299 296 293 296 296.0 6

  4 304 299 288 314 301.5 26

12 Mei 1 298 307 284 298 298.0 23

  2 296 298 297 285 296.5 13

Untuk n = 4 : A5 = 0.828 D6 = 2.33 D5 = 0

Centerline = 295.5 17.0

UCL = 309.6 39.6

LCL = 281.4 0.00

275.0

280.0

285.0

290.0

295.0

300.0

305.0

310.0

315.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Batch

Sa

mp

le M

ed

ian

Produk Volume Chart x~

UCL = 309.6

LCL = 281.4

295.5 x~~

0

4

8

12

16

20

24

28

32

36

40

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Batch

Sam

pel

Ran

ge

R Chart Volume Produk

UCL = 39.6

LCL = 0.0

17.0 R~

Standard given :

Centerline UCL LCL

Chart x 0x

040 σ c s

00 σ A x

06 σ B

Chart R

Chart s

00 σ A x

020 σ d R 02 σ D 01 σ D

05 σ B

Latihan :

Misalnya untuk Contoh Kasus Automatic filling machine diketahui bahwa :

5300 00 σ σ x μ dan

Tgl Batch x1 x2 x3 x4 x-bar R s

8 Mei 1 288 294 278 294 288.5 16 7.5

  2 277 296 277 277 281.8 19 9.5

  3 302 287 300 288 294.3 15 7.8

  4 295 278 286 280 284.8 17 7.6

  5 276 296 304 296 293.0 28 11.9

9 Mei 1 295 300 282 295 293.0 18 7.7

  2 281 298 292 294 291.3 17 7.3

  3 300 300 299 302 300.3 3 1.3

  4 296 297 295 296 296.0 2 0.8

  5 288 282 291 300 290.3 18 7.5

10 Mei 1 283 300 296 278 289.3 22 10.4

  2 295 303 299 299 299.0 8 3.3

  3 279 282 288 282 282.8 9 3.8

  4 300 284 300 300 296.0 16 8.0

11 Mei 1 274 294 274 295 284.3 21 11.8

  2 283 295 299 303 295.0 20 8.6

  3 299 296 293 296 296.0 6 2.4

  4 304 299 288 314 301.3 26 10.8

12 Mei 1 298 307 284 298 296.8 23 9.5

  2 296 298 297 285 294.0 13 6.1

Untuk n = 4 : A = 1.500 D1 = 0 D2 = 4.698 B5 = 0 B6 = 2.088 d2 = 2.059 c4 = 0.9213

Centerline = 300.0 10.3 4.6

UCL = 307.5 23.5 10.4

LCL = 292.5 0.0 0.0

Batch

Sam

ple

Mean

2019181716151413121110987654321

305

300

295

290

285

__X=300

UCL=307.5

LCL=292.5

Batch

Sam

ple

Range

2019181716151413121110987654321

30

20

10

0

_R=10.30

UCL=23.49

LCL=0

6

626

1

6

1

11

6

155

1

5

1

1

11

given Standard- Chart R-x

Test Results for Xbar Chart

TEST 1. One point more than 3.00 standard deviations from center line.Test Failed at points: 1, 2, 4, 7, 10, 11, 13, 15

TEST 2. 9 points in a row on same side of center line.Test Failed at points: 17

TEST 5. 2 out of 3 points more than 2 standard deviations from center line (on one side of CL).Test Failed at points: 2, 3, 4, 5, 6, 7, 11, 13, 15

TEST 6. 4 out of 5 points more than 1 standard deviation from center line (on one side of CL).Test Failed at points: 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20

Test Results for R Chart

TEST 1. One point more than 3.00 standard deviations from center line.Test Failed at points: 5, 18

Batch

Sam

ple

Mean

2019181716151413121110987654321

305

300

295

290

285

__X=300

UCL=307.5

LCL=292.5

Batch

Sam

ple

StD

ev

2019181716151413121110987654321

12

9

6

3

0

_S=4.61

UCL=10.44

LCL=0

6

626

1

6

1

11

6

155

1

5

1

1

111

given Standard- Charts -x

Test Results for Xbar Chart

TEST 1. One point more than 3.00 standard deviations from center line.Test Failed at points: 1, 2, 4, 7, 10, 11, 13, 15

TEST 2. 9 points in a row on same side of center line.Test Failed at points: 17

TEST 5. 2 out of 3 points more than 2 standard deviations from center line (on one side of CL).Test Failed at points: 2, 3, 4, 5, 6, 7, 11, 13, 15

TEST 6. 4 out of 5 points more than 1 standard deviation from center line (on one side of CL).Test Failed at points: 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20

Test Results for S Chart

TEST 1. One point more than 3.00 standard deviations from center line.Test Failed at points: 5, 15, 18