Transcript VARIABLES CONTROL CHARTS

VARIABLES CONTROL CHARTS
PS. SUPERVISOR JAMINAN MUTU PANGAN
PROGRAM DIPLOMA - IPB
x, ~
x, R, s Charts  Tabulasi Data
Pengukuran
Perhitungan
Subgrup (i)
x1i
x2i
...
xnk
xi
~
xi
Ri
si
1
x11
x21
...
xn1
x1
R1
s1
2
x12
x22
...
xn2
x2
~
x1
~
x
R2
s2
3
.
.
.
x13
.
.
.
x23
.
.
.
...
xn3
.
.
.
x3
~
x3
R3
.
.
.
s3
.
.
.
k
x1k
x2k
...
xnk
xk
~
xk
Rk
sk
x
~
~
x
R
s
2
.
.
.
Rumus Perhitungan Centerline
1
x 
k
1
R 
k
k
 xi
i 1
k
 Ri
i 1
~
x  median (~x1 , ~x 2 , ... , ~x k )
1
s 
k
k
 si
i 1
x Chart
Control Limits  μ  3 σ x  μ  3
σ
n
Estimasi Control Limits :
1. Dengan Wilayah (Range)  x  3
2. Dengan Simpangan Baku  x  3
R
d2 
 x  A2 R
n
s c 4 
n
 x  A3 s
R Chart
Control Limits  μ R  3 σ R
d3 
 d3  
Estimasi Control Limits  R  3  R    1  3  R
d2 
 d2  
UCL  D4 R dan LCL  D3 R
s Chart
Control Limit  μ s  3 σ s
 1  c 42
Estimasi Control Limit  s  3 
 c4

UCL  B4 s dan LCL  B3 s

 1  c 42 
s
s  1  3

 c4 



x  R Charts
Centerline
UCL
LCL
x Chart
x
x  A2 R
x  A2 R
R Chart
R
D4 R
D3 R
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
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
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
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
1
298
307
284
298
296.8
23
2
296
298
297
285
294.0
13
Centerline =
292.36
15.85
UCL =
303.91
36.16
LCL =
280.82
0.00
9 Mei
10 Mei
11 Mei
12 Mei
Untuk n = 4 :
A2 = 0.729
D4 = 2.282
D3 = 0
x  R Charts Volume Produk
305
U C L=303.91
Sample M ean
300
295
_
_
X=292.36
290
285
5
LC L=280.82
280
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Batch
40
Sample Range
U C L=36.16
30
20
_
R=15.85
10
0
LC L=0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Batch
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
x  s Charts
Centerline
UCL
LCL
x Chart
x
x  A3 s
x  A3 s
s Chart
s
B4 s
B3 s
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
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
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
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
1
298
307
284
298
296.8
9.5
2
296
298
297
285
294.0
6.1
Centerline =
292.36
7.2
UCL =
304.07
16.29
LCL =
280.44
0.00
9 Mei
10 Mei
11 Mei
12 Mei
Untuk n = 4 :
A3 = 1.628
B4 = 2.266
B3 = 0
x  s Charts Volume Produk
305
U C L=304.07
Sample M ean
300
295
_
_
X=292.36
290
285
5
LC L=280.66
280
1
2
3
4
5
6
7
8
9
11
10
Batch
12
13
14
15
16
17
18
19
20
U C L=16.29
Sample StDev
16
12
_
S =7.19
8
4
LC L=0
0
1
2
TEST 5.
3
4
5
6
7
8
9
11
10
Batch
12
13
14
15
16
17
18
19
20
2 out of 3 points more than 2 standard deviations from center
line (on one side of CL). Test Failed at points: 15
~
x  R Charts
Centerline
UCL
LCL
~
x Chart
~
x
~
~
x  A5 R
~
~
x  A5 R
R Chart
~
R
~
D6 R
~
D5 R
Tgl
Batch
x1
x2
x3
x4
8 Mei
1
288
294
278
2
277
296
3
302
4
9 Mei
10 Mei
11 Mei
12 Mei
Median
R
294
291.0
16
277
277
277.0
19
287
300
288
294.0
15
295
278
286
280
283.0
17
5
276
296
304
296
296.0
28
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
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
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
1
298
307
284
298
298.0
23
2
296
298
297
285
296.5
13
Centerline =
295.5
17.0
UCL =
309.6
39.6
LCL =
281.4
0.00
Untuk n = 4 :
A5 = 0.828
D6 = 2.33
D5 = 0
x~ Chart Volume Produk
315.0
310.0
UCL = 309.6
Sample Median
305.0
300.0
~
x~  295.5
295.0
290.0
285.0
LCL = 281.4
280.0
275.0
1
2
3
4
5
6
7
8
9
10
Batch
11
12
13
14
15
16
17
18
19
20
R Chart Volume Produk
40
UCL = 39.6
36
32
Sampel Range
28
24
20
~
R  17.0
16
12
8
4
0
LCL = 0.0
0
1
2
3
4
5
6
7
8
9
10
Batch
11
12
13
14
15
16
17
18
19
20
Standard given :
Centerline
UCL
LCL
x Chart
x0
x0  A σ 0
x0  A σ 0
R Chart
R0  d 2 σ 0
D2 σ 0
D1 σ 0
s Chart
s0  c 4 σ 0
B6 σ 0
B5 σ 0
Latihan :
Misalnya untuk Contoh Kasus Automatic
filling machine diketahui bahwa :
μ  x 0  300
dan σ  σ 0  5
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
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
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
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
1
298
307
284
298
296.8
23
9.5
2
296
298
297
285
294.0
13
6.1
Centerline =
300.0
10.3
4.6
UCL =
307.5
23.5
10.4
LCL =
292.5
0.0
0.0
9 Mei
10 Mei
11 Mei
12 Mei
Untuk n = 4 : A = 1.500 D1 = 0 D2 = 4.698 B5 = 0 B6 = 2.088
d2 = 2.059 c4 = 0.9213
x - R Chart - Standard given
U C L=307.5
Sample M ean
305
_
_
X=300
300
295
5
290
1
1
1
2
4
5
6
6
7
8
9
10
LC L=292.5
1
1
3
6
2
1
1
1
6
5
1
285
6
6
5
11
12
13
14
15
16
17
18
19
20
Batch
Sample Range
30
1
1
U C L=23.49
20
_
R=10.30
10
LC L=0
0
1
2
3
4
5
6
7
8
9
10
11
Batch
12
13
14
15
16
17
18
19
20
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
x - s Chart - Standard given
U C L=307.5
Sample M ean
305
_
_
X=300
300
295
5
290
1
1
3
4
5
6
6
7
8
9
10
LC L=292.5
1
1
1
2
6
2
1
1
1
6
5
1
285
6
6
5
11
12
13
14
15
16
17
18
19
20
Batch
1
12
1
1
Sample StDev
U C L=10.44
9
6
_
S =4.61
3
LC L=0
0
1
2
3
4
5
6
7
8
9
10
11
Batch
12
13
14
15
16
17
18
19
20
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