NAMA : MOHAMMAD RIZQI AUNILLAH
NIM
: 2105012230043
TUGAS METROLOGI INDUSTRI & KONTROL KUALITAS
SOAL NO 1A (Subgroup size 6)
SUBGROUP NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Total
x̄
x̄̄
20.35
20.4
20.36
20.65
20.2
20.4
20.43
20.37
20.48
20.42
20.39
20.38
20.4
20.41
20.45
20.34
20.36
20.42
20.5
20.31
20.39
20.39
20.4
20.41
20.4
510.01
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
LCL
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
20.228
𝐿𝐶𝐿𝑥 = xധ − 𝐴2 R̄
= 20.4 - (0.483) 0.3556
= 20.228
𝑈𝐶𝐿𝑥 = x̿ + 𝐴2 R̄
= 20.4 + (0.483) 0.3556
= 20. 571
20.7
UCL
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
20.571
Control Chart X
20.6
20.5
20.4
20.3
20.2
20.1
20
19.9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
SUBGROUP NUMBER
x̄̄
UCL
LCL
SUBGROUP NUMBER
x̄̄
UCL
LCL
Karena ada data yang melebihi UCL, maka harus dibuang untuk mendapatkan Control Chart yang b
Data yang harus dihilangkan pada chart X bar adalah data nomer 4.
𝑋𝑑𝑜𝑢𝑏𝑙𝑒 𝑏𝑎𝑟 𝑛𝑒𝑤 =
=
𝑅
𝜎0 = 𝑑0
2
σ 𝑋 𝑏𝑎𝑟 − 𝑋 𝑏𝑎𝑟 𝑑𝑖𝑠𝑐𝑎𝑟𝑑𝑒𝑑
𝑔 − 𝑔 𝑑𝑖𝑠𝑐𝑎𝑟𝑑𝑒𝑑
⬚
⬚
510−20.65
25−1
= 20.39 = 𝑋0 bar
0.34
= 2.534
= 0.134175
𝑈𝐶𝐿𝑥𝑛𝑒𝑤 = x̿ + 𝐴 𝜎0
= 20.39 + (1.225) 0.134175
= 20.554
𝐿𝐶𝐿𝑥𝑛𝑒𝑤 = x̿ - 𝐴 𝜎0
= 20.39 - (1.225) 0.134175
= 20.225
SUBGROUP NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
x̄new
x̄̄new
20.35
20.4
20.36
20.2
20.4
20.43
20.37
20.48
20.42
20.39
20.38
20.4
20.41
20.45
20.34
20.36
20.42
20.5
20.31
20.39
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
UCLnew LCLnew
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
20.554
20.225
21
22
23
24
Total
20.4
20.4
20.4
20.4
20.39
20.4
20.41
20.4
489.36
20.554
20.554
20.554
20.554
20.225
20.225
20.225
20.225
Control Chart X new
20.6
20.5
20.4
20.3
20.2
20.1
20
1
2
3
4
5
x̄new
6 7 8
x̄n
̄ ew
UCLnew
LCLnew
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Karena masih ada data yang melebihi LCL maka proses revised data dilakukan lagi.
𝑋𝑑𝑜𝑢𝑏𝑙𝑒 𝑏𝑎𝑟 𝑛𝑒𝑤 =
=
σ 𝑋 𝑏𝑎𝑟 − 𝑋 𝑏𝑎𝑟 𝑑𝑖𝑠𝑐𝑎𝑟𝑑𝑒𝑑
𝑔 − 𝑔 𝑑𝑖𝑠𝑐𝑎𝑟𝑑𝑒𝑑
⬚
⬚
489.36 −20.2
24−1
= 20.398 = 𝑋0 bar
𝑈𝐶𝐿𝑥𝑛𝑒𝑤 = x̿ new + 𝐴 𝜎0
= 20.398 + (1.225) 0.134175
= 20.562
𝐿𝐶𝐿𝑥𝑛𝑒𝑤 = x̿ new + 𝐴 𝜎0
= 20.398 - (1.225) 0.134175
= 20.233
Control Chart X new 2
20.6
20.5
20.4
20.3
20.2
20.1
20
1
2
3
4
5
6
7
x̄new
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
x̄n
̄ ew
UCLnew
LCLnew
x̄new
x̄n
̄ ew
UCLnew
LCLnew
Chart
SUBGROUP NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Total
R
0.34
0.36
0.32
0.36
0.36
0.35
0.31
0.34
0.3
0.37
0.29
0.3
0.33
0.36
0.34
0.36
0.37
0.73
0.38
0.35
0.38
0.33
0.32
0.34
0.3
8.89
𝑈𝐶𝐿𝑅 = 𝐷4 R
= (2.004) (0.3556)
= 0.7126
𝐿𝐶𝐿𝑅 =𝐷3 R
= 0 (R)
=0
R̄
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
0.3556
Control Chart R
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
SUBGROUP NUMBER
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
SUBGROUP NUMBER
R
UCL
LCL
apatkan Control Chart yang baru.
𝑅 𝑏𝑎𝑟 𝑛𝑒𝑤 =
=
σ 𝑅 − 𝑅 𝑑𝑖𝑠𝑐𝑎𝑟𝑑𝑒𝑑
𝑔 − 𝑔 𝑑𝑖𝑠𝑐𝑎𝑟𝑑𝑒𝑑
8.89 −0.73
25−1
= 0.34
𝑈𝐶𝐿𝑅𝑛𝑒𝑤 = 𝐷2 𝜎0
= 5.078 (0.134175)
= 0.681
𝐿𝐶𝐿𝑅𝑛𝑒𝑤 = 𝐷1 𝜎0
= 0 (0.134175)
=0
SUBGROUP NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
R
0.34
0.36
0.32
0.36
0.36
0.35
0.31
0.34
0.3
0.37
0.29
0.3
0.33
0.36
0.34
0.36
0.37
0.38
0.35
0.38
R̄new
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
0.34
UCLnew
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
21
22
23
24
Total
0.34
0.34
0.34
0.34
0.33
0.32
0.34
0.3
8.16
0.681
0.681
0.681
0.681
Control Chart R new
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
R
SUBGROUP NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Total
10 11 12 13 14 15 16 17 18 19 20 21 22 23
R̄new
UCLnew
LCLnew
x̄new
x̄̄new
20.35
20.4
20.36
20.4
20.43
20.37
20.48
20.42
20.39
20.38
20.4
20.41
20.45
20.34
20.36
20.42
20.5
20.31
20.39
20.39
20.4
20.41
20.4
469.16
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
UCLnew
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
20.562
Chart sudah aman karena tidak ada yang melebihi LCL dan UCL.
UCL
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
0.7126
21 22 23 24 25
LCL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
x̄̄
21 22 23 24 25
LCLnew
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
23 24
LCLnew
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233
20.233