9 10 kendali variabel xr

Peta KendaliVariabel

• Menggambarkan variasi atau penyimpangan yg terjadi pd kecenderungan data variabel

• Kondisi in-out of control tapi tdk identik dg kepuasan pelanggan

Manfaat…

• Perbaikan kualitas

• Menentukan kemampuan proses

• Membuat keputusan berkaitan dg proses produksi dan produk yg dihasilkan

Tahapan…

1. Pemilihan karakteristik kualitas– panjang, berat, volume, waktu– Mempengaruhi kinerja produk– Pemilihan karakteristik dg Diagram Pareto

2. Pemilihan Sub Kelompok

Ukuran Sampel menurut Inspeksi Normal ANSI/ASQC Z1.9-1993

Byknya produk yg dihasilkan Ukuran Sampel

91 – 150

151 – 280

281 – 400

401 – 500

501 – 1200

1201 – 3200

3201 – 10000

10001 – 35000

35001 - 150000

10

15

20

25

35

50

75

100

150

3. Pengumpulan Data

4. Penentuan Batas Kendali untuk pet X-R dan Nilai Faktor Guna

X Chart

Range for sample i

# Samples

Mean for sample i

From Table Nilai Guna

RAxxLCL

RAxxUCL

n

R R

i

n

1i

n

xi

n

ix

Nilai Faktor Guna

Sample Size, n

Mean Factor, A2

Upper Range, D4

Lower Range, D3

2 1.880 3.268 0

3 1.023 2.574 0

4 0.729 2.282 0

5 0.577 2.115 0

6 0.483 2.004 0

7 0.419 1.924 0.076

8 0.373 1.864 0.136

9 0.337 1.816 0.184

10 0.308 1.777 0.223

12 0.266 1.716 0.284 0.184

R Chart

Range for Sample i

# Samples

From Table Nilai Guna

n

R R

R D LCL

R D UCL

i

n

1i

3R

4R

Process Capability Ratio, Cp

process the of deviation standard

6σionSpecificat LowerionSpecificat Upper

pC

Process Capability Cpk

population process the of deviation standard mean process x where

LimitionSpecificatLower x

or , x Limit ionSpecificatUpper

of minimum

3

3pkC

Assumes that the process is:• under control• normally distributed

Warning Conditions…..

Western Electric :1. 1 titik diluar batas kendali ( 3σ)2. 2 dr 3 titik berurutan diluar batas

kendali (2σ)3. 4 dr 5 titik berurutan jauh dari GT

(1σ)4. 8 titik berurutan di satu sisi GT5. Giliran panjang 7-8 titik6. 1/beberapa titik dekat satu batas

kendali7. Pola data TAK RANDOM

Examples: Compute the 3 control charts for X and R from 15 samples of size n=3. Plot the control limits and the X and R values and comment about the underlying process. Sample OBSERVED DIMENSIONS (cm)

1 4.843 4.863 4.859 2 4.925 4.882 4.891 3 4.866 4.914 4.873 4 4.852 4.883 4.88 5 4.92 4.884 4.821 6 4.915 4.902 4.898 7 4.887 4.892 4.858 8 4.868 4.888 4.842 9 4.904 4.863 4.866 10 4.921 4.92 4.894 11 4.914 4.884 4.899 12 4.892 4.896 4.887 13 4.866 4.829 4.88 14 4.85 4.875 4.872 15 4.867 4.9 4.885

Sample OBSERVED DIMENSIONS (cm) mean range1 4.843 4.863 4.859 4.855 0.0202 4.925 4.882 4.891 4.899 0.0433 4.866 4.914 4.873 4.884 0.0484 4.852 4.883 4.88 4.872 0.0315 4.92 4.884 4.821 4.875 0.0996 4.915 4.902 4.898 4.905 0.0177 4.887 4.892 4.858 4.879 0.0348 4.868 4.888 4.842 4.866 0.0469 4.904 4.863 4.866 4.878 0.041

10 4.921 4.92 4.894 4.912 0.02711 4.914 4.884 4.899 4.899 0.03012 4.892 4.896 4.887 4.892 0.00913 4.866 4.829 4.88 4.858 0.05114 4.85 4.875 4.872 4.866 0.02515 4.867 4.9 4.885 4.884 0.033

4.882 0.037

844.4)037(.023.1882.4

920.4)037(.023.1882.4

x

x

LCL

UCL

x Chart

Six Sigma Control Chart (x-bar)

4.840

4.850

4.860

4.870

4.880

4.890

4.900

4.910

4.920

4.930

0 2 4 6 8 10 12 14 16

Observation

cm

Sample Mean

Upper Control Limit

Lower Control Limit

Center Line

R- Chart

0951.037.57.24 RD

0037.03 RD

Range Example

0

0.02

0.04

0.06

0.08

0.1

0.12

0 2 4 6 8 10 12 14 16

Sample Number

ran

ge

(cm

) Upper Control Limit

Center Line

Lower Control Limit

Sample Range

Contoh

No Hasil Pengukuran Xֿ R

1

2

3

4

5

6

7

8

9

10

20,22,21,23,22

19,18,22,20,20

25,18,20,17,22

20,21,22,21,21

19,24,23,22,20

22,20,18,18,19

18,20,19,18,20

20,18,23,20,21

21,20,24,23,22

21,19,20,20,20

Jumlah/Rata-rata

n =

A2 =

D4 =

D3 =

• GT =

• BKA =

• BKB =

n = 5

A2 = 0,577

D4 = 2,115

D3 = 0

• GT =

• BKA =

• BKB =

No X1 X2 X3 X4 X5 X6 X7 X¯ R

1

2

3

4

5

6

7

8

9

10

6

11

9

12

16

10

15

12

16

7

9

7

6

11

10

4

16

14

9

13

10

8

13

10

8

9

10

16

13

10

15

10

9

10

9

7

13

6

15

12

10

5

10

7

8

8

13

11

4

8

7

5

12

9

7

6

13

11

10

Jumlah/Rata-rata

• X¯(rata-rata) = ni (Xi)/ni

= n1X1 +n2X2 +……niXi

ni

• R¯ = ni (Ri)/ni

= n1R1 +n2R2 +……niRi

ni

• BP-X¯ = X¯rata-rata ± A2.R¯

• BPA-R = R¯D4

• BPB-R = R¯D3

No X¯ BPA BPB R BPA BPB

1

2

3

4

5

6

7

8

9

10

8,57

8,17

13,25

10,00

13,25

13,74

15,65

13,25

6,75

6,26

4,35

6,75

11

6

7

6

14,91

15,53

17,69

14,91

0,59

0

0

0.59

• Xֿ(rata-rata) = GT peta kendali X = 7(8,57) +6(8,17)+…+4(13,25)+7(10) 7+6+7+……+4+7 = • Rֿ = GT peta kendali R =7(11)+6(6)+7(7)…+4(7)+7(6) 7+6+7+…+4+7 = Ada 10 macam BATAS KENDALI