Lecture 4Lecture 4Control Chart for Control Chart for Variables Variables -- 11

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Review ►QUIZ ( 10 menit )

� Sebutkan pembagian penyebab variasipada proses manufaktur ? Berikancontoh ?contoh ?

� Kapan proses disebut in control dankapan out of control ? Berikan contoh?

JANGAN LUPA BERI NAMA DAN NIM

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Review

� Penyebab Variasi� Chance Cause ( Penyebab Umum )

Sesuatu yang melekat pada proses

25 October 2010 Materi ke-3

Sesuatu yang melekat pada proses( sesuatu yang alamiah ). Contoh : Suhu ruangan

� Assignable Cause ( PenyebabKhusus )Sesuatu yang dapat ditentukanContoh : salah alat, kesalahan operator

Review

� Proses in control ketika proses yang berjalan hanya disebabkan oleh Chance Cause ( Penyebab Umum )Proses out of control ketika proses yang

25 October 2010 Materi ke-3

� Proses out of control ketika proses yang berjalan disebabkan oleh Assignable Cause ( PenyebabKhusus )

Pengambilan Sampel

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Pemilihan subgroup

� Aturan : memilih subgrup sedemikiansehingga variasi yang terjadi dalam subgruphanya disebabkan oleh chance causes.

� Pengambilan subgrup berdasarkan waktu

25 October 2010 Materi ke-3

� Pengambilan subgrup berdasarkan waktu� Besarnya subgrup ( Subgroup Size ) adalah

jumlah produk yang diambil pada setiapsubgrup.

� Banyaknya sampling adalah jumlah subgrupdalam sampling.

Pemilihan subgroup

subgroup size ( besarnya subgrup )

1 2 3 4 5 x s

subgrup ke-1 → 1

2

.

7

.

.

.

.

subgrup ke-35 → 35

↑

Jumlah sampel

( banyaknya

subgroup )

X

S

Pendahuluan

• Variabel - karakteristik kualitas tunggal yang dapat diukur dalam skala numerik.

• Ketika bekerja dengan variabel, kita harusmemantau baik nilai rata-rata karakteristik dan

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memantau baik nilai rata-rata karakteristik danvariabilitas yang terkait dengan karakteristik.

Pendahuluan

� Mean = kecenderungan pemusatandari proses.

� Variability = dispersi proses

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� Variability = dispersi proses

µ0 µ1LSL USL

Pendahuluan

σ0

10

µ0LSL USL

σ1

IntroductionIntroduction

� Monitor Mean Quality Level� x-bar control chart

Monitor Process Variability Quality

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� Monitor Process Variability Quality Level� Control chart for standard deviation, S

chart� Control chart for the range, R chart

Selection Char. for Investigation

� There can be many possible quality characteristics

� The decision making process becomes

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� The decision making process becomes more complicated

� Selecting a few vital quality char. from the many candidate ( using Pareto analysis )

Construction of Control Chart

� Selection of Rational Subgroups� Dif. among subgroups : maximized� Dif. within subgroups : minimized

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� Dif. within subgroups : minimized

� Subgroup Size� Normally between 4 – 10 ( 4 or 5 )

� Frequency of Subgroups Selection� Type of Measuring Instrument� Design of Recording Form for Data

Construction of Control Chart

Notation for variables control charts� n - size of the sample (sometimes called a

subgroup) chosen at a point in time� m - number of samples selected

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� m - number of samples selected� = average of the observations in the ith

sample (where i = 1, 2, ..., m)� = grand average or “average of the

averages (this value is used as the center line of the control chart)

ix

x

� Ri = range of the values in the ithsample

Ri = xmax - xmin

Construction of Control Chart

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Ri = xmax - xmin

� = average range for all m samples� µ is the true process mean� σ is the true process standard

deviation

R

Contoh : Control Chart for the Mean and Range

Month Week 1 Week 2 Week 3 Week 41 6,60 7,16 3,12 6,032 8,81 4,98 6,38 5,763 0,51 4,56 4,68 7,744 5,05 5,82 5,47 3,455 9,64 8,57 6,31 6,356 0,85 10,00 1,95 4,037 5,68 8,34 5,69 9,60

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7 5,68 8,34 5,69 9,608 5,47 4,11 1,72 7,239 2,46 4,46 2,22 6,9710 6,05 2,04 5,44 7,8111 4,72 4,84 4,22 10,5312 7,12 6,35 6,44 0,5013 6,60 0,88 8,99 7,0714 7,86 5,93 3,09 6,8215 11,32 8,57 5,62 4,2116 4,38 2,50 8,43 7,2117 7,51 6,13 2,14 9,8418 6,60 7,16 3,12 6,0319 8,83 4,99 4,77 1,5420 4,42 7,34 5,11 6,77

Contoh : Control Chart for the Mean and Range

� Development of the Chart

Rn

X

gg

n

i i

R

XXX

∑∑

∑ = −==minmax

1 ,

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gR

gX

g

i i

g

i i RX ∑∑ == == 11 ,

( ) RAXLCLUCLXX 2, ±=

RDLCLRDUCL RR 34 , ==

Contoh : Control Chart for the Mean and Range

Month Week 1 Week 2 Week 3 Week 4 X (Avg) Range

1 6,60 7,16 3,12 6,03 → 5,73 4,04

2 8,81 4,98 6,38 5,76 → 6,48 3,83

19 8,83 4,99 4,77 1,54 → 5,03 7,29

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19 8,83 4,99 4,77 1,54 → 5,03 7,29

20 4,42 7,34 5,11 6,77 → 5,91 2,92

Sum(X)= 113,9025 Sum(R)= 110,7

X= 5,695125 R= 5,535

A2= 0,729 D4= 2,282

UCL(X)= 9,73014 D3= 0

LCL(X)= 1,66011 UCL= 12,63087

LCL= 0

A2,D4 dan D3 dari tabel

Contoh : Control Chart for the Mean and Range

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Contoh : Control Chart for the Mean and Range

8,00

10,00

12,00

0,00

2,00

4,00

6,00

8,00

0 5 10 15 20 25Month

X(Avg) X UCL LCL

Contoh : Control Chart for the Mean and Range

10,00

12,00

14,00

0,00

2,00

4,00

6,00

8,00

0 5 10 15 20 25Month

Range R UCL LCL

Example

The thickness of magnetic coating on audio tape is an important

Samplenumber

Sample mean

sample stdv

1 36,4 4,6

2 35,8 3,7

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important characteristics. Table shows the mean and standard dev for 20 samples. The spec are 38 ± 4.5 . ( Note n = 4 )

2 35,8 3,7

3 37,3 5,2

18 39,2 4,8

19 36,8 4,7

20 37,7 5,4

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Example� Find the trial control limit for an X and s Chart

79.420

8.95

20

20

1 ==== ∑ =s

sCL i i

s

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0)79.4)(0(

854.10)79.4)(266.2(

79.42020

3

4

===

===

====

sBLCL

sBUCL

sCL

s

s

s

Example� Find the trial control limit for an X and s Chart

075.3720

5.741

20

20

1 ==== ∑ =X

XCL ii

X

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277.29)79.4)(628.1(075.37

873.44)79.4)(628.1(075.37

2020

3

3

=−=−=

=+=+=

sAXLCL

sAXUCL

X

X

X

Example : S chart

4

5

6

7

CL

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0

1

2

3

4

1 3 5 7 9 11 13 15 17 19 LCL

Example : X Chart

37383940

CL

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313233343536

1 3 5 7 9 11 13 15 17 19

Example� Assuming the thickness to be normally dist. what

proportion of the product will not meet spec ?

199.59213.0

79.4ˆ ===

c

sσ

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1492.004.1199.5

075.375.42

2451.069.0199.5

075.375.33

199.59213.0

1

1

4

⇒=−=

⇒−=−=

===

z

z

cσ

proportion of the product not meet spec = 0.2451 + 0.1492 = 0.3943

Kata Inspirasi Hari Ini

Semakin luas Anda mengait-ngaitkan berbagai hal , semakin

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ngaitkan berbagai hal , semakin banyak anda belajar

QuizQuiz

1. Definisikan variabel menurut anda dan contohnya ?Apa yang dapat dimonitor oleh

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2. Apa yang dapat dimonitor oleh peta kendali variabel ?

3. Apa perbedaan fungsi X-chart dan R-chart ?