introduction to statistical quality control, 5th edition · pdf filetitle: introduction to...

Ayundyah Kesumawati

Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.

Copyright (c) 2005 John Wiley & Sons, Inc. 2

Chapter 8 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.


CUSUM STATUS



MINITAB VERSION OF CUSUM

STATUS CHART



MINITAB calculates

the lower cusum this

way

CUSUM DENGAN

MINITAB

Data lama waktu (tahun) hidup mikrofon sampai rusaknya.

Spesifikasi perusahaan: 2 tahun.



Data

3 1

1 3

1 5

3 1

3 3

TABULAR CUSUM

μ1 adalah rata-rata dari sampel = 2,4

σ tidak diketahui, maka diestimasi dengan standar deviasi

= 1,35

K = (| μ1 – μ0|) / 2 = 0,2

h = 5.K = 1

H = σ.h = 1,35





TABULAR CUSUM DENGAN

MINITAB

Stat >> Control-ChartS >> CUSUM



TABULAR CUSUM

Klik Options



V-MASK CUSUM



V-MASK CUSUM

K = (| μ1 – μ0|) / 2

h* = h/2

d = h*/K

Contoh:

Data lama waktu (tahun) hidup mikrofon sampai rusaknya.

Spesifikasi perusahaan: 2 tahun.

Data

3 1

1 3

1 5

3 1

3 3



V-MASK CUSUM



V-MASK CUSUM

Misal observasi ke 8 adalah outlier.

Bagaimana diagram cusum yang lebih tepat???



V-MASK CUSUM

• K = (| μ1 – μ0|) / 2

• h* = h/2

• d = h*/K

Rumus di atas tidak mutlak.

Pada beberapa kasus terkadang dipilih K = 0.5 karena pergeseran mean proses yang ingin dideteksi berada dalam rentang 1.

Terkadang pula dipilih nilai h = 4 atau 5, tergantung keperluan.



V-MASK CUSUM



V-MASK CUSUM

Stat >> Control-ChartS >> CUSUM



V-MASK CUSUM

TASK STATISTICAL QUALITY CONTROL

1. The data that follow give the number of nonconforming bearing and seal

assemblies in samples of size 100. Construct a fraction nonconforming

control chart for these data. If any points plot out of control, assume that

assignable causes can be found and determine the revised control limits.



Sample Number

Number of

Nonconforming

Assemblies

Sample Number

Number of

Nonconforming

Assemblies

1 7 11 6

2 4 12 15

3 1 13 0

4 3 14 9

5 6 15 5

6 8 16 1

7 10 17 4

8 5 18 5

9 2 19 7

10 7 20 12

2. Based on the following data, if an np chart is to be established, what

would you recommend as the center line and control limits ?

Assume that n = 500



Day Number of Nonconforming Units

1 3

2 4

3 3

4 2

5 6

6 12

7 5

8 1

9 2

10 2

3. A maintenance group improves the effectiveness of its repair work

by monitoring the number of maintenance requests thet require a

second call to complete the repair. Twenty weeks of data are

available



Week Total

Request

Second

Visit

Required

Week Total

request

Second

Visit

Requeried

1 200 6 11 100 1

2 250 8 12 100 0

3 250 9 13 100 1

4 250 7 14 200 4

5 200 3 15 200 5

6 200 4 16 200 3

7 150 2 17 200 10

8 150 1 18 200 4

9 150 0 19 250 7

10 150 2 20 250 6

4. Bath concentrations are measured hourly in a chemical process. Data (in ppm) for

the last 32 hours are shown here (read down from left).

The process target is 𝜇0 = 175 ppm.

a. Estimate the process standart deviation

b. Construct a tabular cusum for this process using standardized values of h = 5 and k =

1/2



160 186 190 206

158 195 189 210

150 179 185 216

151 184 182 212

153 175 181 211

154 192 180 202

158 186 183 205

162 197 186 197

introduction to statistical quality control, 5th edition · pdf filetitle: introduction to...

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