ISS (Statistical Services) Statistics Paper IV: Questions 9 - 11 of 92

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Question 9

Describe in Detail

Essay▾

A machine is manufacturing mica discs. Samples of size 5 are drawn every hour and their thickness in units is recorded as follows. From this data construct 3-σ control limits for and R charts.

What is the 3 Sigma Control Limit for X Bar-Chart and R Chart
Sample No.Observstions
18915411
2710768
3111210910
41286912
5111061411
67710411
710741010
88111177
981181412
10129121711
117791713
12994411
131012121212
14811968
151013949
169118511

Explanation

Control limits for R chart :

For n = 5, from the tables we the value of and

= 0

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Question 10

Describe in Detail

Essay▾

The following are the figures of defectives in 22 lots each containing 2,000 bulbs. Obtain the 3-σ control limits for the p chart.

Given Are Observations Find Control Limits for P Chart
425430216341225322280306337305356
402216264126409193326280389451420

Explanation

we have n = 2000

Given Are Observations Control Limits for P Chart
S. No.d
14250.2125
24300.215
32160.108
43410.1705
52250.1125
63220.161
72800.14
83060.153
93370.1685
103050.1525
113560.178
124020.201
132160.108
142640.132
151260.063
164090.2045
171930.0965
183260.163
192800.14
203890.1945
214510.2255
224200.21
Total3.5095

Control limits for :

3-σcontrol limits for the p ch…

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Question 11

Describe in Detail

Essay▾

A electric Company uses a process to paint cars with a coat of enamel. During each shift, a sample of five cars is selected and the thickness of the paint in mm is determined. On the basis of and R charts, Check whether the production is under control?

Find if Production is under Control
Sample No.Observations
12.62.32.62.72.7
22.62.62.42.82.3
32.42.32.42.52.3
42.72.42.32.62.8
52.62.62.52.82.1
62.22.22.72.32.6
72.02.62.42.22.3
82.52.62.62.72.8
92.42.42.22.82.3
102.62.32.02.52.4
113.13.03.52.83.0
122.42.82.22.92.5
132.13.22.52.62.8
142.22.82.12.22.4
152.43.02.52.52.0
163.12.62.62.82.1
172.92.42.91.31.8
181.91.62.63.33.3
192.32.62.72.83.2
202.02.82.31.82.9

Explanation

From the tables, for n = 5, we have , ,

Control limits for :

And

Check Whether Production is under Control X Bar Chart

The control chart shows that a observation corresponding to the 11th sample falls outside the control limits indicating that the process is not in control.

Control limits for R chart :

= 0

Check Whether Production is under Control – R Chart

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