Quality Lab Manual (INP 363) 2022-2023

EXPERIMENT NO. 2
Experiments to be conducted with
Shewharts Normal Bowl.

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 Quality Lab Manual (INP 363) 2022-2023
EXPERIMENT NO

AIM: Experiments to be conducted with Shewharts Normal Bowl.

a) Establishment of relationship between

1) Universe Mean & SampleMean.
2) Universe standard deviation & Standard deviation of means ofsamples.
b) To plot a model control chart from the drawings obtained in the previousexperiments
3) To make changes in the known Universe & observe their effect on control charts.

PROCEDURE: To establish the above relation one needs to create the universe as a first step. One of the
methods followed is creation of Shewharts Normal bowl .Following will be the contents of Shewharts normal bowl.
Total 998 chips have to be made as follows.

Marking Marking Marking

Number Number Number
on chip on chip on chip
of Chips of Chips of Chips
X X X
60 1 39 27 19 22
59 1 38 29 18 19
58 1 37 31 17 17
57 1 36 33 16 15
56 1 35 35 15 13
55 2 34 37 14 11
54 2 33 38 13 9
53 3 32 39 12 8
52 4 31 40 11 7
51 4 30 40 10 5
50 5 29 40 9 4
49 7 28 39 8 4
48 8 27 38 7 3
47 9 26 37 6 2
46 11 25 35 5 2
45 13 24 33 4 1
44 15 23 31 3 1
43 17 22 29 2 1
42 19 21 27 1 1
41 22 20 24 0 1
40 24

Once the normal bowl is made the students will draw samples from it, with a subgroup size of 3,4 or 5 and record
the observation in the table given below.
For n=4

Sample X1 X2 X3 X4 Mean Range

Drawings
1 47 32 44 35
2 33 33 34 34
3 34 34 31 34
4 12 21 24 47
5 35 23 38 40

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 Quality Lab Manual (INP 363) 2022-2023
6 19 37 31 27
7 23 45 26 37
8 33 12 29 43
9 25 22 37 33
10 29 32 30 13
11 40 18 30 11
12 21 18 36 34
13 26 35 31 29
14 52 29 21 18
15 26 20 30 20
16 19 1 30 30
17 28 34 39 17
18 29 25 24 30
19 21 37 32 25
20 24 22 16 35
21 20 38 27 32
22 30 14 37 43
23 28 29 32 35
24 35 30 37 26
25 51 13 45 55
26 28 39 23 21
27 41 32 46 12
28 14 23 41 42
29 32 28 46 27
30 42 34 22 34
31 34 19 11 16
32 32 28 41 40
33 14 31 20 35
34 25 44 29 27
35 18 22 20 33
36 21 31 39 25
37 17 44 54 13
38 36 48 19 41
39 25 31 38 30
40 35 21 20 34
41 21 22 44 19
42 39 22 24 29
43 40 44 24 18
44 23 25 46 29
45 23 37 44 34
46 36 52 30 28
47 35 23 11 5
48 33 15 40 29
49 18 30 22 25
50 23 30 20 19
51 7 32 36 38
52 29 30 39 31
53 36 12 25 39
54 36 37 29 29
55 38 9 31 25
56 11 44 12 27
57 31 18 32 44
58 22 47 32 27
59 29 24 43 29
60 42 26 23 39
61 29 40 52 28
62 23 22 23 24
63 34 27 16 28
64 27 40 39 32
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 Quality Lab Manual (INP 363) 2022-2023
65 34 38 25 42
66 39 19 38 39
67 42 25 10 28
68 30 25 10 16
69 43 22 34 25
70 17 31 39 32
71 40 49 38 37
72 22 39 26 18
73 30 36 34 18
74 41 37 27 32
75 5 20 43 26
76 38 26 38 25
77 27 38 40 33
78 20 23 28 35
79 29 29 34 29
80 25 35 37 42
81 42 59 38 28
82 24 32 22 22
83 38 40 31 52
84 22 52 33 54
85 46 32 20 50
86 27 29 24 15
87 31 26 34 35
88 32 46 30 32
89 35 20 34 46
90 55 25 33 54
91 22 46 52 42
92 14 24 2 43
93 36 52 19 50
94 29 21 17 9
95 33 31 32 18
96 52 34 17 5
97 23 41 21 29
98 28 22 45 21
99 32 27 16 30
100 23 23 27 36

3. Calculate value of X bar, R and s for each subgroup. AND find out X-double bar,R bar and s bar, where

̿=∑ 𝑋
𝑋 ̅ / N , R bar = ∑R/N and s bar= ∑s/N.

SOLUTION & RESULTS

1. The mean of normal distribution created has 𝑿 ̅ ‘ =30.For the 100 subgroups, X double bar = __________
. This is very close to 30.000,the average distribution in the bowl.
2. The std deviation of the averages is represented as 𝑥 ̅. 𝜎 𝑥̅ for the 100 subgroups is _________.This is very
𝜎′
close to where 𝜎′= 9.954
√𝑛

INTERPRETATION & CONCLUSION:

̿ obtained from above observation is equal to 𝑋
1. It is to be verified 𝑋 ̅ ‘. That is sample mean is approximately
equal to universal mean.
𝜎′ ̅
𝑅
2. 𝜎 𝑥̅ is std deviation of samples which is approximately equal to .Other way of this verification is𝜎’=𝑑2 .
√𝑛

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 Quality Lab Manual (INP 363) 2022-2023

EXPERIMENT NO. 3
Demonstration of the fact that sample
mean distribution is always normal even if
the universe is not normally distributed.

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 Quality Lab Manual (INP 363) 2022-2023

EXPERIMENT NO

AIM: Demonstration of the fact that sample mean distribution is always normal even if the
universe is not normally distributed.

PROCEDURE: For this take one set of playing cards. The students will draw sample from this card
set. Universe distribution is uniform or constant .It will be a discrete uniform distribution.

Samples will be from set with a subgroup size of 4 the observations to be recorded in the following
table. Total 30 samples is to be recorded.

Sample NO X1 X2 X3 X4 R
1
2
AND SO ON

The above observation will give a non normal universe. But the sample distribution will be normal
distribution.

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