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A Six Sigma expert observes rising complaints in a textile company about cotton fabric, especially concerning its shrinkage. He tries to improve the production process

A Six Sigma expert observes rising complaints in a textile company about cotton fabric, especially concerning its shrinkage. He tries to improve the production process that happens in three shifts daily. He records the shrinkage (in mm) by testing a sample of 5 shirts from every shifts production to understand the process and keep it under control. Based on the customer requirements, the company has set a specification range from 75 to 185. The following table presents 20 samples, each of five pieces produced by this process.

Sample No. 1 2 3 4 5
1 138.10 110.80 138.70 137.40 125.40
2 149.30 142.10 105.00 134.00 92.30
3 115.90 135.60 124.20 155.00 117.40
4 118.50 116.50 130.20 122.60 100.20
5 108.20 123.80 117.10 142.40 150.90
6 102.80 112.00 135.00 135.00 145.80
7 120.40 84.30 112.80 118.50 119.30
8 132.70 151.10 124.00 123.90 105.10
9 136.40 126.20 154.70 127.10 173.20
10 135.00 115.40 149.10 138.30 130.40
11 139.60 127.90 151.10 143.70 110.50
12 125.30 160.20 130.40 152.40 165.10
13 145.70 101.80 149.50 113.30 151.80
14 138.60 139.00 131.90 140.20 141.10
15 110.10 114.60 165.10 113.80 139.60
16 145.20 101.00 154.60 120.20 117.30
17 125.90 135.30 121.50 147.90 105.00
18 129.70 97.30 130.50 109.00 150.50
19 123.40 150.00 161.60 148.40 154.20
20 144.80 138.30 119.60 151.80 142.70

Trial control limits are established first and they are revised after making necessary corrections in the process. 10 new samples collected were examined with the revised control limits.

Sample No. 1 2 3 4 5
21 131.00 184.80 182.20 143.30 212.80
22 181.30 193.20 180.70 169.10 174.30
23 154.80 170.20 168.40 202.70 174.40
24 157.50 154.20 169.10 142.20 161.90
25 216.30 174.30 166.20 155.50 184.30
26 186.90 180.20 149.20 175.20 185.00
27 167.80 143.90 157.50 171.80 194.90
28 178.20 186.70 142.40 159.40 167.60
29 162.60 143.60 132.80 168.90 177.20
30 172.10 191.70 203.40 150.40 196.30

Further, 10 samples collected were examined for control with the revised control limits established with the first 20 samples.

Sample No. 1 2 3 4 5
31 131.50 143.10 118.50 103.20 121.60
32 111.00 127.30 110.40 91.00 143.90
33 129.80 98.30 134.00 105.10 133.10
34 145.20 132.80 106.10 131.00 99.20
35 114.60 111.00 108.80 177.50 121.60
36 125.20 86.40 64.40 137.10 117.50
37 145.90 109.50 84.90 129.80 110.60
38 123.60 114.00 135.40 83.20 107.60
39 85.80 156.30 119.70 96.20 153.00
40 107.40 148.70 127.40 125.00 127.50

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