Q 1. A process involves the filling of bags with sand. Each bag is supposed to weigh a minimum

of 50 pounds and a maximum of 51 pounds. The process has an automatic method of weighing

the bags. Once the bag reaches the desired weight, the filling operation is supposed to stop. To

determine how much variation there is in the bag weights, an operator takes the first four bags

filled each hour and manually weighs them using calibrated scale. The data is shown in the

table given below. Find out whether this process is consistent or not. Measure the process

capability and show the improvement in process capability removing outliers (assuming that

these outliers can be perfectly removed). (A2=0.729, D3=0, D4=2.282). (15)

Sub group

Number (k)

Bag Weight Results (n=4)

1 2 3 4

1 50.4 50.2 50.5 50.8

2 50.7 50.8 50.1 50.5

3 50.7 50.3 50.4 50.2

4 50.1 50.3 50.3 50.1

5 50.4 50.4 50.5 50.4

6 50.4 50.4 50.8 50.5

7 50.5 50.4 50.9 50.7

8 51 50.4 50.8 50.2

9 50.6 50.7 50.9 50.5

10 50.4 50.6 50.4 50.7

11 50.2 50.3 50.2 50.4

12 50.5 50.5 50.4 50.9

13 50.2 50.4 50 50.8

14 50.2 50.4 50.7 50.6

15 50.7 50.6 50.2 50.3

16 50.6 50.6 50.3 50.5

17 50.5 50.6 50.5 50.3

18 50.9 50.6 50.5 50.7

19 50.7 50.4 50.3 50.7

20 50.3 50.2 50.6 50.67