l Kime\'s bowling ball factory makes bowling balls of bowling .. $6.8 Bill and w
ID: 3340679 • Letter: L
Question
l Kime's bowling ball factory makes bowling balls of bowling .. $6.8 Bill and weight only. The standard deviation in the weight of roduced at the factory is known to be 0.12 pounds. Each adull siall bowling ball day balls produced that day has been assessed as follows: nds, of nine of the bowling Average (lb) 16.3 15.9 15.8 15.5 16.3 16.2 16.0 16.1 15.9 16.2 15.9 15.9 Day Day Average (lb) 16.3 15.9 16.3 16.2 16.1 15.9 16.2 15.9 15.9 16.0 15.5 15.8 15 16 17 19 20 21 10 23 24 12 a) Establish a control chart for monitoring the average weights of th bowling balls in which the upper and lower control limits are each two standard deviations from the mean. What are the values of th control limits? val b) If three standard deviations are used in the chart, how do these ues change? Why? Px C uses statistical process control iarain sandwich loaveExplanation / Answer
Day
Weight
X bar
lcl
ucl
1
16.3
16
15.76
16.24
2
15.9
16
15.76
16.24
3
15.8
16
15.76
16.24
4
15.5
16
15.76
16.24
5
16.3
16
15.76
16.24
6
16.2
16
15.76
16.24
7
16
16
15.76
16.24
8
16.1
16
15.76
16.24
9
15.9
16
15.76
16.24
10
16.2
16
15.76
16.24
11
15.9
16
15.76
16.24
12
15.9
16
15.76
16.24
13
16.3
16
15.76
16.24
14
15.9
16
15.76
16.24
15
16.3
16
15.76
16.24
16
16.2
16
15.76
16.24
17
16.1
16
15.76
16.24
18
15.9
16
15.76
16.24
19
16.2
16
15.76
16.24
20
15.9
16
15.76
16.24
21
15.9
16
15.76
16.24
22
16
16
15.76
16.24
23
15.5
16
15.76
16.24
24
15.8
16
15.76
16.24
Standard deviation = 0.12 lbs.
X bar will be the mean of the given weights which is 16 pounds
Control limits are set within 2 sigma limits
Upper Control Limit, UCL= X bar+ (2*0.12) = 16+ 0.24 = 16.24
Lower Control Limit, LCL= X bar- (2*0.12) = 16- 0.24 = 15.76
Day
Weight
X bar
lcl
ucl
1
16.3
16
15.64
16.36
2
15.9
16
15.64
16.36
3
15.8
16
15.64
16.36
4
15.5
16
15.64
16.36
5
16.3
16
15.64
16.36
6
16.2
16
15.64
16.36
7
16
16
15.64
16.36
8
16.1
16
15.64
16.36
9
15.9
16
15.64
16.36
10
16.2
16
15.64
16.36
11
15.9
16
15.64
16.36
12
15.9
16
15.64
16.36
13
16.3
16
15.64
16.36
14
15.9
16
15.64
16.36
15
16.3
16
15.64
16.36
16
16.2
16
15.64
16.36
17
16.1
16
15.64
16.36
18
15.9
16
15.64
16.36
19
16.2
16
15.64
16.36
20
15.9
16
15.64
16.36
21
15.9
16
15.64
16.36
22
16
16
15.64
16.36
23
15.5
16
15.64
16.36
24
15.8
16
15.64
16.36
If the control limits are set to 3 standard deviations we can see that the upper control limit have changed to 16.36 lbs. and lower control limit to 15.64 lbs. Now the average weights of only two days (4 and 23) are out of control. But in the previous case, the values of three other days were also out of control.
These changes are there because of the fact that the control limits are now more widened and the values are now allowed to vary within 3 standard deviation limits. Even then the process is out of control.
Day
Weight
X bar
lcl
ucl
1
16.3
16
15.76
16.24
2
15.9
16
15.76
16.24
3
15.8
16
15.76
16.24
4
15.5
16
15.76
16.24
5
16.3
16
15.76
16.24
6
16.2
16
15.76
16.24
7
16
16
15.76
16.24
8
16.1
16
15.76
16.24
9
15.9
16
15.76
16.24
10
16.2
16
15.76
16.24
11
15.9
16
15.76
16.24
12
15.9
16
15.76
16.24
13
16.3
16
15.76
16.24
14
15.9
16
15.76
16.24
15
16.3
16
15.76
16.24
16
16.2
16
15.76
16.24
17
16.1
16
15.76
16.24
18
15.9
16
15.76
16.24
19
16.2
16
15.76
16.24
20
15.9
16
15.76
16.24
21
15.9
16
15.76
16.24
22
16
16
15.76
16.24
23
15.5
16
15.76
16.24
24
15.8
16
15.76
16.24
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