The Take-Charge Company produces batteries. From time to time a random sample of
ID: 411014 • Letter: T
Question
The Take-Charge Company produces batteries. From time to time a random sample of six batteries (n=6) is selected from the output and the voltage of each battery is measured, to be sure that the system is under control. Here are statistics on 16 such samples.
SAMPLE MEAN RANGE
1. 4.99 0.41
2. 4.87 0.57
3. 4.85 0.59
4. 5.26 0.74
5. 5.09 0.74
6. 5.02 0.21
7. 5.13 0.56
8. 5.09 0.92
9. 5.01 0.49
10 5.19 0.56
11. 5.40 0.44
12. 5.15 0.63
13. 5.00 0.35
14. 4.89 0.45
15. 4.99 0.54
16. 5.05 0.33
A2 = 0.48 D3 = 0 D4 = 2.00 n = 6
CALCULATE THE UPPER (UCL) AND LOWER (LCL) CONTROL LIMITS FOR AN
Explanation / Answer
Following are to be noted :
Xbar-bar = Mean of mean values = Sum of all mean values / 16 ( i.e number of observations)= 80.98/16 = 5.061
Rbar = Mean of Range values = Sum of all Range values / 16 ( i.e. number of observations ) = 8.53/16 = 0.533
With the given values of A2, D4 and D3 and sample size = n = 6, following are the control limits:
Xbar chart :
Upper Control Limit : Xbar-bar + A2.Rbar = 5.061 + 0.48x 0.533 = 5.061 + 0.255 = 5.316
Lower Control Limit = Xbar-bar – A2.Rbar = 5.061 – 0.48 x 0.533 = 5.061 – 0.255 = 4.806
Range chart :
Upper Control Limit = D4.Rbar = 2 x 0.533 = 1.066
Lower Control Limit = D3.Rbar = 0
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