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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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