We are establishing a quality control program for a process and need to establis

Question

We are establishing a quality control program for a process and need to establish the mean and standard deviation for the process. The first 10 batches had samples of size 5 taken, and the following data were recorded.

Batch

x s

1. 43.6, 2.55

2. 45.3, 1.85

3. 42.6, 1.93

4. 46.2, 2.67

5. 44.1, 3.13

6. 42.9, 2.59

7. 45.0, 2.01

8. 47.4, 2.35

9. 46.2 , 1.87

10. 43.1, 2.95

Which of the following are the upper and lower control limits for an x control chart?

a.(37.012, 52.268)

b.(37.470, 51.810)

c.(42.228, 47.052)

Explanation / Answer

Answer is below:

Take out average of Xbar (bar-bar) and s ( stdev bar) to get: 44.64 and 2.39 respectively.

Now, LCL and UCL will be given as Xbar-bar -3 *s-bar to Xbar-bar +3 *s-bar

Therefore, 44.64 -3*2.39 to 44.64 +3*2.39

=37.47 to 51.81

Answer is b. (37.470, 51.810)

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