A medical facility does MRIs. Occasionally, the test yield inconclusive results and have to be repeated. Using the following sample data and n = 100, determine the UCL (to three decimals) for a two-sigma control chart. Sample 1 2 3 4 5 6 7 8 9 10
Number of Retests 4 11 6 10 4 6 1 6 9 11
a) 0.118.
b) 0.068.
c) 0.144.
d) 0.129.

a) 0.118.

Explanation:

The computation of the UCL is shown below:

Given that

N = 100

Sample    Sample size      Number of retests       fraction defective

1                      100                     4                                0.04

2                     100                      11                               0.11

3                     100                      6                               0.06

4                     100                      10                              0.1

5                     100                     4                                0.04

6                     100                      6                              0.04

7                     100                      1                                0.01

8                     100                      6                               0.06

9                     100                      9                              0.09

10                   100                      11                               0.11

Total              1,000                   68

Now p is

= 68 ÷ 1000

= 0.068

Now the standard deviation is

= √p(1 - p) ÷ √n

= √0.068 × (1 - 0.068) ÷ √100

= 0.025

Now the UCL is

= p + z × standard deviation

= 0.068 + 2 × 0.025

= 0.118

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