Question

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.

Answer 1

a) 0.118.

Step-by-step 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