Question

Suppose that you collect data for 15 samples of 30 units each, and find that on average, 2.5 percent of the products are defective. What are the UCL and LCL for this process? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round up negative LCL values to zero. Round your answers to 3 decimal places.)

Answer 1

The UCL is
`UCL = 0.054`

The LCL is
`LCL \approx 0`

Explanation:

From the question we are told that

The quantity of each sample is n = 30

The average of defective products is
`p = 0.025`

Now the upper control limit [UCL] is mathematically represented as

`UCL = p + 3 \sqrt{(p(1-p))/(n) }`

substituting values

`UCL = 0.025 + 3 \sqrt{(0.025 (1-0.025))/(30) }`

`UCL = 0.054`

The upper control limit (LCL) is mathematically represented as

`LCL = p - 3 \sqrt{(p(1-p))/(n) }`

substituting values

`LCL = 0.025 - 3 \sqrt{(0.025 (1-0.025))/(30) }`

`LCL = -0.004`

`LCL \approx 0`