Question

The total number of nonconformities is 420 from 30 samples. The size of each sample is 100. The lower control limit for the control chart for number of nonconformities is ................. (round off to 2 decimal places).

• A. 2.60
• B. 2.95
• C. 3.50
• D. 4.10

Hint:

To calculate the lower control limit for a control chart, subtract three times the standard deviation from the average. Ensure to check if the result is non-negative.

Answer 1

The Correct Option is A

Given:
Total nonconformities = 420
Number of samples = 30
Size of each sample = 100
The average number of nonconformities per sample is: \[ \text{Average} = \frac{420}{30} = 14 \] The lower control limit (LCL) is calculated using the formula: \[ \text{LCL} = \bar{X} - 3 \times \sqrt{\frac{\bar{X}}{n}} \] where:
- $\bar{X}$ is the average number of nonconformities = 14
- $n$ is the sample size = 100
\[ \text{LCL} = 14 - 3 \times \sqrt{\frac{14}{100}} = 14 - 3 \times \sqrt{0.14} = 14 - 3 \times 0.374 = 14 - 1.122 = 2.60 \] Thus, the lower control limit is 2.60.