Asked by Kristopher Curry on Jul 23, 2024
Verified
For an x-bar chart where the standard deviation is known, the Upper Control Limit
A) is 3 . ? below the mean of sample means for a 3? control chart.
B) is 3 . ? above the mean of sample means for a 3? control chart.
C) is 3 . ?/ n\sqrt { n }n below the mean of sample means for a 3? control chart.
D) is 3 . ?/ n\sqrt { n }n above the mean of sample means for a 3? control chart.
E) Cannot be calculated unless the average range is known.
Upper Control Limit
A statistical measure in quality control, representing the highest acceptable value for a process variable to stay within controlled and expected limits.
- Implement elementary statistical formulas for determining control limits and grasp the significance of these limits within SPC charts.
Verified Answer
YS
Yaren SaracogluJul 26, 2024
Final Answer :
D
Explanation :
The Upper Control Limit (UCL) for an x-bar chart, when the population standard deviation (σ) is known, is calculated as the mean of sample means plus 3 times the standard deviation of the sampling distribution of the mean. The standard deviation of the sampling distribution of the mean is given by σ/√n, where n is the sample size. Therefore, the UCL is 3σ/√n above the mean of sample means.
Learning Objectives
- Implement elementary statistical formulas for determining control limits and grasp the significance of these limits within SPC charts.