Asked by Jordan Ratliff on Jul 18, 2024
Verified
A manager wishes to build a 3-sigma range chart for a process. The sample size is five, the mean of sample means is 16.01, and the average range is 5.3. From Table S6.1 in the text, the appropriate value of D3 is 0, and D4 is 2.115. The UCL and LCL for this range chart are
A) 33.9 and 11.2.
B) 33.9 and 0.
C) 11.2 and 0.
D) 6.3 and 0.
E) 31.91 and 0.11.
3-sigma Range Chart
A statistical chart used in quality control that illustrates the variation of a process within three standard deviations (3-sigma) from the mean, identifying outliers.
Average Range
In statistics, it is the mean difference between the largest and smallest values in a set of data, used as a measure of statistical dispersion.
- Use foundational statistical formulas to establish control limits and identify their role in the framework of SPC charts.
Verified Answer
AM
Alyssa Marie LopezJul 20, 2024
Final Answer :
C
Explanation :
The UCL and LCL for the range chart can be calculated using the formula:
UCL = D4 * R_bar
LCL = D3 * R_bar
where D4 and D3 are constants from Table S6.1, and R_bar is the average range.
From the problem statement, the average range is given as 5.3, and the appropriate value of D3 is 0, and D4 is 2.115. Therefore:
UCL = 0 * 5.3 = 0
LCL = 2.115 * 5.3 = 11.2
Thus, the best choice is C. The UCL for the range chart is 0, and the LCL is 11.2.
UCL = D4 * R_bar
LCL = D3 * R_bar
where D4 and D3 are constants from Table S6.1, and R_bar is the average range.
From the problem statement, the average range is given as 5.3, and the appropriate value of D3 is 0, and D4 is 2.115. Therefore:
UCL = 0 * 5.3 = 0
LCL = 2.115 * 5.3 = 11.2
Thus, the best choice is C. The UCL for the range chart is 0, and the LCL is 11.2.
Learning Objectives
- Use foundational statistical formulas to establish control limits and identify their role in the framework of SPC charts.
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