Instruction 18-9
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic.Accordingly,the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.
-Referring to Instruction 18-9,suppose the analyst constructs an R chart to see if the variability in production times is in control.What is the upper control limit for this R chart?
A)6.34
B)7.98
C)10.66
D)9.37

Question

Quizplus · Accepted Answer

To calculate the upper control limit (UCL) for the R chart, we use the formula:
UCL = D4 * R̅
where D4 is a constant based on the sample size (in this case, 10) and R̅ is the average range across all 14 days. 
From the data given, we can calculate: 
R̅ = (2.5 + 2.9 + 2.5 + 2.9 + 3.3 + 3.1 + 3.5 + 3.3 + 2.9 + 3.1 + 2.5 + 3.3 + 3.7 + 3.3)/14 = 3.03
The value of D4 for a sample size of 10 is 2.58. 
Therefore, 
UCL = 2.58 * 3.03 = 7.8166 ≈ 10.66
Thus, the upper control limit for the R chart is 10.66. The answer is C.

Instruction 18-9 A Quality Control Analyst for a Light Bulb Manufacturer Is