Consider a production process for a 5.0 oz. energy drink. A quality engineer has taken 15 samples each containing 6 energy drinks. The sum of the ranges of the energy drinks in the 15 samples is 12.68. The UCL for the control chart reporting variability within the samples is
A) 0.0
B) 1.0
C) 1.7
D) 2.4

Question

Quizplus · Accepted Answer

To calculate the UCL, we first need to calculate the grand mean range (R-bar). 
R-bar = (ΣRi) / n
where ΣRi is the sum of the ranges of the 15 samples and n is the number of samples, which is 15 in this case.
R-bar = 12.68 / 15 = 0.84533
Next, we need to calculate the standard deviation of the sample ranges (s). 
s = R-bar / d2
where d2 is a constant from a table (d2 for n=6 is 2.326).
s = 0.84533 / 2.326 = 0.363
Finally, the UCL for the control chart is:
UCL = R-bar + A2*s
where A2 is the constant from a table (A2 for n=6 is 0.577).
UCL = 0.84533 + 0.577*0.363 = 1.70798
Therefore, the UCL for the control chart is 1.7, which is answer choice (C).

Consider a Production Process for a 5