Consider a production process for a 5.0 o. energy drink. A quality engineer has taken 15 samples each containing 6 energy drinks. The sum of the average of the energy drinks in the 15 samples is 80.20. The sum of the ranges of the energy drinks in the 15 samples is 12.68. The LCL for the control chart reporting variability between the sample means is
A) 4.50
B) 4.65
C) 4.79
D) 4.94

Question

Quizplus · Accepted Answer

To calculate the LCL for the control chart reporting variability between sample means, we can use the formula:

LCL = X-doublebar - A2(R-bar)

Where X-doublebar is the grand mean, A2 is a constant factor based on sample size, and R-bar is the average range of the samples.

First, we need to find X-doublebar:

X-doublebar = Sum of sample means / Number of samples
X-doublebar = 80.20 / 15
X-doublebar = 5.347

Next, we need to find R-bar:

R-bar = Sum of sample ranges / Number of samples
R-bar = 12.68 / 15
R-bar = 0.8453

Finally, we can calculate the LCL:

LCL = X-doublebar - A2(R-bar)
LCL = 5.347 - (2.704)(0.8453)  (using A2 = 2.704 for n = 6)
LCL = 4.9416

Therefore, the best choice is D, with an LCL of 4.94.

Consider a Production Process for a 5