Random samples of four items are selected from a manufacturing process at regular intervals and a certain quality characteristic is measured. After 25 samples, ΣX = 15,350 and ΣR = 411.4. To construct a mean chart, what is the upper control limit (UCL) for the mean?
A) 614.00
B) 411.4
C) 625.996
D) 3837.5

Question

Quizplus · Accepted Answer

To determine the UCL for the mean, we need to use the formula:
UCL = X̄ + A2(R̄)
where X̄ is the average of the sample means, A2 is a constant from the standard normal distribution (usually found in a table), and R̄ is the average range.

First, calculate the sample mean:
X̄ = ΣX / n = 15,350 / (25 x 4) = 154

Next, calculate the average range:
R̄ = ΣR / n = 411.4 / 25 = 16.456

From the standard normal distribution table, A2 for n = 4 is 0.577.

Plugging in the values into the formula, we get:
UCL = 154 + 0.577(16.456) = 625.996

Therefore, the best choice is C, with an explanation as shown above.

Random Samples of Four Items Are Selected from a Manufacturing