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 lower control limit (LCL) for the mean?
A) 602.004
B) 411.400
C) 625.666
D) 0.00

Question

Quizplus · Accepted Answer

The lower control limit (LCL) for the mean chart is calculated using the formula: LCL = X̄ - A2 * R̄. Here, X̄ = ΣX / (number of samples * sample size) = 15,350 / (25 * 4) = 153.5. R̄ = ΣR / number of samples = 411.4 / 25 = 16.456. For a sample size of 4, A2 is approximately 0.729. Thus, LCL = 153.5 - (0.729 * 16.456) = 602.004.

Random Samples of Four Items Are Selected from a Manufacturing