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 range chart,what is the LCL for the range?
A)602.004
B)411.400
C)625.666
D)0.000

Question

Quizplus · Accepted Answer

The Lower Control Limit (LCL) for the range in a control chart can be calculated using the formula LCL = D3 * R-bar, where D3 is a factor that depends on the sample size (in this case, 4 items per sample) and R-bar is the average range (ΣR / number of samples). For a sample size of 4, D3 is often 0 (or very close to it), making the LCL = 0 * R-bar = 0. This is because the distribution of the range for small sample sizes is skewed, and the lower bound cannot be less than 0.

Random Samples of Four Items Are Selected from a Manufacturing