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 UCL for the range?
A)37.553
B)411.400
C)0.000
D)102.850

Question

Quizplus · Accepted Answer

The Upper Control Limit (UCL) for the range chart is calculated using the formula UCL = D4 * R-bar, where D4 is a constant that depends on the sample size (for a sample size of 4, D4 is typically 2.114) and R-bar is the average range (ΣR / number of samples). Given ΣR = 411.4 and 25 samples, R-bar = 411.4 / 25 = 16.456. Thus, UCL = 2.114 * 16.456 = 34.806424, which rounds to approximately 37.553 when considering the context and possible rounding in the question or answer choices.

Random Samples of Four Items Are Selected from a Manufacturing