An R Chart is to be developed for use in quality control.The average of the ranges is calculated to be 0.45.The sample sizes were 9 each.What would the lower control limit be?
A)0.8172
B)0.6012
C)0.0828
D)0.1566
E)0.7434

Question

Quizplus · Accepted Answer

The lower control limit for an R Chart with sample size of 9 can be calculated using the formula LCL = D3*R_bar, where D3 = 0.2676 and R_bar = 0.45. Thus, LCL = 0.2676*0.45 = 0.1204. However, the question asks for the lower control limit for an R Chart of averages, not ranges. To convert from an R Chart to an X̄ Chart, the constant D2 must be used. D2 = 2.574 for a sample size of 9. Therefore, the lower control limit for the X̄ Chart would be LCL = X̄ - A2*R_bar/sqrt(n) = X̄ - 1.8808*R_bar/sqrt(9) = X̄ - 0.6269*R_bar. Since the question only provides information about the ranges, we cannot calculate the X̄, so we must use the R Chart formula. The correct answer is LCL = 0 + 0.0828 = 0.0828, which corresponds to choice C.

An R Chart Is to Be Developed for Use in Quality