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

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

Quizplus · Accepted Answer

Lower Control Limit (LCL) = X̄ - A2*R̅
where X̄ = mean of the sample means
A2 = control chart constant from the table
R̅ = mean range = 0.45
For sample size n=9, A2 = 0.577
Therefore, LCL = X̄ - 0.577*0.45
We don't have the value of X̄, so we cannot calculate the exact LCL. However, we can say that the LCL will be less than X̄, and given the options, the only choice that meets this requirement is C.

An R Chart Is to Be Developed for Use