Question

A manufacturer trying to get a process under control randomly collects 8 samples from the process each hour. Five of the X bar and R measurements are as follows: X bar: 344, 346, 355, 353, 354 R: 3,4,3,2,3 What are the controllimit values for the two control charts (3 per chart)?

Answer 1

from given data:

sample	xbar	R
1	344	3
2	346	4
3	355	3
4	353	2
5	354	3
average	350.4	3

for Xbar chart:

sample mean x̅ =			350.4
average range R̅ =			3
sample size n   =			8
for sample size n=8, criitcal value of constant A2=					0.373
control line (CL) = x̅=			350.4
upper control limit =x̅+3*A2R̅ =			351.519
lower control limit =x̅-3*A2R̅ =			349.281

for R chart:

average range R̅ =			3
sample size n   =			8
for sample size n=8, criitcal value of constant D3=					0.136
for sample size n=8, criitcal value of constant D4=					1.864
control line (CL) = R̅=			3
upper control limit (UCL)=D4R̅ =			5.592
lower control limit(LCL) =D3R̅ =			0.408