Question

Three samples were taken of 4 different dog food bags and their weights were recorded:

Sample/Observation	1	2	3	4	Mean	Range
1	30.0	29.0	28.3	27.4	28.675	2.6
2	31.5	30.5	32.6	29.5	31.025	3.1
3	28.2	29.7	30.5	30.7	29.775	2.5

1. Find the LCL for the xbar-chart.
2. Is this process in control (in terms of the xbar-chart)?

Answer 1

Sample/Observation	1	2	3	4	Mean	Range
1	30	29	28.3	27.4	28.675	2.6
2	31.5	30.5	32.6	29.5	31.025	3.1
3	28.2	29.7	30.5	30.7	29.775	2.5
				average	29.825	2.73333

sample mean x̅ =			29.825
average range R̅ =			2.7333
sample size n   =			4
for sample size n=4, criitcal value of constant A2=					0.729
control line (CL) = x̅=			29.825
upper control limit =x̅+3*A2R̅ =			31.818
lower control limit =x̅-3*A2R̅ =			27.832

from above:

LCL for the xbar-chart =27.832

since sample mean of all three samples fall inside the control limits, the process is in control