(a) Sample means:
xMon=(23+22+23+24)/4=23
xTue=(23+21+19+21)/4=21
xWed=(20+19+20+21)/4=20
xThu=(18+19+20+19)/4=19
xFri=(18+20+22+20)/4=20
Mean of all sample means:
x=(23+21+20+19+20)/5=20.6
(b) Subgroup ranges:
RMon=24−22=2
RTue=23−19=4
RWed=21−19=2
RThu=20−18=2
RFri=22−18=4
Average R value:
R-bar = (2+4+2+2+4)/5 = 2.8
A2 = 0.729 (for subgroup size 4)
X-bar Chart Upper Control Limit:
UCL(X-bar) = x + (A2 * R-bar) = 20.6+(0.729*2.8) = 22.6
X-bar Chart Lower Control Limit
LCL(X-bar) = x - (A2 * R-bar) = 20.6-(0.729*2.8) = 18.6
(c) D4 = 2.282 (for subgroup size 4)
UCL(R) = R-bar * D4 =2.8*2.282 = 6.39
D3 = 0 (for subgroup size 4)
LCL(R) = R-bar * D3 =2.8*0 = 0
(d) xMon is above UCL(X-bar). The process is out of control.
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