Small Sma ll boxes boxes of of Nutra NutraFla Flakes kes cere cereal al are are label labeled ed "net "net weig weight ht 10 10 ounces ounces." ." Each Each hour hour,, rando random m sampl samples es of sie sie n ! are w
+eight
ime
/ox 1
/ox 10.
/ox 2.2
/ox
2 a.m.
2.3
10.
10 a.m.
10.1
10.
2.2
2.3
11 a.m.
2.2
10.4
10.
10.1
Noon
2.5
2.3
10.
10.
1 6.7.
2.5
10.1
2.2
2.2
&sin &s ing g thes these e data data,, cons constr truc uctt limi limits ts for for x' x' and and ('ch ('char arts ts.. )s the the pro proce cess ss in in cont contro rol* l* +ha +hatt othe otherr step steps s shou should ld the the - de
Time
Box 1
Box 2
Box 3
Box 4
Sample Means
Sample Range
9:00 AM
9.8
10.4
9.9
10.3
10.1
0.6
10:00 AM
10.1
10.2
9.9
9.8
10
0.4
11:00 AM
9.9
10.5
10.3
10.1
10.2
0.6
Noon 1:00 PM
9.7 9.7
9.8 10.1
10.3 9.9
10.2 9.9
10 9.9
0.6 0.4
The control control limits limits are: are: (a !or Mean Mean "ei#ht$ "ei#ht$ %&% ' 9.6605 9.6605 onces$ )&% ' 10.3895 10.3895 onces onces an* (+ !or !or ,an#e$ % The -rocess is in control since there are no -oints lin# otsi*e the control limits in +oth /+ar chart an* , c See all the sheets for the calculaon calculaonss and tables. The process is in stascal control. control.
ighed to check process control Fi#e hours of obser#ations $ielded the following%
partment follow at this point*
% ' 0$ )&% ' 1.141 onces art.
ontrol hart alculaons 10.6
10.4
10.2
n a e M e l p m a S
10
ar %&% &ente r
9.8
)&%
9.6
9.4
9.2 0.5
1
1.5
2
2.5
3
3.5
4
4.5
ontrol hart alculaons 1.2
1
0.8
e g n a R e l p m a S
,an# e %&%, &ente r, )&%,
0.6
0.4
0.2
0 0.5
1
1.5
2
2.5
3
3.5
4
4.5
Nm+er
ar
,an#e
%&%,
&enter, )&%,
%&%
&enter )&%
1
10
0.4
0
0.5
1.141
9.6605
10.025
10.3895
2 3
10.2 10
0.6 0.6
0 0
0.5 0.5
1.141 1.141
9.6605 9.6605
10.025 10.025
10.3895 10.3895
4
9.9
0.4
0
0.5
1.141
9.6605
10.025
10.3895
A 1
B
C
4
Data Sample/Subgroup Size
4
5 6 7 8 9
R Chart Intermediate Calculations R!ar "3 Factor "4 Factor
0.5 0 2.282
R Chart Control Limits Lower Control Limit Center Upper Control Limit