Problem 1: R Chart and Xbar Chart
Thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world. Results from the last five samples are shown in the table. Draw and R Chart and an xbar chart. Based on the charts, is the process under control?
(See attachment for chart)
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answer
body preview (14 words)
check xxxxxxxx xxxxx xxx xx xxx have any doubts then xxxx xx a message.
file1.xlsx preview (85 words)
xxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxObservations  
xxxxxx  1  x  x  x  x  average(xbar)  range(R)  
x  xxxx  xxxx  72.2  xxxx  xx  xxxxx  xxx  1  xxxxx  71.928  xxxxxxxxxxxxxxxxxx  xxxxxxxxxxxxxxxxxx 
x  xxxx  xx  xxxx  xxxx  72.2  xxxxx  xxx  2  xxxxx  71.928  70.199600000000004  73.656399999999991 
x  xx  72.6  71.9  xxxx  73.3  72.04  3.3  x  72.039999999999992  71.928  70.199600000000004  xxxxxxxxxxxxxxxxxx 
4  xxxx  70.6  xxxx  74.2  xxxx  xxxxx  xxx  4  xxxxxxxxxxxxxxxxxx  71.928  xxxxxxxxxxxxxxxxxx  73.656399999999991 
x  70.8  70.7  70.7  xxxx  xxxx  71.36  2.8  x  xxxxxxxxxxxxxxxxxx  71.928  70.199600000000004  xxxxxxxxxxxxxxxxxx 
xxxxxxxx  xxxxxxxx bar  xxxxx  xxxxxxxxxxxxxxxxxx  
x  xxx xxxxx control xxxxxx  xxxxxxxxxxxxxxxxxx  2.9799999999999995  
xxx x xdouble bar + xxx xxxxxxx  
xxx = xdouble xxx  A2*(Rbar)  
since, xxx of observations is xx A2 x xxxx  
xxxxxx  
UCL x  73.656399999999991  
xxx x  xxxxxxxxxxxxxxxxxx  
This process is xxxxx xxxxxxx xxxxx xxxxx xx xxx sample is between LCL xxx xxxx 
xxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  1  x  3  x  5  xxxxxxxxxxxxxx  xxxxxxxx  
1  xxxx  70.8  72.2  xxxx  xx  72.22  xxx  2.98  0  xxxxxxxxxxxxxxxxxx 
x  71.3  71  xxxx  72.7  72.2  72.06  2.1  2.98  0  6.2877999999999998 
x  70  72.6  71.9  xxxx  73.3  xxxxx  xxx  2.98  x  xxxxxxxxxxxxxxxxxx 
x  71.1  xxxx  70.3  xxxx  xxxx  71.96  xxx  xxxx  x  xxxxxxxxxxxxxxxxxx 
5  xxxx  xxxx  xxxx  xxxx  71.1  71.36  xxx  xxxx  0  6.2877999999999998 
xxxxxxxx  xxxxxxxx xxx  Rbar  
71.928  2.9799999999999995  
Rchart control xxxxxx  
UCL = D4*(Rbar)  
LCL = xxxxxxxxxx  
for n = xx xx x 0 xxx xx = xxxx  
xxxxxx  
xxx x  xxxxxxxxxxxxxxxxxx  
LCL=  0  
xxxx process is under xxxxxxxx 
xxxxxx
Try it before you buy it 
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Please see the attachment for solution. If you need any clarification please ask me. Thanks.
body preview (15 words)
Please xxx xxx attachment xxx xxxxxxxxx xx xxx xxxx xxx clarification please ask xxx xxxxxxx
file1.doc preview (335 words)
1. xxxxxxxxxxx xxx subjected to rigorous xxxxxxx xxxxxx xxxx xxx shipped xx air conditioning technicians xxxxxx the world. xxxxxxx xxxx the xxxx xxxx samples xxx shown in xxx table. Draw and x xxxxx and xx xbar xxxxxx xxxxx xx the charts, is xxx xxxxxxx under control? xxx xxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  
Sample  x  2  3  4  5 
x  xxxx  xxxx  72.2  xxxx  xxxx 
x  71.3  71.0  xxxx  xxxx  xxxx 
3  xxxx  xxxx  71.9  72.4  73.3 
4  xxxx  xxxx  70.3  74.2  73.6 
5  xxxx  xxxx  xxxx  73.5  xxxx 
The xxxx and xxxxx xxx xxxx xxxxxx is xxxxxxxx in the xxxxxxxxx table
xxxxxxxxxxxxxxxxxxxxxxxxxxxx
 xxxxxxxxxxxx 

 
Sample  x  x  3  x  x  xxxxx  R 
x  73.5  xxxx  xxxx  73.6  xx  xxxxx  xxx 
x  71.3  71  xxxx  xxxx  xxxx  72.06  xxx 
3  xx  72.6  xxxx  72.4  xxxx  xxxxx  3.3 
x  71.1  xxxx  xxxx  xxxx  xxxx  71.96  3.9 
x  xxxx  70.7  xxxx  73.5  71.1  xxxxx  2.8 
xxxxxxx  xxxxxx  xxxx 
xxxx the given xxxxxx
x xxxxxxx
xx xxxxx
Since xxx subgroup xxxxx n = 5, = 0.577, = 0, = 2.114
Control xxxxxx xxx Rchart:
xxx x x 2.98
xxxx x �� EMBED Equation.3 = (2.114)(2.98) x xxxxxx
xxxx = xxxxxx xxxxx Equation.3 x (0)(2.98) = x
xxxxxxx limits for Xbar xxxxxxx
CL x x xxxxxx
UCL = x xxxxxx xxxxx Equation.3 x 71.928 x xxxxxxxxxxxxx = 73.6475
xxxx = – xxxxxx EMBED xxxxxxxxxx x 71.928 – (0.577)(2.98) = xxxxxxx
xxx x chart xxx xxxxx xxxxx xxx shown xxxxxx
Here all the xxxxxx are xxxxxx the control limits. So xxx xxxxxxx xx xx control.
_1350757728.unknown
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_1353609077.unknown
_1353609087.unknown
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xxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  x  2.98  xxxxxxx  
xxx  0  2.98  xxxxxxx  
xxx  0  2.98  xxxxxxx  
3.9  x  2.98  6.29972  
2.8  0  xxxx  6.29972  0  xxxx  xxxxxxx 
xxxxxxxxxxxxxxx
xxxxThis xxxxxxxxx xxxxxxxx xxxxxx xxxxxxxx for xxxxxxxx xxxxxxx 
Xbar xxxx 
   more text follows   
file2.xls preview (100 words)
xxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxThis worksheet contains values xxxxxxxx for xxxxxxxx charts.  
Xbar Plot xxxx  
xxxxx  70.20854  71.928  73.64746  
72.06  xxxxxxxx  71.928  73.64746  
72.04  70.20854  xxxxxx  xxxxxxxx  
xxxxx  xxxxxxxx  71.928  xxxxxxxx  
xxxxx  70.20854  71.928  xxxxxxxx  70.20854  71.928  73.64746 
Rbar Plot xxxx 6/12/2012 6:30.48.000  
xxx  0  xxxx  xxxxxxx  
2.1  0  xxxx  xxxxxxx  
3.3  x  2.98  xxxxxxx  
xxx  x  2.98  xxxxxxx  
xxx  x  xxxx  6.29972  0  2.98  6.29972 
xxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxObservations  
Sample  1  2  x  4  x  xxxxx  x 
1  73.5  70.8  72.2  73.6  xx  72.22  2.8 
2  71.3  xx  73.1  xxxx  xxxx  72.06  2.1 
3  70  72.6  71.9  72.4  xxxx  xxxxx  3.3 
4  xxxx  xxxx  xxxx  74.2  xxxx  71.96  xxx 
5  70.8  70.7  xxxx  73.5  71.1  xxxxx  xxx 
xxxxxxx  xxxxxx  xxxx  
Since the sugroup xxxxx x x xx  xx x  0.577  D3 =  0  xx =  2.114  
Control limits xxx x xxxxxx  
CL x  2.98  
xxxx  0  
LCL=  6.2997  
Control limits xxx xxxxx xxxxxx  
CL x  71.928  
UCL=  73.6475  
xxxx  xxxxxxx  
Here all the xxxxxx xxx xxxxxx xxx control limits. So xxx process is in control. 
xxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxQuality xxxxxxx xxxxxxx xxxxxx  
Sample xxxx  5  
Number xx xxxxxxx  x  
xxxx  xxxxx  
Upper Control Limit, UCL  73.6475  6.2997 
xxxxxx  xxxxxxx  xxxxxx 
Lower Control Limit, xxx  xxxxxxx  0.0000 
xxxxxxxxx 6:30.48.000 
xxxxxx
xxxxxxxxxxxxxxxxx  xxxxxxxx  71.928  73.64746  
72.06  70.20854  71.928  73.64746  
xxxxx  xxxxxxxx  xxxxxx  xxxxxxxx  
xxxxx  xxxxxxxx  xxxxxx  73.64746  
71.36  70.20854  71.928  xxxxxxxx  xxxxxxxx  xxxxxx  73.64746 
2.8  0  2.98  xxxxxxx  
xxx  0  xxxx  xxxxxxx  
3.3  x  xxxx  6.29972  
xxx  0  2.98  xxxxxxx  
xxx  0  xxxx  xxxxxxx  0  xxxx  6.29972 
Try it before you buy it 