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 attached xxxxx and xx xxx have xxx xxxxxx xxxx send xx a xxxxxxxx
file1.xlsx preview (156 words)
xbar
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxObservations  
Sample  1  x  3  4  5  xxxxxxxxxxxxxx  range(R)  
x  73.5  xxxx  xxxx  xxxx  xx  72.22  xxx  x  72.22  xxxxxx  xxxxxxxxxxxxxxxxxx  73.656399999999991 
x  xxxx  71  xxxx  xxxx  xxxx  72.06  xxx  x  72.06  xxxxxx  xxxxxxxxxxxxxxxxxx  xxxxxxxxxxxxxxxxxx 
3  70  72.6  71.9  72.4  xxxx  72.04  3.3  x  72.039999999999992  xxxxxx  xxxxxxxxxxxxxxxxxx  73.656399999999991 
x  xxxx  70.6  xxxx  74.2  73.6  71.96  xxx  4  xxxxxxxxxxxxxxxxxx  71.928  70.199600000000004  73.656399999999991 
5  xxxx  70.7  70.7  73.5  xxxx  xxxxx  2.8  5  xxxxxxxxxxxxxxxxxx  xxxxxx  70.199600000000004  73.656399999999991 
averages  xxxxxxxx bar  xxxxx  71.927999999999997  
x  bar chart xxxxxxx xxxxxx  xxxxxxxxxxxxxxxxxx  2.9799999999999995  
xxx x xxxxxxxx bar x xxx (Rbar)  
xxx x xxxxxxxx xxx  A2*(Rbar)  
xxxxxx no. of observations is 5, A2 = 0.58  
xxxxxx  
UCL =  73.656399999999991  
xxx =  70.199600000000004  
xxxx xxxxxxx is uncer xxxxxxx since means xx all sample xx between LCL xxx xxxx 
xxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxSample  1  2  x  x  5  xxxxxxxxxxxxxx  range(R)  
1  73.5  xxxx  xxxx  73.6  71  xxxxx  2.8  xxxx  0  6.2877999999999998 
x  xxxx  71  73.1  72.7  72.2  72.06  xxx  2.98  x  6.2877999999999998 
x  70  xxxx  xxxx  xxxx  xxxx  xxxxx  xxx  xxxx  0  xxxxxxxxxxxxxxxxxx 
4  71.1  xxxx  70.3  74.2  73.6  71.96  3.9  2.98  0  6.2877999999999998 
x  xxxx  xxxx  70.7  xxxx  71.1  71.36  2.8  xxxx  x  6.2877999999999998 
xxxxxxxx  xxxxxxxx xxx  xxxxx  
xxxxxx  2.9799999999999995  
xxxxxxx control limits  
xxx x xxxxxxxxxx  
xxx x D3*(Rbar)  
xxx x = 5, xx = 0 and xx = xxxx  
hence,  
UCL x  6.2877999999999998  
xxxx  0  
this process is under control. 
Sheet3
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Please see the attachment for solution. If you need any clarification please ask me. Thanks.
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xxxxxx xxx the attachment for solution. xx you need any xxxxxxxxxxxxx xxxxxx ask xxx Thanks.
file1.doc preview (689 words)
1. Thermostats are xxxxxxxxx to xxxxxxxx testing before they are shipped xx xxx xxxxxxxxxxxx xxxxxxxxxxx xxxxxx xxx xxxxxx Results xxxx xxx last xxxx xxxxxxx xxx shown xx the table. Draw and x xxxxx and xx xxxxx chart. xxxxx on xxx charts, is the xxxxxxx under xxxxxxxx (20 xxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  
xxxxxx  x  x  3  4  5 
1  xxxx  70.8  xxxx  73.6  71.0 
2  71.3  71.0  xxxx  xxxx  72.2 
x  70.0  72.6  71.9  xxxx  xxxx 
4  xxxx  xxxx  xxxx  74.2  xxxx 
5  70.8  70.7  xxxx  xxxx  xxxx 
The mean xxx xxxxx xxx each sample is xxxxxxxx xx xxx following table
xxxxxxxxxxxxxxxxxxxxxxxxxx
 Observations 

 
xxxxxx  1  x  x  4  5  xxxxx  x 
1  xxxx  xxxx  72.2  xxxx  xx  xxxxx  xxx 
x  xxxx  71  xxxx  72.7  xxxx  xxxxx  xxx 
3  70  72.6  71.9  72.4  xxxx  xxxxx  3.3 
4  xxxx  xxxx  xxxx  xxxx  xxxx  xxxxx  3.9 
5  70.8  70.7  xxxx  73.5  71.1  71.36  2.8 
xxxxxxx  71.928  2.98 
From xxx given data,
x xxxxxxx
xx 2.98
xxxxx xxx subgroup size, n x 5, = xxxxxx = xx = xxxxxx
Control Limits for Rchart:
xxx = = xxxx
UCL x xxxxxx EMBED Equation.3 = (2.114)(2.98) x xxxxxx
LCL = �� xxxxx xxxxxxxxxx x xxxxxxxxx x x
Control limits xxx xxxxx xxxxxxx
CL x = xxxxxx
xxxx x x �� xxxxx Equation.3 = xxxxxx + (0.577)(2.98) = 73.6475
xxxx = – �� EMBED
   more text follows   
file2.xls preview (212 words)
ChartDataSheet_
xxxxxxxxxxxxxxxxxxxxxxxxxxxThis worksheet contains values xxxxxxxx xxx xxxxxxxx xxxxxxx  
xxxx xxxx xxxx  
xxxxx  70.20854  xxxxxx  xxxxxxxx  
xxxxx  70.20854  xxxxxx  73.64746  
72.04  xxxxxxxx  71.928  xxxxxxxx  
71.96  xxxxxxxx  xxxxxx  73.64746  
71.36  70.20854  71.928  xxxxxxxx  xxxxxxxx  71.928  73.64746 
xxxx Plot data xxxxxxxxx 6:30.48.000  
2.8  x  2.98  6.29972  
2.1  0  2.98  6.29972  
3.3  0  2.98  xxxxxxx  
3.9  x  2.98  6.29972  
xxx  x  2.98  6.29972  x  xxxx  xxxxxxx 
xxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  
xxxxxx  1  2  3  x  x  xxxxx  R 
1  xxxx  xxxx  xxxx  xxxx  71  72.22  xxx 
x  xxxx  xx  73.1  xxxx  72.2  72.06  2.1 
x  xx  xxxx  71.9  xxxx  73.3  72.04  xxx 
x  xxxx  xxxx  xxxx  xxxx  73.6  71.96  xxx 
x  70.8  70.7  70.7  xxxx  71.1  71.36  xxx 
xxxxxxx  71.928  xxxx  
Since the xxxxxxx size, x = xx  xx =  xxxxx  xx x  0  xx =  xxxxx  
Control limits for x xxxxxx  
CL =  2.98  
xxxx  x  
xxxx  xxxxxx  
xxxxxxx xxxxxx xxx xxxxx xxxxxx  
CL =  xxxxxx  
xxxx  xxxxxxx  
xxxx  xxxxxxx  
xxxx all the xxxxxx xxx within the xxxxxxx xxxxxxx xx xxx xxxxxxx xx in control. 
Output
xxxxxxxxxxxxxxxxxQuality Control xxxxxxx xxxxxx  
xxxxxx size  x  
xxxxxx of xxxxxxx  x  
xxxx  xxxxx  
Upper Control Limit, xxx  xxxxxxx  xxxxxx 
Center  xxxxxxx  xxxxxx 
xxxxx xxxxxxx Limit,    more text follows    
Try it before you buy it 