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Question
Submitted by Clay1203 on Fri, 2012-06-08 16:48
due on Fri, 2012-06-15 18:59
answered 2 time(s)
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Problem 1: R Chart and X-bar 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 x-bar chart. Based on the charts, is the process under control?

(See attachment for chart)

Attachments: 
Answer
Submitted by zext on Thu, 2012-06-14 13:41
teacher rated 73 times
4.90411
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price: $5.00

Answer rating (rated one time)

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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)

x-bar

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Observations
Sample1x 34 5 xxxxxxxxxxxxxx range(R)
x73.5 xxxxxxxxxxxx xx 72.22 xxx x72.22xxxxxx xxxxxxxxxxxxxxxxxx73.656399999999991
x xxxx 71 xxxxxxxx xxxx72.06 xxx x 72.06 xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
3 70 72.671.9 72.4xxxx72.04 3.3x72.039999999999992xxxxxxxxxxxxxxxxxxxxxxxx 73.656399999999991
xxxxx 70.6xxxx 74.2 73.671.96 xxx4 xxxxxxxxxxxxxxxxxx71.928 70.199600000000004 73.656399999999991
5xxxx 70.7 70.773.5 xxxxxxxxx 2.8 5 xxxxxxxxxxxxxxxxxxxxxxxx70.19960000000000473.656399999999991
averagesxxxxxxxx barxxxxx 71.927999999999997
x - bar chart xxxxxxx xxxxxx xxxxxxxxxxxxxxxxxx 2.9799999999999995
xxx x xxxxxxxx bar x xxx (R-bar)
xxx x xxxxxxxx xxx - A2*(R-bar)
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

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Sample12x x5xxxxxxxxxxxxxx range(R)
173.5xxxx xxxx 73.6 71 xxxxx 2.8 xxxx06.2877999999999998
xxxxx 71 73.172.772.272.06 xxx2.98x6.2877999999999998
x 70xxxx xxxxxxxxxxxx xxxxxxxxxxxx 0 xxxxxxxxxxxxxxxxxx
471.1xxxx 70.374.2 73.6 71.96 3.92.9806.2877999999999998
x xxxx xxxx 70.7 xxxx71.171.362.8 xxxx x6.2877999999999998
xxxxxxxx xxxxxxxx xxx xxxxx
xxxxxx2.9799999999999995
xxxxxxx control limits
xxx x xxxxxxxxxx
xxx x D3*(R-bar)
xxx x = 5, xx = 0 and xx = xxxx
hence,
UCL x 6.2877999999999998
xxxx0
this process is under control.

Sheet3


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Answer
Submitted by StatSolver on Mon, 2012-06-11 20:06
teacher rated 56 times
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Answer rating (rated one time)

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Please see the attachment for solution. If you need any clarification please ask me. Thanks.

body preview (15 words)

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

xxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxx

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 R-chart:

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_

xxxxxxxxxxxxxxxxxxxxxxxxxxx
This worksheet contains values xxxxxxxx xxx xxxxxxxx xxxxxxx
xxxx xxxx xxxx
xxxxx70.20854xxxxxx xxxxxxxx
xxxxx70.20854 xxxxxx73.64746
72.04xxxxxxxx 71.928xxxxxxxx
71.96 xxxxxxxxxxxxxx 73.64746
71.3670.2085471.928 xxxxxxxx xxxxxxxx71.928 73.64746
xxxx Plot data xxxxxxxxx 6:30.48.000
2.8 x 2.986.29972
2.1 0 2.986.29972
3.3 0 2.98xxxxxxx
3.9 x 2.986.29972
xxxx2.98 6.29972 xxxxxxxxxxxx

xxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxx
xxxxxx 123 xxxxxxx R
1 xxxx xxxxxxxxxxxx7172.22xxx
x xxxxxx 73.1xxxx72.2 72.062.1
xxxxxxx71.9xxxx 73.372.04xxx
xxxxxxxxxxxxx xxxx73.6 71.96xxx
x 70.870.7 70.7xxxx 71.171.36 xxx
xxxxxxx71.928 xxxx
Since the xxxxxxx size, x = xx xx = xxxxxxx x 0xx = 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

xxxxxxxxxxxxxxxxx
Quality Control xxxxxxx xxxxxx
xxxxxx size x
xxxxxx of xxxxxxxx
xxxx xxxxx
Upper Control Limit, xxxxxxxxxxxxxxxx
Centerxxxxxxx xxxxxx
xxxxx xxxxxxx Limit,

- - - more text follows - - -



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