it all comes out in the washers
DESCRIPTION
It All Comes Out In the Washers. PhET Interactive Simulations University of Colorado http://phet.colorado.edu. It All Comes Out in the Washers. Created by Brian Domroes. We will learn about…. Mathematics in Engineering. We will learn about…. Normal Distributions. - PowerPoint PPT PresentationTRANSCRIPT
It All Comes OutIn the Washers
PhET Interactive SimulationsUniversity of Coloradohttp://phet.colorado.edu
Created byBrian Domroes
It All Comes Out in the Washers
We will learn about…• Mathematics in Engineering
We will learn about…• Normal Distributions
http://encefalus.com/philosophical/logic/
http://encefalus.com/philosophical/logic/
We will learn about…• Standard Deviation
http://encefalus.com/philosophical/logic/
We will learn about…• Z scores
Model Search• Ideal Height is 5’9”
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Ideal and Limits5’6”
6’
5’9”
Women’s Height
1 standard deviation below
64.4” – 2.4” = 62”
34% 62” – 64.4”
http://encefalus.com/philosophical/logic/http://encefalus.com/philosophical/logic/
Random Sample
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Women’s Height
Standard Deviation 2.4”
Mean is 64.4”
Good Fit?
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Women’s Height
Standard Deviation 2.4”
Mean is 64.4”5’6”
6’
5’9”
Where Should I Look?• 3 different groups–Your class–Group A–Group B
Height Data
Recording Data
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Did our data look like this?
XX XX
X XX XX
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XXX
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X
Results – 100 Trials
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Results – 500 Trials
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Results – 10,000 Trials
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5’6”
6’
5’9”Mean 70.7”Median 70”Standard Deviation 3.16”
Does Group A fit criteria?
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5’6”
6’
5’9”Mean 67.8”Median 68”Standard Deviation 2.91”
Does Group B fit criteria?
Combined Samples
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D 1 SwimmersD 1 Basketball
Both
Standard Deviation 2.91”Mean 67.8”
Standard Deviation 3.16”Mean 70.7”
5’6”
6’
5’9”
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Standard Deviation Ordering
A B
C
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Answer
Which is which?
The swimmers must be…..hmm?
Standard Deviation 2.91”Mean 67.8”
Standard Deviation 3.16”Mean 70.7”
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And the answer is..Standard Deviation 2.91”Mean 67.8”
Standard Deviation 3.16”Mean 70.7”
D 1 Swimmers D 1 Basketball
Z scores• Shows % within limits
Determining Percent
http://encefalus.com/philosophical/logic/
Z Score Calculations
What % fits height limits?
Standard Deviation 2.91”
Mean is 67.8”
Lower height limit 66”
Upper height limit 72”
Swimmer Data
5 a)
What % fits height limits?
Standard Deviation 2.91”
Mean is 67.8”
Lower height limit 66”
Upper height limit 72”
Swimmer Data
5 b)
65.7% of Swimmers
72 “66 “
z = -.619 z = 1.443
What % fits data?
Standard Deviation 3.16”
Mean is 70.7”
Lower height limit 66”
Upper height limit 72”
Basketball Data
59.1% of Basketball
72 “66 “
z = -1.487 z = .411
More Swimmers in Limits
65.7% 59.1%
Division 1 Swimmers Division 1 Basketball
Manufacturing
Presence of Error• Human• Random
http://encefalus.com/philosophical/logic/
Manufacturing
Voice of the Process
Mean
6
http://encefalus.com/philosophical/logic/
Customer’s Needs
Voice of Customer
Lower specification
limit
7
Upperspecification
limit
Washer Activity
Responsibilities Set 1• Weighing Washers
Responsibilities Set 2• Arranging Washers
Responsibilities Set 3• Input Data
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Observations
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200 Fastenal Washers
3.75 - 3.85 3.86 - 3.96 3.97 - 4.07 4.08 - 4.18 4.19 - 4.29 4.30 - 4.40 4.41 - 4.51 More0
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Fastenal Washers per Weight
3.753.78
3.813.84
3.87 3.93.93
3.963.99
4.024.05
4.084.11
4.144.17 4.2
4.234.26
4.294.32
4.354.38
4.414.44
4.47 4.50
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200 Sales Washers
5.87 - 5.92 5.93 - 5.98 5.99 - 6.04 6.05 - 6.1 6.11 - 6.16 6.17 - 6.22 6.23 - 6.28 More0
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Sales Washers per Weight
5.875.89
5.915.93
5.955.97
5.996.01
6.036.05
6.076.09
6.116.13
6.156.17
6.196.21
6.236.25
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Comparing Standard Deviation
10
5 grams 6 grams
Fastenal Washers Sales Washers
Comparing Your Data
Fastenal WashersMean 4.278
Standard Deviation .096
Sales WashersMean 6.124
Standard Deviation .071
Voice of the Process
Fastenal Washers
Sales Washers
Business Proposals• Pretend that you are the washer manufactures
BMW and Lowes
How many washers?• Weight – 6.08 g to 6.18 g
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What Sales is capable of making
Z scores• What percent is good?
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Determining Percent
http://encefalus.com/philosophical/logic/
Z Score Calculations
Z Score Calculations
Round to the nearest thousandth
BMW Z score Lower Limit
= 6.08 – 6.124.071
≈ -.6201
BMW Z score Upper Limit
= 6.18 – 6.124.071
≈ .7892
BMW Probability• 51.7% washers in range
z ≈ -.620 Z ≈ .789a.
Lowe’s Z Score Calculation
Lowe’s Z score Lower Limit
= 4.20 – 4.278.096
≈ -.8131
Lowe’s Z score Upper Limit
= 4.41 – 4.278.096
≈ 1.3752
Lowe’s Probability• 70.7% washers in range
z ≈ -.813 z ≈ 1.375a.
Top Quality
Cost/Benefit Analysis
