Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
1
2
3
4
5
6
7
B C D
normal
distribution
99
100
101
102
103
A B C D
97 3.57E-03 3.57E-01
98 3.37E-03 3.37E-01
99 3.18E-03 3.18E-01
= 49.5
= 28.9
99
100
101
102
103
A B C D
=1+B98
=EXP( -0.5 *( (B99-B$102)
=C99*100
=1+B99
=EXP( -0.5 *( (B100-B$102
=C100*100
=1+B100
=EXP( -0.5 *( (B101-B$102
=C101*100
= =AVERAGE(B2:B101)
= =STDEVP(B2:B101)
Normal distribution
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
1.20E-02
1.40E-02
1.60E-02
112 23 34 45 56 67 78 89 100
x value
Frequency, %
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
Random numbers in range 0 – 99
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
1 9 17 25 33 41 49 57 65 73 81 89 97
x value
Random number
Normal distribution
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
1.20E-02
1.40E-02
1.60E-02
110 19 28 37 46 55 64 73 82 91 100
x value
Probility density
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
Method 1:
NORMDIS
N x, Cutoff Fraction <= x Number <= x
Case a) 300 123 23 140 =NORMDIST(E39, C39, D39, TRUE)
=B39*F39
Case b) 300 123 32.5 140 =NORMDIST(E40, C40, D40, TRUE)
=B40*F40
Case c) 300 123 41 140 =NORMDIST(E41, C41, D41, TRUE) =B41*F41
Method 2) Uses NORMSDIST (z)
See: http://www.exceluser.com/explore/statsnormal.htm
NORMSDIST(z)
NORMSDIST translates the number of standard deviations (z) into cumulative probabilities. It’s the unshaded area on the first chart.
To illustrate:
=NORMSDIST(-1) = 15.87%
Therefore, the probability of a value being within one standard deviation of the mean is the difference between these values, or 68.27%.
This range is represented by the shaded area of the second chart.
Method 2:
NORMSDIST
N x, Cutoff Z value
Fraction
<= x
Number
<= x
Case a) 300 123 23 140 0.739 0.770
231
Case b) 300 123 32.5 140 0.523 0.700
210
Case c) 300 123 41 140 0.415 0.661 198
Method 2:
NORMSDI
N x, Cutoff Z value Fraction <= x Number <= x
Case a) 300 123 23 140 = (E69-C69)/D69 =NORMSDIST(F69)
=B69*G69
Case b) 300 123 32.5 140 = (E70-C70)/D70 =NORMSDIST(F70)
=B70*G70
Case c) 300 123 41 140 = (E71-C71)/D71 =NORMSDIST(F71) =B71*G71
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
Only a rough sketch is all that is needed.
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
How: Cost of rejects increases with increasing
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
12-29. You are a new quality control engineer at a company that manufactures bottled drinking
water. All the bottles and the filling water are checked hourly to make sure that there are no
contaminants. Monday morning you notice that for some reason the water that was used to wash
the bottles before filling was not tested over the weekend. Now you have several carloads of
product ready to be shipped. What do you do?
a. Have the shipment destroyed and start filling them over again.
b. Test random samples for the shipment and if they pass send the shipment.
c. Tell your supervisor and let him or her decide what to do.
d. Since the wash water has never been contaminated in the past, do nothing and release the
shipment.
Use the Engineering Ethics Matrix.
1) In Engineering Ethics Matrix format:
Options
Canons
a) Destroy
and refill
b) Test
random
samples
c) Tell
supervisor
d) Do
nothing-
release
shipment
Hold
paramount the
safety, health
and welfare of
the public.
Meets canon
May not meet
canon unless
random
sampling has
been verified
as assuring
safety
Meets canon
Does not meet
canon
Perform
services only
in the area of
your
competence
Meets canon
May not meet
canon if you
are not the
company’s
safety
authority
Meets canon
Does not meet
canon
Issue public
statements
only in an
objective and
truthful
manner
Does not
apply
Does not
apply
Does not
apply
Does not
apply
Act for each
employer or
client as
faithful agents
Does not meet
canon unless
this is what
you have been
Does not meet
canon unless
this is what
you have been
Meets canon
Does not meet
canon
Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition
or trustees
instructed to
do
instructed to
do
Avoid
deceptive acts
Meets canon
May meet
canon if this is
policy
Meets canon
Does not meet
canon
Conduct
themselves
honorably …
Meets canon
May meet
canon
Meets canon
Does not meet
canon
Do c). Pass the buck – tell your supervisor (that’s what he is there for!)