Variation and Quality (2.008x Lecture Slides)

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Variation and Quality
MIT 2.008x
Prof. John Hart
Prof. Sanjay Sarma

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Quality: the relentless pursuit of perfection
Lexus, 1992: https://www.youtube.com/watch?v=AktHnnA9QIM

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Quality
Variation
Tolerance

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Quality: Conformity to
requirements or specifications.
In other words, the ability of a
product or service to consistently
meet customer needs.
Variation: A change in outcome
of a process.
Tolerance: Permissible limit of
variation of a process.

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What are the measures of
Lego quality?
Drawing from Clipstone, C. J., Hahn, S., Sonnenberg, N., White, C., and Zhuk,
A., 2004, “Razor blade technology.”
Blade edge:
https://scienceofsharp.files.wordpress.com/2014/05/astra_stainless_x_05.jpg
and for Gillette razors?

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Car body measurement using a CMM (Nikon)
Excerpt from: https://www.youtube.com/watch?v=A5zXdSv60Ag

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Car body build variation: production launch
Figure 4 from Ceglarek D, Shi J. "Dimensional Variation Reduction forAutomotive Body Assembly."
Manufacturing Review Vol. 8, No. 2, 1995:139-154.
2 mm body project: http://www.atp.nist.gov/eao/gcr-709.htm
6 standard deviations from the mean: 3.4 defects per million!

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Car body assembly hierarchy
Figure 5 from Ceglarek D, Shi J. "Dimensional Variation Reduction forAutomotive Body Assembly."
Manufacturing Review Vol. 8, No. 2, 1995:139-154.

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What do we need to
know?
§ What the customer wants (i.e.
what is ‘good quality’) and how
to relate this to our
specifications.
§ How to quantify variation
(statistically).
§ What causes process variation,
and how to minimize variation
as needed.
§ How to monitor variation and
maintain process control.

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Agenda: Variation and
Quality
§ The normal distribution
§ Error stackup and simple fits
§ The lognormal distribution
§ Process sensitivity
§ Principles of measurement
§ Statistical process control
§ Conclusion

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Variation and Quality:
2. The Normal
Distribution

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Measured variation:
hex nuts
Mean = 5.58 mm
Stdev = 0.033
Frequency
Hex nut thickness [mm]

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Hex nut thickness:
observations
§ What do we learn from the
distribution of values?
§ Would the values be different
if we measure freehand
versus on the bolt?
Why/not?
§ What is the meaning of the
variation we measured?

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The normal distribution
Figure 36.3b, Kalpkjian and Schmid, Manufacturing Engineering and Technology
n → ∞
The histogram of x with n samples approaches the normal
distribution as
Denoted by
: mean (à shift)
: standard deviation (à flatness)
sometimes denoted s; e.g., 2s
= 2 standard deviations
2
2
( )
21
( )
2
x
x x
x
f x e σ
πσ
−
−
=
x
xσ
x ∈ N x,σx( )
σx
=
1
N
xi
− x( )
2
i=1
N
∑

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Normal probability density function (PDF)
f (x) =
1
2π s
⋅e
−
x−x( )
2
2s2
#
$
%
%
&
'
(
(
From https://en.wikipedia.org/wiki/Normal_distribution (public domain)

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Cumulative distribution function (CDF)
( )
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡ ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ −
− 2
2
2
2
1 s
xx
e
sπ
From https://en.wikipedia.org/wiki/Normal_distribution (public domain)

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Probability: { }
{ } 1)(
)(
==∞≤≤∞−
=≤≤
∫
∫
∞
∞−
dxxfxP
dxxfbxaP
b
a
Normalized to “Z-scores”
{ } ∫
−
=≤≤
−
=
2
1
2
2
21
2
1
z
z
dz
z
ezzzP
s
xx
z
π
b
z
P
x
f(x)
a
0
f (x) =
1
2π s
⋅e
−
x−x( )
2
2s2
#
$
%
%
&
'
(
(

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Z-scores
z =
x − x
s
Z 0 0.02 0.04 0.06 0.08
-3 0.0013 0.0013 0.0012 0.0011 0.0010
-2.5 0.0062 0.0059 0.0055 0.0052 0.0049
-2 0.0228 0.0217 0.0207 0.0197 0.0188
-1.5 0.0668 0.0643 0.0618 0.0594 0.0571
-1 0.1587 0.1539 0.1492 0.1446 0.1401
-0.5 0.3085 0.3015 0.2946 0.2877 0.2810
0 0.5000 0.5080 0.5160 0.5239 0.5319
0z
P

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Z-scores
z =
x − x
s
0z
P
Z 0 0.02 0.04 0.06 0.08
0 0.5000 0.5080 0.5160 0.5239 0.5319
0.5 0.6915 0.6985 0.7054 0.7123 0.7190
1 0.8413 0.8461 0.8508 0.8554 0.8599
1.5 0.9332 0.9357 0.9382 0.9406 0.9429
2 0.9772 0.9783 0.9793 0.9803 0.9812
2.5 0.9938 0.9941 0.9945 0.9948 0.9951
3 0.9987 0.9987 0.9988 0.9989 0.9990

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Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990

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Example: manipulating the normal
distribution
Car tires have a lifetime that can be
modeled using a normal distribution with a
mean of 80,000 km and a standard
deviation of 4,000 km.
à What fraction of tires can be expected
to wear out within ±4,000 miles of the
average?

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Solution: how many wear out between 76,000
and 84,000 miles?
à Area under the curve between these points
z(1) – z(-1) = 0.8413 – 0.1587 = 0.6826
= 68% will wear out
0.8413
0.1587
+1.00-1.00
0.6826

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Example: manipulating the normal
distribution
Car tires have a lifetime that can be
modeled using a normal distribution with a
mean of 80,000 km and a standard
deviation of 4,000 km.
à What fraction of tires can be expected
to wear out within ±4,000 miles of the
average?
à 68% will wear out
à What fraction of tires will wear out
between 70,000 km and 90,000 km?

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Solution: failures within 70,000-90,000 miles
à % of tires that will wear out =
z(2.5) – z(-2.5) = 0.9938 – 0.0062 = .9876
à 98%
0.99380.0062
0 +2.5-2.5
0.9876

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3. Error stackup and
simple fits

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Measured variation: hex nuts
Single hex nut
Stack of two hex nuts
Mean = 5.58 mm
Stdev = 0.033
Mean = 11.15 mm
Stdev = 0.049
Stack thickness [mm]
Hex nut thickness [mm]

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Modeling ‘stackup’: superposition of random
variables
Proof: http://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables
1 2y x x= ±
1 2y x x= ±
1 2
2 2
y x xσ σ σ= +
( )σ,1 xNx ∈ ( )σ,yNy∈
( )σ,2 xNx ∈
1 2 3 n
In general, if we define a new random variable
y = c1x1 + c2x2 + c3x3 + c4x4 + …
• ci are constants
• xi are independent random variables
It can be shown that: µy = c1µ1 + c2µ2 + c3µ3 + c4µ4 + ...
σy
2 = c1
2σ1
2 + c2
2σ2
2 + c3
2σ3
2 + c4
2σ4
2

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What is the the probability of a successful
assembly?
c = D − d
The new critical dimension
is the clearance (c):
c = D − d
σc
= σD
2
+σd
2
The distribution of
clearances is defined by: DD t±
dd t±

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ANSI hole-shaft fit classification

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4. The lognormal
distribution

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Lognormal distribution
à The logarithm of x is distributed normally
From http://en.wikipedia.org/wiki/Log-normal_distribution (public domain)
Probability density function (PDF)
Example: size distribution of particles in a powder, size distribution of
grains within a metal
N(ln x;µ,σ ) =
1
xσ 2π
e
−
(ln x−µ)2
2σ 2
µ = ln
m
1+ v / m2
!
"
##
$
%
&& σ = ln 1+ v / m2
( )
m, v = mean and variance of raw data
Cumulative distribution function (CDF)

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Lognormal distribution: metal powder for 3D printing
GE fuel nozzle: http://www.gereports.com/post/116402870270/the-faa-cleared-the-first-3d-printed-part-to-fly/
SEM image: http://advancedpowders.com/our-plasma-atomized-powders/products/ti-6al-4v-titanium-alloy-powder/#15-45_m
Ti6Al4V
Specification: 15-45 um
Selective Laser Melting (SLM)

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5. Process sensitivity

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How hex nuts are made
Excerpt from: https://www.youtube.com/watch?v=MR6q_nXH2IQ

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What can cause
process variation?
§ The process: inherent capability;
change of settings.
§ Material: raw material variation,
defects.
§ Equipment: tool wear, equipment
needs maintenance/calibration
§ Operator: procedure, fatigue,
distraction, etc.
§ Environment: temperature,
humidity, vibration, etc.
§ Measurement: Capability of
measurement tool; change of
performance (à calibration needed)
§ …

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Climb milling (first cut) versus
conventional milling (second cut)
6061-T6 Aluminum with ¼”
endmill
Spindle Speed: 4000 rpm
Feed: 20.0 in/min
Depth of cut: 0.400”
Width of cut: 0.070”

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Example: climb versus conventional milling
Expected width of material .610”
Conventional cut width (red):
Top edge .609”, Bottom of cut .611”
Climb cut width (green):
Top edge .612”, Bottom of cut .619”
Conventional
§ Chip from thin à thick
§ Lower forces but rougher
surface
Climb
§ Chip from thick à thin
§ Higher forces but
smoother surface

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Heat
Force
Reference
frame
The ‘structural loop’
The machine, tool, and workpiece are flexible
Tool
Error
Work

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Injection molding
process window
à We also must understand the
sensitivities to process variables within the
window.

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Injection molding: varying process parameters
Note the mean shifts compared to the variation
40.60
40.65
40.70
40.75
40.80
40.85
40.90
40.95
41.00
0 10 20 30 40 50 60
WidthofPart(mm)
Number of Run
Run Chart for Injection Molded Part
Width (mm)
Average
Holding Time = 5 sec
Injection Press = 40%
Part%radius%[mm]
Run%number
Hold = 5 sec
Pressure = 40% of max
Hold = 5 sec
P = 40% max
Hold = 10 sec
P = 40% max
Hold = 5 sec
P = 60% max
Hold = 5 sec
P = 40% max

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à Systematic (“special cause”)
variation: influences of process
parameters or external
disturbances that can be isolated
and possibly predicted or removed.
à Random (“common cause”)
variation: caused by uncontrollable
factors that result in a steady but
random distribution of output
around the average of the data. In
other words, this is the ‘noise’ of
the system.

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A general model of process variation
Process
Input (u) Output (Y)
Disturbances, such as:
§ Equipment performance changes
§ Material property changes
§ Temperature fluctuations
Control inputs (process
parameter settings)
Sensitivity
Disturbance (α)
ΔY =
∂Y
∂α
Δα +
∂Y
∂u
Δu

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Some example sensitivities
(if all other parameters are held constant)
Injection molding
§ Relationship between molecular weight of polymer
(determines viscosity) and accuracy (final part
dimension compared to mold)
§ Relationship between injection pressure and accuracy
Machining
§ Relationship between depth of cut and surface
roughness (= spatial frequency of tool marks)
§ Relationship between tool life (sharpness) and accuracy
(= workpiece deformation via higher force and
temperature rise)

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All together, this determines the amount of variation, and thus
a reasonable tolerance that can be specified!
When the process is ‘under control’:
If tolerances are too tight:
§ Extra cost (slower rate)
§ More process steps (e.g.
finishing)
§ Lots of scrap (rejects)
§ Manufacturer “no quote”
(unreasonable expectations)
ΔY =
∂Y
∂α
Δα +
∂Y
∂u
Δu
Figure 13.30 from Ashby, Material Selection in Mechanical Design

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6. Principles of
measurement

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à Where must the
Resolution be on
this chart?
True (exact) value
Repeatability
Accuracy
Probabilitydensity

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Accuracy = “the ability to tell the truth”
à Difference between the measured and true value
Repeatability = “the ability to tell the same story many times”
à Difference between consecutive measurements intended to be
identical
Resolution = “the ability to tell the difference”
à Minimum increment that can be measured
A. Slocum, Precision Machine Design

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A. Slocum, Precision Machine Design

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Mitutoyo high performance micrometer
§ A highly rigid frame and high-performance constant-force
(7-9 N) mechanism enable more stable measurement*
*Patent pending in Japan, the United States of America, the European Union, and
China.
§ Body heat transferred to the instrument is reduced by a
(removable) heat shield, minimizing the error caused by
thermal expansion of the frame when performing
handheld measurements.
http://ecatalog.mitutoyo.com/MDH-Micrometer-High-Accuracy-Sub-Micron-Digimatic-Micrometer-C1816.aspx
Range = 0-25 mm
Resolution = 0.0001 mm (0.1 micron)
Accuracy = 0.0005 mm (0.1 micron)
Flatness: 0.3 micron (across ‘jaws’)
Parallelism: 0.6 micron

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Machine vision (Keyence)
Photos taken at IMTS 2014

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Robot-mounted 3D scanner (Creaform)
“70 micron accuracy over the “size of a pickup truck” à correcting for low
robot accuracy by imaging dots on the sphere
At IMTS 2014

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7. Statistical Process
Control

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Monitoring a process: CONTROL CHARTS
invented by Walter A. Shewhart (Bell Labs, 1920’s)
§ Needed to improve reliability of telephone transmission systems
§ Stressed the need to eliminate all but “common cause” variation, and
minimize this variation
à “a process under surveillance by periodic sampling maintains a constant
level of variability over time”
0.990
0.995
1.000
1.005
1.010
0 10 20 30 40 50 60 70 80 90 100
Run number
Average(of10samples)Diameter
Upper control limit
Lower control limit
Step disturbance
66.3%
95.5%
99.7%

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OPERATION CHARACTERISTIC DATES
MACHINE SAMPLE SIZE SAMPLE FREQUENCY REMARKS
ACTION
INSTRUCTIONS
1.
2.
3.
4.
5.
6.
NOTES:
X
AVERAGESORINDIVIDUALS
R
RANGES/STD.DEV.
DATE OR TIME
INDIVIDUAL
READINGS
1
2
3
4
5
SUM
X
R
S
BASE PREDEPOSITION SHEET RESISTANCE 2/80 - 2/24, 1988
FCE #5 4 EVERY 5th LOT NOTE UNUSUAL OCCURANCES
40
35
30
25
20
15
15
10
5
2/8 2/8 2/9 2/9 2/10 2/10 2/11 2/11 2/11 2/12 2/12 2/15 2/16 2/16 2/17 2/17 2/18 2/18 2/19 2/22 2/22 2/23 2/24 2/242/9
32 28 31 32 34 33 30 33 35 39 37 33 34 29 32 30 34 33 29 30 29 28 30 2929
27 25 29 26 32 26 27 29 31 32 31 27 26 25 27 25 27 28 27 28 20 26 23 3122
27 29 27 25 29 25 25 31 26 30 35 28 30 22 24 22 25 26 27 26 22 25 25 2622
34 30 25 30 28 33 23 27 27 34 30 25 31 25 26 20 28 25 27 25 25 24 26 2527
120 112 112 113 123 117 105 120 119 135 133 113 121 101 109 97 114 112 110 109 96 103 104 111100
30 28 28 28.3 30.8 29.3 26.3 30 29.8 33.8 33.3 28.3 30.3 25.3 27.3 24.3 28.5 28 27.5 27.3 24 25.8 26 27.825
7 5 6 7 6 8 7 6 9 9 7 8 8 7 8 10 9 8 2 5 9 7 7 65
LOW ON SOURCE -
MORE ADDED*
UCL
X
= 33.16
LCL
X
= 23.08
X
UCL
R
= 15.97
R
* *

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What might be going on here?
à “a process under surveillance by periodic
sampling maintains a constant level of
variability over time”
UCL
CL
LCL
0 10 20 30 40 50
57
60
63UCL
CL
LCL
0 10 20 30 40 50
5.0
5.6
6.2
? ?

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Basic types of control charts
Average chart: plot of mean values
of each sample , centered around
the grand average (mean of all
samples)
Range chart: plot of range of each
sample (max - min), centered
around the average range.
à Why do we need both charts?
Figure 36.5 from "Manufacturing Engineering & Technology (7th Edition)" by Kalpakjian,
Schmid. (c) Upper Saddle River; Pearson Publishing (2014).
Control charts are constructed from measurements of samples (each with n parts)
from the population (N, all parts manufactured).

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Reveals shift
Process mean is
shifting upward
Does not reveal
shift
When the mean shifts:
Sampling
Distribution
x-Chart
R-chart
UCL
LCL
UCL
LCL

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Does not reveal
increase
Process variability
is increasing
Reveals increase
When the mean shifts:
Sampling
Distribution
x-Chart
R-chart
UCL
LCL
UCL
LCL

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How do we choose the sample size (n) and frequency
of sampling?
§ Likelihood of unexpected disturbances
§ Importance (cost) of defects
§ Cost of measurement
àTypically based on experience and knowledge of the above
(sometimes trial and error)
How do we define the control limits (LCL, UCL)?
§ Based on pre-tabulated statistics of sample variation versus
sample size

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Calculating the control limits
Average chart
Grand average:
Control limits:
Range chart
Average range:
Control limits:
Figure 36.5 from "Manufacturing Engineering & Technology (7th Edition)" by Kalpakjian,
Schmid. (c) Upper Saddle River; Pearson Publishing (2014).
LCL = X − A2
R
UCL = X + A2
R
LCL = D3
R
UCL = D4
R
R =
Ri
i=1
N
∑
N
X =
X i
i=1
N
∑
N

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Factors for calculating control limits
à These constants are for a 3-sigma approach, i.e., control limits are
placed at +/- 3 standard deviations from the estimated process mean
Table 36.2 from "Manufacturing Engineering & Technology (7th Edition)" by
Kalpakjian, Schmid. (c) Upper Saddle River; Pearson Publishing (2014).
Average chart
Grand average:
Control limits:
Range chart
Average range:
Control limits:
LCL = X − A2
R
UCL = X + A2
R
LCL = D3
R
UCL = D4
R
R =
Ri
i=1
N
∑
N
X =
X i
i=1
N
∑
N

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Process control vs. capability
à Even if a process is in control (i.e., constant mean and variation), it
may not be capable (i.e., giving what we want as set by the
specifications a.k.a. the tolerances)
Upper control limit
(UCL)
Lower control limit
(LCL)
In Control and Capable
(Variation from common cause reduced)
In Control but not Capable
(Variation from common causes excessive)
Lower specification
limit(LSL) Upper specification
limit(USL)

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Control limits vs. tolerances (specification
limits)
Control limits are:
§ Based on process mean and variability.
§ Dependent on the sampling parameters.
à Thus, control limits are a characteristic of the process
and measurement method.
Tolerances (specification limits) are:
§ Based on functional considerations.
§ Used to establish a part’s conformability to the design
intent.
à Thus, we must have a formal method of comparison.

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Process capability: compares process
variation to tolerances
use whichever is smaller,
because à
Cp
=
USL− LSL
6σx
Cpk
=
USL−µx
3σx
Cpk
=
µx
− LSL
3σx
or
General rule: Cp should be at least 1.33
LSL, USL = tolerance limits
σx = process stdev
LSL USL
LSL USL
9.80 10.00 10.05 10.20 (mm)
Design
Intent
True process

2.008x
0.990
0.995
1.000
1.005
1.010
0 10 20 30 40 50 60 70 80 90 100
Run number
Average(of10samples)Diameter
Example: calculating Cp, Cpk
Assume:
µx = 1.000”
σx = 0.001”
Specification = 0.999” +/- 0.005”
Upper control limit
Lower control limit
Step disturbance
66.3%
95.5%
99.7%

2.008x
Recommended values of process capability
à How do we really judge what’s good enough?
Knowledge of the ‘cost’ of defects in our product, thereby
defining a ‘quality loss function’ (beyond scope today).
Recommended process
capability for two-sided
specifications
Defects (parts out of
spec) per million
operations
Existing (stable) process 1.33 63
New process 1.50 8
Existing process, safety-
critical
1.50 8
New process, safety-critical 1.67 1
Six-sigma quality 2.00 0.002

2.008x
8. Conclusion

2.008x
The big picture
‘Pilot’ production
This is a control chart
Design for
Manufacturing (DFM)
$$
Does not
conform
Conforms
(good!)
Change design?
Modify process
(know what to do)

2.008x
Embracing the variation: Apple
Excerpt from: https://youtu.be/7cIRpmgYBJw?t=274

2.008x
Embracing the variation: Intel
§ The speed of each processor made is
measured, and this sets the specification
and price
§ As production improves, faster processors
are released for sale
Image © Intel Corporation 2016 http://www.intel.com/content/www/us/en/embedded/products/bay-trail/atom-processor-e3800-platform-brief.html
http://ark.intel.com/compare/78416,80270,80269,80268
Product Name
Intel® Atom™
Processor Z3740D
(2M Cache, up to
1.83 GHz)
Intel® Atom™
Processor Z3745
(2M Cache, up to
1.86 GHz)
Intel® Atom™
Processor Z3775D
(2M Cache, up to
2.41 GHz)
Intel® Atom™
Processor Z3775
(2M Cache, up to
2.39 GHz)
Performance
# of Cores 4 4 4 4
# of Threads 4 4 4 4
Processor Base
Frequency
1.33 GHz 1.33 GHz 1.49 GHz 1.46 GHz
Burst Frequency 1.83 GHz 1.86 GHz 2.41 GHz 2.39 GHz
Scenario Design
Power (SDP)
2.2 W 2 W 2.2 W 2 W

2.008x
Reflection: learning objectives
§ Recognize how process tolerances are defined and
variation is monitored, and how a manufacturing process
is established to control variation.
§ Be fluent with manipulation of normally distributed
dimensions, combinations of dimensions (e.g., to predict
fits, lifetimes, etc.).
§ Understand how process physics influence statistical
outcomes (e.g., mean, variation). What are the sensitive
parameters, and how can the variation be addressed?
§ Understand accuracy, repeatability, resolution; assess
the suitability of a measurement technique to monitor a
process.
§ Know how to construct and interpret control charts and
evaluate process capability.

2.008x
References
1 Introduction
iPhone with a cracked screen, photo by User: Philipp Zurawski (Freetagger) - Pixabay
CC0. This work is in the public domain.
Lexus Commercial Video by Anthony Slanda on YouTube. © Lexus, a Division of Toyota
Motor Sales, U.S.A., Inc
LEGO brick assembly, photo by User: M W (Efraimstochter) - Pixabay CC0. This work is
in the public domain.
Gillette razor blade section, Figure 1 from "Razor blade technology US6684513 B1" by
Clipstone, et al. (2004). This work is in the public domain.
Car body inspection using a Nikon coordinate measurement machine, video © 2016
Nikon Metrology, Inc.
Dimensional Variation Reduction for Automotive Body Assembly: Figure 4 by Ceglarek
and Shi; Manufacturing Reivew 8 (2), June 1995, pp 139-154. (c) 1995 American Society
of Mechanical Engineers.
Hierarchical groups for fault tracking: Figure 5 by Ceglarek and Shi; Manufacturing
Reivew 8 (2), June 1995, pp 139-154. (c) 1995 American Society of Mechanical
Engineers.

2.008x
References
2 Normal Distribution
Normal distribution: Figure 36.3b in "Manufacturing Engineering & Technology (7th
Edition)" by Kalpakjian, Schmid. (c) Upper Saddle River; Pearson Publishing (2014).
Normal probability distribution function, image by User: Inductiveload via wikimedia. This
work is in the public domain.
Cumulative distribution function, Image by User: Inductiveload via wikimedia. This work is
in the public domain.
Automobile tire, photo by User: Robert Balog (Bergadder) - Pixabay CC0. This work is in
the public domain.
3 Variation Stackup
ANSI hole-shaft fit classification, image © International Organization for Standardization
(ISO)

2.008x
References
4 Lognormal Distribution
Log-normal probability distribution function, image by User: Krishnavedala via wikipedia -
CC0. This work is in the public domain.
General Electric aircraft engine fuel nozzle, image © 2016 General Electric
Particle size distribution for Ti-6Al-4V powder stock of various size ranges from Advanced
Powders and Coatings (APC), figure 5 from Title: Raymor AP&C: Leading the way with
plasma atomised Ti spherical powders for MIM; Journal: Powder Injection Moulding
International; Vol: 5; No: 4; December 2011; pages: 55-57. © Inovar Communications Ltd
5 Sensitivity
Hex nut production: "How It's Made" Video on YouTube Copyright © 2016 Discovery
Conventional vs. climb milling: Figure 24.3 in "Manufacturing Engineering & Technology
(7th Edition)" by Kalpakjian, Schmid. (c) Upper Saddle River; Pearson Publishing (2014).

2.008x
References
Normal distribution: Figure 36.3b in "Manufacturing Engineering & Technology (7th
Edition)" by Kalpakjian, Schmid. (c) Upper Saddle River; Pearson Publishing (2014).
Process tolerance charts: Figure 36.3b in "Materials Selection in Mechanical Design (4th
Edition)" by Ashby, Copyright © 2013 Elsevier Inc. All rights reserved.
6 Measurement
Accuracy, resolution and repeatability: Figure 2.1.1 in "Precision Machine Design" by
Alexander H. Slocum; Publisher: Prentice Hall; Year: 1992; ISBN: 0136909183. (c)
Prentice Hall 1992.
ESPN Monday Night Football, ESPN broadcast footage (c) Disney Corporation.
Digital micrometer, image Copyright © 2016 Mitutoyo America Corporation. All rights
reserved.

2.008x
References
7 SPC
Control charts of averages and ranges of sample measurements: Figure 36.5 from
"Manufacturing Engineering & Technology (7th Edition)," Kalpakjian, Schmid. (c) Upper
Saddle River; Pearson Publishing (2014).
Control charts of averages and ranges of sample measurements: Figure 36.5 from
"Manufacturing Engineering & Technology (7th Edition)," Kalpakjian, Schmid. (c) Upper
Saddle River; Pearson Publishing (2014).
Control limit equation constants as a function of sample size: Table 36.2
from"Manufacturing Engineering & Technology (7th Edition)," by Kalpakjian, Schmid. (c)
Upper Saddle River; Pearson Publishing (2014).
8 Conclusion
iPhone 5 optical part matching for optimal fit, image (c) Apple Inc.
Intel Atom processor, image © Intel Corporation

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