manufacturing process performance - mitweb.mit.edu/2.810/www/files/lectures/lec4-process... ·...
TRANSCRIPT
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Manufacturing Process
Performance
2.810
T. GutowskiSee Refs and extra slides at end
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State of the Teams:
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Comparing Mfg Processes
Ref University Loughborough, UK
Conventional
casting
3D Printed
Two steps: comparing for same part, redesign for process
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Manufacturing process
performance attributes
• Cost* - direct costs, DFM
• Rate and Time* – process rate & system rate
• Quality/Variation – physics & statistics
• Energy*/ CO2 – processes & systems
*Assuming alternatives meet part performance requirements
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Manufacturing process
performance attributes
• Cost* - see Boothroyd et al handouts
• Rate and Time* – by process & for systems
Oct 31 Dr. Stan Gershwin
• Quality/Variation – Oct 3, Prof. Dave Hardt
• Energy*/ CO2 – Lecture 11/28
*Assuming alternatives meet part performance requirements
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Profit = Sales - Costs
Ostwald
Direct
costs: “touch”
labor, direct
materials
& tooling…
Indirect
costs: common
activities that
support many
products
Our focus: the cost to make a product
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Components of Direct Cost:
Direct Recurring Costs (Variable C = VN):
•Materials, including Buy to Fly, auxiliary…
•Labor, usually “touch”, but…
•Energy, usually small for parts
•Equipment (Prices as a “rental”)
Direct Non-recurring costs (Fixed C = F):
•Tooling, special equipment..
BMW
TRM tool
ORNL/
Cincinnati
BAAM
Machine
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Unit cost: C/N =F/N + V
Serial processes takelonger, larger variable costsSpecialty mat’l add to variablecosts
Parallel processes require tooling,larger fixed costs, but short cycle time
N*
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Estimate breakeven
N*
Waterjet
Extrusion
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Cost comparison; breakeven
part volume
Extrusion
• Fixed = extrusion die
• Variable =
(30grams/part)
• Material = aluminum
billet
• Labor = mostly set-up
• Machine = mostly set-
up, maintenance
Water jet
• Fixed = ???,
• Variable = (30g part, 90
secs/part)
• Materials = aluminum
bar, waste, abrasive
• Labor = some
monitoring needed
• Machine = includes
machine, financing,
installation, maintenance
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Aluminum Extrusion
• Extrusion die = $5,000
• Extrusion rate, less than 1 second to extrude one part
• Equipment rate ~ $40/hr
• Labor rate ~ $50/hr
• Materials billet aluminum,
some start up loss, kerf loss
• Setup/cleanup times dominates
Equip and Labor
• Sawing, post processing
• Cost = $5,000 + $0.40N
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Nest Parts for Waterjet, waste
~30%
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Waterjet cutting
• Variable Costs:
• Aluminum bar stock ~ $ 5/lb (~$10/kg)
• 30 gram part + waste = 40g/part = $0.40/ part
• Run time ~ 90 sec
• Abrasive ~ $0.30/part
• Machine cost (~$100k/5years/1shift (1000h/y)
+ maintenance) ~ $25/hr
• Labor cost ~ $35/hr
• Cost = $2.2N
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Estimated breakeven
N* ~ 3,000 parts
Breakeven cost $2.20/part
Waterjet
Extrusion
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Big Blue Saw quote
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Big Blue Saw quote
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Additive Mfg Vs Injection Mold
Ref. Cassandra Telenko et al
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Components of Indirect Cost:
Indirect Costs
•Support activities that can be charged “evenly” to all products
i.e. “overhead” includes things like; design, programming,
maintenance, quality control,purchasing, marketing, sales,
general and administrative expenses…
e.g.Composites parts
may require more
inspection than
metal parts
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Indirect costs..
• Become more important for higher
levels of automation,
• Become more difficult to allocate as the
number of products and variation grows.
• Use “Activity Based Costing” and other
tools
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Cincinnati MAXIM FMS Cell
(5) Machines
(24) Pallets
(3) Shifts
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System H; (2,000/35,000)
System 2;
(20/1,500)
System 3; (200/ 10,600)Part Types/ Total Produced
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Cost Models
• Time & Motion; F.W.Taylor, Ostwald, Polgar
• Machine Parameters: e.g. Mastercam
• DFM and DFA: Boothroyd, Dewhurst & Knight (Parametric
Models)
• Software -
• On-line– http://www.custompartnet.com/wu/die-casting
• Quotes- see for example, “Big Blue Saw” for water jet quotes, on-line metals…
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Pros & Cons of
Parametric Models
• Hint at the problem
• Become dated, and need
updating
Handouts for
1. Machining
2. Injection molding
3. Sheet Metal
4. Assembly
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Example: Time Estimation for
Manual Assembly• Handling
pick up
orient
• Insertion
location (obstructed view? Self locating?)
hold down and resistance
securing method
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Symmetry
Handling Issues
0 180 180 90 360 360
0 0 90 180 0 360
Size Fragile/Sharp
Nest/TangleSlippery/Flexible
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B-D Manual handling chart
Handling difficulties: nest, tangleslippery, sharp…
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Insertion Issues
Obstructed Access/View
Alignment
Insertion Force
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B-D Manual insertion chart
screws
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1 – screw(2) (steel) not easy to align
2 – cover(steel) not easy to align – assembly worker’s fingers must be used to align edges
3 – spring(steel) (closed ends) subject to continuous cycling and
must be spring steel
4 – piston stop(plastic) edge is chamfered for ease of alignment5 – piston(aluminum) obstructed
access for insertion of spindle into bottom of bore
6 – main block(plastic) depth of bore is 28mm with small through hole for piston spindle
Pneumatic Piston Sub-Assembly
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B-D Manual handling chart
piston
screws cover
spring
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B-D Manual insertion chart A
coverpiston
spring
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B-D Manual insertion chart B
screws
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Pneumatic Piston Sub-Assembly
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Boothroyd/Dewhurst Design Rules
1. Reduce part count and part types
2. Strive to eliminate adjustments
3. Design parts to be self-aligning and self-locating
4. Ensure adequate access and unrestricted vision
5. Ensure the ease of handling of parts from bulk
6. Minimize the need for reorientations during assembly
7. Design parts that cannot be installed incorrectly
8. Maximize part symmetry if possible or make parts obviously asymmetrical
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Rules to reduce part count
1. During operation of the product, does the part move relative to all other parts already assembled?
Only gross motion should be considered – small motions that can be accommodated by elastic hinges, for example, are not sufficient for a positive answer
2. Must the part be of a different material than or be isolated from all other parts already assembled?
Only fundamental reasons concerned with material properties are acceptable
3. Must the part be separate from all other parts already assembled because otherwise necessary assembly or disassembly of other separate parts would be impossible?
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1 – snap on cover and stop (plastic)
2 – spring(steel)
3 – piston (aluminum)
4 – main block (plastic)
Redesign: Pneumatic Piston Sub-Assembly
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Re-design
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Process Rate Limits
• Machining – limits on (MRR), large forces…
• Injection Molding – heat transfer
• Sheet metal forming – lead time for dies, die
changes
• Assembly – shimming, unavailable resources
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See extra slides at end
Nominal Mfg Process Rates
Vary by more than 8 orders
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See extra slides at end
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Life Cycle Perspective
Mfg. Process Equipment
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Mat’l
Prod
Mfg. Use EOL
Raw
Mat’ls
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Life Cycle Perspective
Product
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Mat’l
Prod
Mfg. Use EOL
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Production Rate
• Process rate – slow machines = large
capital investment
• System rate
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Metal Additive Part
String ribbon process for PV
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Production Rate
• Process rate - physics
• System rate – waiting for needed resource
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System Time & Rate
• Oct 31, Dr. Stan Gershwin
– Little’s Law,
– unreliable machines,
– Buffers (zero, infinite and finite)
– M/M/1 queue
– Simulations
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Quality Issues at the Process
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Satisfied customer and meeting target specification
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Where you find the problem
matters
• Product recalls
• Customer complaints
• Warranty claims
• Dealer returns
• In-house inspection
• Assembly
• Observed at the process
Increasing
CostRepair and upgrade of the Hubble Telescope
Fix problems close to home!
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Inspecting in Quality
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Ref M. Phadke
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Quality Loss Function
51Ref M.Phadke
After G Taguchi
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52Kalpakjian and Schmid 7th ed
Nominal Process Variation(process in conrol)
Surface RoughnessDimensional Tolerance
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Process variation/tolerance
What are the
most important
variables?
Kalpakjian
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Process variation/tolerance
elevated temperature
machining
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Process variation
size
temperature
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Quality Control Actions
Y = (+, U)
Ref Hardt, 2001
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How to control variation
output variationdisturbance
sensitivitycontrol action
ref. D. Hardt
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Real Time Control
output variationdisturbance
sensitivitycontrol action
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Designed Experiments
output variationdisturbance
sensitivitycontrol action
Output
feature
Controllable parameter
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Statistical Process Control
output variationdisturbance
sensitivitycontrol action
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Mean drift, and variance of the
output Y
Mean on target, but
large variation due to
many random effects
Mean drift has
assignable cause,
tight grouping
means small variation
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Comparing the variation with
the specifications
Goals: 6s < (USL-LSL)
and mean centered
out of spec
partsout of spec
parts
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If UCL-LCL = 6s
and the process mean
is in the center, then
The out of compliance
parts are given by
2(0.500-(3s)) =
2(0.500-0.4987) =
0.0026 or 0.26% or 2600ppm
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Some propose a process capability index Cp that
compares the tolerance interval USL-LSL vs the
process variation 6s.
Upper Specification Limit
Lower Specification Limit
Target
Cp % out ppm
⅔ 4.55 45,500
1 0.26 2600
1 ⅓ .0063 63
2 .00034 3.4
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Mean Drift
Upper Specification Limit
Lower Specification Limit
Target
0.135%
13.6
+2.1
+0.135
15.835
+0.135
15.97
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2.810 Manufacturing
Processes and
Systems - Process
Control66 Slide taken from D. Hardt
“Not In-Control”
i
i+1
i+2
...
The Parent
Distribution
Changes with Time
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Statistical Control Methods
Strategy:
1. Monitor process when under control
2. Determine Centerline & Control Limits
3. Data outside of UCL/LCL indicates change
4. Investigate and eliminate causes of shift
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Mean drift Vs Normal Variance
• Statistical Process Control
Lower Control Limit
Sampling period
Upper Control Limit
Centerline
“Shewhart Control Charts”
How likely is
this to occur?
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Histogram for CNC Turning
From Dave Hardt
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Sampling Frequency
Factors that determine the appropriate
sampling frequency:
– Stability of process
– Potential loss
– Cost of sampling inspection
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What causes variation in dimensions?
• Machine variation
– e.g. change in settings, environment, equipment
• Material variation
– e.g.suppliers, substitutes, mixtures..
• Operator variation
– Jim instead of Joe, or Alice instead of Mary
• Method variation
– Late Friday afternoon, Mary always does it this
way…
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“x-bar charts”Mean of the means
• Mean
Where, n = sample size
k = number of samples
A2 = constant from Table C.1
R = defined next slideAlso see alternative method
Presented by Dave Hardt
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“R-charts” Range = high - low
Where, n = sample size
k = number of samples
D3 , D4 = constants from Table C.1
• Standard Deviation can be estimated from R
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Estimate of standard deviation from range
ref. P. Lyonnet
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Robustness Vs Sensitivity
• Mean shift by 1s requires on average
44 data points to observe
• Alternatives
– ±2s; two consecutive observations
– ±1s; three consecutive observations
– other charts (e.g. “Cusum”)
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Source Identification; Ishikawa
Cause and Effect DiagramMan Machine
Material Method
Effect
Finding the cause of a disturbance is the most difficult part of quality control. There are only aids to help you with this problem solving exercise like the Ishikawa Diagrams which helps you cover all categories, and the “5 Whys” which helps you go to the root cause.
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SPC - Statistical Process Control in Injection
Molding and Extrusion By Chris Rauwendaal
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Summary
• Cost – direct cost comparisons
• Time and Rate – process & system
• Quality/Variance –random/assignable
• Energy – process overview
80
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Extra slides
1. Energy Intensity of Mfg Processes
2. Math Tools: Expectation and Variation
Operators (Composites Example)
3. Propagation of Errors
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Energy Used by
Manufacturing Processes
• Fixed power usage during processing –
auxiliary equipment
• Variable power usage – scales with the
rate of material processing e.g.
machining spindle power ~ MRR
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Energy intensity of Mfg Processes
1. Machining
2. Grinding
3. Casting
4. Injection Molding
5. Abrasive Waterjet
6. EDM
7. Laser DMD
8. CVD
9. Sputtering
10. Thermal Oxidation
Electricity requirements for
manufacturing processes
MJ electricity/kg processed
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Energy Requirements at the Machine
Tool
Production Machining Center Automated Milling Machine
From Toyota 1999, and Kordonowy 2002.
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Electric Energy Intensity for
Manufacturing ProcessesP
ow
er
(kW
)
Process Rate (cm3/sec)
physics
auxiliary equipment & infrastructure
Process Rate (cm3/sec)Specific
Energ
y (
MJ/c
m3
)
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Injection Molding Machines
Does not account for the electric grid.
So
urc
e:
[Th
irie
z ‘0
6]
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Thermal Oxidation, SiO2
Ref: Murphy et al
es&t 2003
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Power Requirements
Ref: Murphy et al
es&t 2003
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In General, over many
manufacturing processes,
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Gu
tow
ski e
t a
l JIE
20
17
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Measuring Process Variation: ReviewProcess measurement reveals a distribution in output
values.
Discrete probability distribution based upon measurements
Continuous “Normal” distribution
In general if the randomness is due to many different factors, the distribution of the means will tend toward a “normal” distribution. (Central Limit Theorem)
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If the dimension “X” is a random variable, the mean is given by
m = E(X) (1)
and the variation is given by
Var(x) = E[(x - m)2] = s2 (2)
both of these can be obtained from the probability density function p(x).
For a discrete pdf, the expectation operation is:
(3)
Expectation and Variance Operators
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p
1/2
1/4
x1 2 3
Sample calculation of E(x) = m, and Var(x) = s2
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Properties of the Expectation
1. If Y = aX + b;
where Y, X are random variables; a, b are constants,
E(Y) = aE(X) + b (4)
2. If X1,…Xn are random variables,
E(X1 + … + Xn) = E(X1) +…+ E(Xn) (5)
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Properties of the Variance
1. For a and b constants,
Var(aX + b) = a2Var(X) (6)
2. If X1,…..Xn are independent random variables
Var(X1+…+ Xn) = Var(X1)+ Var(X2)+ + Var(Xn)
(7)
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“Tolerance Stack up”, really about variance,
recall that
E(X1 + … + Xn) = E(X1) +…+ E(Xn)
but how about
Var(X1 +…+ Xn) = ?
X1 Xn
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If X1 and X2 are random variables and not necessarily
independent, then
Var(X1 + X2) = Var(X1) + Var(X2) + 2Cov(X1X2) (8)
this can be written using the standard deviation “s”, and the
correlation “r” as
(9)
where L = X1 + X2
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If X1 and X2 are correlated (r = 1), then
(14)
for X1 = X2 = X0
(15)
for N (16)
or (17)
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Now, if X1 and X2 are uncorrelated (r = 0) we get the result as in
eq’n (7) or,
(10)
and for N (11)
If X1=X =Xo (12)
Or (13)
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“Tolerance Stack-up”
As the number of variables grow so does the variation in the system; but when normalized…
correlated
uncorrelated
Where L = NLo
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**
* **
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e.g.Thermal expansion 1-D
change in
dimension
coef. of
thermal
expansion
length of
sample
change in
temperature
L
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Random variables
If the variables are independent:
..and if the variation is small, linearize to get:
Ref: Lipschutz
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Propagation of errors y =·x
Ref. Young
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This gives…
• this result is called “quadrature”,
in general, if y=x, with , x independent
random variables with small variation,
then
with Var (x) = sx2
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A more general results is…
• for any relationship like y=zx, with z, x
independent random variables with
small variation, then
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Hence for Thermal Expansion…
If the variables are independent:
..and the variation is small:
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References
• Random Variables Ch 5 Seymour Lipschutz
• Statistical Process Control (SPC), Hogg & Ledolter
• Propagation of Errors, Statistical Treatment of Experimental Data, Hugh Young
• “hockey stick diagram” for energy and rate, Gutowski et al, See “ electrical energy used in manufacturing processes” p 1586-1588 your text
• also see your text, topics are listed in the index. For the 7th edition: SPC section 36.8, Cost section 40.10, and Energy sections 40.5 &40.6 these topics are also listed in other places in the text, see index in the back of the book.