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Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Lecture #15
ERDM
Prof. John W. Sutherland
Feb. 13, 2004
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Introduction
Objective: Present recent work that links variation,quality, and post use options.
• Product performance variation
• Effect of Wear & Aging
• Loss and Benefit Models
• Product Value
Create economic model that supports the environment.
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Product Performance Variation
Product
Design
Manufacture
& Assembly
Process
Product
UseNominal
Design
Variable
Levels
Actual
Variable
Values
Manufacturing &
Assembly Noise
Product Use
Noise
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Product Performance Variation (cont.)
Design-Mandated Target
Manufacturing Variation
Parts “as manufactured”
Outer Noise
Performance ObservedDuring Product Use
Inner Noise
Performance of Prod.at point in Future
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Product Function
Function deteriorates because of wear and aging.
Time
Function
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Function Behavior -- Distribution
Process mean and variability change over time. True?
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Toner Cartridge Data
t
Mean - xVariance - o
x o
x
xx
xx
x
x
o
o
oooo
o
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Quality
Traditionally defined as conformance to engineeringspecifications.
µx x
σxLower Spec
Nominal Value
Upper Spec
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Quality (cont.)Traditional definition of quality does not promotenotion of never-ending improvement.
We need some definition of quality that promotesbeing on target and penalizes variation.
Nominal Value
x
Upper SpecLower Spec
BestUnacceptable
Good
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Loss Function
The loss function meets our need and we will use tocharacterize quality. Quadratic form:
L = k(x - m)2
Loss increases as we move away from the target
Nominal Value
x
Loss
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Expected Loss
Since the characteristic X is a random varb., loss isalso a random varb. - chararacterizes “average” loss
Loss
mx
µx
σx
E L X( )[ ] k µx m–( )2 σx2
+=
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Loss Behavior - Deteriorating Product
0
20
40
60
80
100
0 3 6 9 12 15 18 21 24 27 30 33 36 39
time
mean
variance
Expected Loss
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Consider Use & Throw-away Strategy
0 T1 T2
Product Replacement Points
0 T1 T2
Loss (Cost)
Loss (Cost)
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
A Problem with the Loss Function
• Lengthening the time between product replacementsdoes not seem to produce a societal benefit.
• Problem is that the loss function only considers thenegative aspects of using a product. We mustconsider benefits as well.
• Previous graph suggests that we consider thecumulative effect of loss (same would apply tobenefits).
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Post-Use Product Disposition
NatureRaw Materials/Energy Acquisition
MaterialRefinement
ProductProduct DisposalCreation
ProductReuse
Remanufacturing
Recycling
MaterialDisposal
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Post-use Options
We need a metric that is consistent with our desire tobe more environmentally responsible, i.e., thatencourages longer use cycles.
Also, if we are seriously looking at “take-back”, weneed to know the value of the used products comingback.
High value used products -- refurbishment / reuseLower value used products -- recycling
The action to be taken depends on the product value.
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
A New Metric: Satisfaction
x
Loss
BenefitB(x)
L(x)
S(x)=B(x)-L(x)
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Value
Value Definition: The cumulative satisfactionremaining in a product.
t
S(x)
T
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Expected ValueFrom our previous work, we know that S(x) is
The expected satisfaction for a set of products is
The mean and variance are linear functions of time,
S x( ) S0 K x m–( )+2
=
E S X( )[ ] S0 K µx m–( )2 σx2
++=
µx µ0 k0t+=
σx2 σ0
2k1t+=
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Expected Value (cont.)
The value of a product at time, t, is the cumulativesatisfaction still left in the product at time t
V(0) = the value of a new product
V(T) = the value of a product when it reaches the endof its life -- useful from environment standpoint
CV(t) = V(0) - V(t) = Value consumed up to time t
V t( ) S t( ) td
t
T
∫=
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
An Example
Nominal = 20, k=2
So, want to center manufacturing process at µ = 20.
0
5
10
15
20
25
15 17 19 21 23 25
Characteristic, x
Sa
tisf
act
ion
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Satisfaction -- Over Time(need to consider value function for process centering)
17
18.5
20
21.5
23
0
4
8-40
-20
0
20
Mean
Time
If we centerthe process at20, we slowlyget worse dueto wear &aging.
Maybe weshould startwith a smallermean.
Then, on theaverage wewould becloser to thetarget of 20.
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Value Function -- Another Example
00.01
0.020.03
0.040.05
8.4
8.45
8.5
8.55
8.60
5
10
15
20
Mean in.
Val
ue in
dol
lars
($)
Standard deviation in.Mean in.
Val
ue($
x10
)
Environmentally Responsible Design & Manufacturing (MEEM 4685/5685)Dept. of Mechanical Engineering - Engineering MechanicsMichigan Technological University© John W. Sutherland
Summary• What we pay for a product is assumed to be equal to
the value remaining in a product.
• Product deterioration over time -- product valuechanges over time.
• Satisfaction metric includes both positive andnegative aspects of product usage.
• Value is the cumulative satisfaction remaining in aproduct.
• Select initial process centering to control value at endof use cycle