lecture #15 erdm prof.johnw.sutherland feb. 13, 2004€¦ · environmentally responsible design...

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


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.


Product Performance Variation

Product

Design

Manufacture

& Assembly

Process

Product

UseNominal

Design

Variable

Levels

Actual

Variable

Values

Manufacturing &

Assembly Noise

Product Use

Noise


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


Product Function

Function deteriorates because of wear and aging.

Time

Function


Function Behavior -- Distribution

Process mean and variability change over time. True?


Toner Cartridge Data

t

Mean - xVariance - o

x o

x

xx

xx

x

x

o

o

oooo

o


Quality

Traditionally defined as conformance to engineeringspecifications.

µx x

σxLower Spec

Nominal Value

Upper Spec


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


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


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

+=


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


Consider Use & Throw-away Strategy

0 T1 T2

Product Replacement Points

0 T1 T2

Loss (Cost)

Loss (Cost)


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).


Post-Use Product Disposition

NatureRaw Materials/Energy Acquisition

MaterialRefinement

ProductProduct DisposalCreation

ProductReuse

Remanufacturing

Recycling

MaterialDisposal


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.


A New Metric: Satisfaction

x

Loss

BenefitB(x)

L(x)

S(x)=B(x)-L(x)


Value

Value Definition: The cumulative satisfactionremaining in a product.

t

S(x)

T


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+=


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

∫=


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


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.


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

)


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

lecture #15 erdm prof.johnw.sutherland feb. 13, 2004€¦ · environmentally responsible design...

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