Componet Replacement

Component Replacement Policies

2008/9/23

October 2008

Component Replacement Policies
Dr. Albert H.C. Tsang

Phone: (852) 2766–6591

Fax: (852) 2362–5267

email: albert.tsang@polyu.edu.hk

Outline
Short-term Deterministic Optimization Constant-interval Replacement Policy Age-based Replacement Policy Glasser’s Graphs References

© 2008 by Albert H.C. Tsang

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Replacement of Items with Increasing Operating Costs
In the short time frame, an asset does not fail, but its operating cost increases with use Use Life Cycle Evaluation to determine its optimal replacement times

© 2008 by Albert H.C. Tsang

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Hot flue gases Cold air
Hot air

Air heater Soot deposits steam Boiler fuel

© 2008 by Albert H.C. Tsang

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Short-term deterministic optimization
1.2

$ per unit of Steam Generated

1

0.8

0.6

0.4

0.2

tr
time

0Where on the increasing operating cost curve is it economically justifiable to make a replacement (that is, clean the air heater) ?
© 2008 by Albert H.C. Tsang Component Replacement Policies 5

Short-term deterministic optimization
Operating cost (fuel) Total Cost
Cost / Unit Time

Replacement Cost (Cleaning Cost)

0 0

Optimal tr
© 2008 by Albert H.C. Tsang

Interval between replacementtr

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Model Construction
c(t) : Operating cost per unit time at time t after replacement Cr : Cost of a replacement C(tr) : Total cost per unit time for preventive replacement at time t, where tr is the length of replacement intervals
tr

cost of operating+cost ofreplacement C (tr ) = = length of interval
© 2008 by Albert H.C. Tsang Component Replacement Policies

∫ c(t )dt +C
0

r

tr
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Model Construction
Cr
Cost / Unit Time

c(t)

t tr

© 2008 by Albert H.C. Tsang

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Example
c(t ) = A − B exp[− kt ]
Where A= $100, B=$80, and k=0.21/week.

Cr = $100
1 C (tr ) = tr ⎡ tr ⎤ (100 − 80 exp[−0.21t ]dt + 100) ⎥ ⎢∫ ⎢0 ⎥ ⎣ ⎦

© 2008 by Albert H.C. Tsang

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Example
100

$/weeks

c(t)=A-Be-kt

20 0

Time (weeks)

© 2008 by Albert H.C. Tsang

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2008/9/23Example
Optimal Replacement Age
tr C(tr) 1 127.8 2 84.7 3 74.0 4 70.9 5 70.5 6 71.5 7 72.5

© 2008 by Albert H.C. Tsang

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Further Comments
One Replacement Cycle Operation Replacement

0
tr

tr

tr+Tr

C (tr ) =
© 2008 by Albert H.C. Tsang

∫ c(t )dt + C
0

r

tr + Tr
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Total cost Curve

C(tr)

tr

© 2008 by Albert H.C. Tsang

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Sensitivity Analysis of Cost Function
Overlap Curves obtained by varying Cr

Optimal values of tr for different values of Cr

Interval between replacement, tr

© 2008 by Albert H.C. Tsang

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Preventive Replacement of Items Subject to Failure
Check the following conditions:
the risk of failure increases with age or usage the cost of preventive replacement is lower than the cost of corrective replacement

© 2008 by Albert H.C. Tsang

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RCM Methodology Logic...