Replacing one asset with another of a different model adjusts the overall replacement timing depending on the life cycle of the new asset. In this synopsis will we use timber window frames replaced with aluminum frames

The graph illustrates an in-kind replacement at the optimal age of 60 based on the increasing marginal cost of the existing asset (Timber frame)shown in red and the EAC minimum life cycle cost of the existing and new asset(Aluminum frame) of the same type shown as the dashed line.

Timber frame  :      EAC: R141     /     EUL: 43yrs    /    Failure distribution rate :0.42
Aluminum frame:  EAC: R79      /     EUL: 41yrs    /     Failure distribution rate : 0.42

The minimum life cycle cost of the new asset is lower, however, perhaps because the new asset will have a lower failure probability, lower maintenance costs, or lower capital cost.

The optimal replacement time for an asset is where the EAC equals the marginal cost of an asset. 

In this scenario a timber frame optimal replacement can be at age 25 , 43 , 60, depending on the marginal cost .

The normalized failure distribution for timber frames render the optimal EUL and replacement at age 43, where the marginal cost = EAC. As depicted in the graph is the failure distribution curve shifted by the maintenance approach/strategy which render a higher or lower decay/failure rate.

The distribution curve shift:

  • to the left for reactive maintenance strategies, due to higher early failures and thus a reduced EUL, rendering the optimal replacement at age 25
  • to the right for proactive maintenance strategies due to the reduced decay rate and thus extended EUL , rendering the optimal replacement at age 60

With a differing asset is the optimal replacement position on the EAC line for the differing asset. With a aluminum frame having a lower EAC is the optimal replacement thus +- 12 years earlier due to the benefits (lower  EAC – lower annual cost) of the new asset. This should make intuitive sense: as the benefits of replacement increase (or the costs decrease) your incentive to replace is higher, so you’ll do it sooner.