EP 1130-2-500
27 Dec 96
APPENDIX F
EXAMPLE OF COMBINING RISKS AND CONSEQUENCES
F-1. Introduction. The evaluation procedures for major rehabilitation require the Districts to use
risk-based benefit-cost analysis incorporating the existing and future risk of "unsatisfactory
performance" of structures and equipment. These risks are then combined with estimates of the
costs of unsatisfactory performance to generate an expected reliability based cost. Alternative
rehabilitation strategies are then proposed to reduce this cost. Each alternative can either change
the risk, change the cost of unsatisfactory performance or both. A complicating difficulty is that
the analysis must be carried out over the "life-cycle" to the project, up to 50 years. That is, the
cost estimated is the present value of all costs associated with the operation, maintenance, and
repair of the facility where each cost is weighted by the probability of occurrence.
F-2. Description of Simplified Evaluation Problem. Suppose that the rehabilitation problem is the
potential unsatisfactory performance of a hydropower plant. For simplicity, assume that the plant
is composed of two generating units. Each of these units, in turn, is composed of two
components: a turbine and a generator. The information available for each component of each
unit is shown in Table F-1. Table F-2 shows the system energy and capacity opportunity costs as
a function on the number of units out of service simultaneously. It is assumed that all the units
provide the same contribution to system energy and capacity. Sometimes, the energy and
capacity contributions will differ across the units. In addition, a rehabilitation strategy may
include efficiency improvements on a unit by unit basis.
Table F-1: Example Hydropower Rehabilitation Assumptions
Unit 1
Unit 2
Turbine
Turbine
Generator 2
1
2
Initial Risk
.01360
.01176
.01510
.02520
Annual rate of change in
.00017
.00042
.00017
.00042
risk
Risk after repair
.00017
.00042
.00017
.00042
Risk after rehabilitation
.00017
.00042
.00017
.00042
Number of months to
24
12
24
12
repair
F-1
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