PSI - Issue 19

Aaron Stenta et al. / Procedia Structural Integrity 19 (2019) 27–40 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Note, that adding in installation and even inspection and repair costs for a single inspection (at the end of the operating cycle) do not change this result for the final return, because they would simply shift the return function up and down by a constant amount, which would not affect the optimal time. For example, adding in these costs to H would lead to   0 B F F I R H C t P t C C C         , (3) where 0 C , I C , and R C are the installation, inspection, and repair costs, respectively. Note, these constants drop out when the time derivative is taken of H directly, but since we are actually optimizing h , these terms will remain in that case. 3. Bayesian Decision Networks One very powerful, graphical approach for decision optimization is to use Bayesian Decision Networks (BDN). A BDN is a probabilistic graphical model that represents cause-effect relationships by using arrows connecting nodes from causes to their effects. The strength of these connections are measured by conditional probabilities. In addition to probabilistic (chance) nodes, a BDN has decision and utility nodes for assessing the cost and benefit of decisions as well as the cost of uncertain events such as failure. By constructing a BDN, it is possible to determine an optimal decision strategy from all possible decisions by using a method known as Single Policy Updating (SPU).

Fig. 3. A generic Bayesian Decision Network (BDN) for the Life Cycle Management decision flow diagram in Figure 1b.

In a similar manner, one can set up a decision network for the LCM decision flow diagram illustrated in Figure 2. The basic structure of such a network is illustrated in Figure 3. There are four decision nodes, i.e. Inspect , Repair , Perform FFS , and Run Time . Discrete states can be used to represent different possible decisions. For example, the Run Time node might have the values: 0 years, 1 year, 2 years, 3 years, …, et cetera. The Inspect node might have the values: None, Highly Effective, Moderately Effective, and Barely Effective. The Repair node might have the values: No Repair, Highly Effective, Moderately Effective, Barely Effective. The Perform FFS node might have the values: No FFS, Level 1, Level 2, Level 3. The Failure chance node could have simple Yes and No