# N-Monitoring

## Description

The $N$-monitoring problem is described in ^{[1]}, sections 4.1 and 6.1.

## Influence Diagram

The incluence diagram of generalized $N$-monitoring problem where $N≥1$ and indices $k=1,...,N.$ The nodes are associated with states as follows. **Load state** $L=\{high, low\}$ denotes the load, **report states** $R_k=\{high, low\}$ report the load state to the **action states** $A_k=\{yes, no\}$ which decide whether to fortificate **failure state** $F=\{failure, success\}.$ Finally, the utility at target $T$ depends on the whether $F$ fails and the fortification costs.

We draw the magnitude and cost of fortification $c_k∼U(0,1)$ from a uniform distribution. Fortification is defined

The probability that the load is high. We draw $x∼U(0,1)$ from uniform distribution.

The probabilities of the report states correspond to the load state. We draw the values $x∼U(0,1)$ and $y∼U(0,1)$ from uniform distribution.

The probabilities of failure which are decresead by fortifications. We draw the values $z∼U(0,1)$ and $w∼U(0,1)$ from uniform distribution.

Utility from consequences at target $T$ from failure state $F$

Utility from consequences at target $T$ from action states $A_k$

Total utility at target $T$

## References

- 1Salo, A., Andelmin, J., & Oliveira, F. (2019). Decision Programming for Multi-Stage Optimization under Uncertainty, 1–35. Retrieved from http://arxiv.org/abs/1910.09196