In the 窶# Main simul. runs窶 field you enter the number of runs in the 窶廴ain simulation窶 phase. Obviously, if you increase this number, the 窶廴ain simulation窶 phase will need more time to finish. However, your results will be more numerically precise. It is not possible to state a general rule for how many runs you need in any given situation. This depends heavily both on the model itself, and how precise results you need in your analysis.
If you have a large complex risk model, it may be a good idea to use a small number, e.g., 100-1000, during the model development. When your model is finished, however, you should consider increasing the number to at least 2000.
During the 窶廴ain simulation窶 phase DynRisk calculates all nodes in the traced set determined from your simulation set. Moreover, the output values of those nodes in the simulation set which have their 窶彜im.窶 attribute switched 窶徙n窶, are stored in the result file. This is repeated for each simulation run. When the 窶廴ain simulation窶 phase is finished, DynRisk calculates some summary statistics for all nodes in the simulation set, and stores these in the result file.
# Crit. simul. runs
In the 窶# Crit. simul. runs窶 field you enter the number of runs in the 窶廚rit. simulation窶 phase. As with the 窶廴ain simulation窶 phase, if you increase this number, the 窶廚rit. simulation窶 phase will need more time to finish. However, your results will be more numerically precise.
Both theoretical considerations and practical experiences indicate that you need at least as many runs in the 窶廚rit. simulation窶 phase as in the 窶廴ain simulation窶 phase to obtain stable results.
Note that the time needed for the 窶廚rit. simulation窶 phase is affected not only by the number of runs, but also by the number of 窶廚rit.窶 and 窶彜ens.窶 attributes being switched 窶徙n窶 in the simulation set. Moreover, if you calculate the criticality or sensitivity of a low level node with a high level node as goal node, this takes longer time than if you calculate the criticality or sensitivity of a high level node with the same goal node.
During the 窶廚rit. simulation窶 phase DynRisk calculates once more all nodes in the traced set determined from your simulation set. However, in this phase no output values are stored in the result file. Instead DynRisk proceeds as follows:
Assume that in a particular run in the 窶廚rit. simulation窶 phase, the output values of the traced set of nodes are listed in the order of calculation:
X(1), X(2), ... , X(n)
The values at the beginning of this sequence, are outputs from the nodes at the lowest level in the model, while the values at the end of the sequence, are outputs from the higher level nodes. Typically, (but not strictly necessary) the last node in the sequence, is the goal node. To simplify the present discussion we will assume that this is the case here.
Suppose that 窶廸ode A窶 is a node in the current simulation set whose 窶廚rit.窶 attribute is switched 窶徙n窶, and let X(k) be the corresponding value in the sequence. Then DynRisk modifies the sequence temporarily first by replacing X(k) by the mean value of 窶廸ode A窶 estimated during the 窶廴ain simulation窶 phase, and then by updating the sequence accordingly. In particular, DynRisk computes a modified value of the goal node. Thanks to the way the sequence is ordered, this can be done by recalculating only the subsequence:
X(k+1), X(k+2), ... , X(n)
Similarly, if 窶廸ode A窶 has its 窶彜ens.窶 attribute is switched 窶徙n窶, and has an 窶彜.fact.窶 attribute equal to S(k), then DynRisk modifies the sequence temporarily first by replacing X(k) by S(k)*X(k), and then by updating the sequence accordingly. In particular, DynRisk obtains another modified value of the goal node. Again thanks to the way the sequence is ordered, this is done by recalculating only the subsequence mentioned above.
Note, that if 窶廸ode A窶 is a low level node, the subsequence may still be very long. Hence, it typically takes longer time to calculate criticality and sensitivity of lower level nodes compared to higher level nodes.
During a single run in the 窶廚rit. simulation窶 phase, DynRisk calculates modified values of the goal node as explained above, for each node whose 窶廚rit.窶 or 窶彜ens.窶 attributes are switched on. For nodes where both of these attributes are switched on, DynRisk needs to calculate two different modified goal node values. The modified goal node values are used to accumulate statistics, i.e., mean values and variances.
This is repeated for each simulation run. When the 窶廚rit. simulation窶 phase is finished, DynRisk calculates the requested criticalities and sensitivities, and stores these in the result file.
Criticality
DynRisk provides two measures of the criticality of a node with respect to a goal node:
窶｢ Criticality mean
窶｢ Criticality variance
The criticality mean is calculated by using the following formula:
[M(G) - M(G | X = M(X))]/M(G)
where G is the goal node, X is the current node, M(G) and M(X) denotes the mean values of G and X respectively, and M(Gﾂ |ﾂ X = M(X)) denotes the conditional mean of G given that X is equal to its mean value. Thus, the criticality mean measures the effect of the uncertainty in X on the mean value of the goal node. M(G) and M(X) are estimated based on the results in the 窶廴ain simulation窶 phase, while M(Gﾂ |ﾂ X = M(X)) is estimated based on the modified goal node values obtained during the 窶廚rit. simulation窶 phase.
The criticality variance is calculated by using the following formula:
[V(G) - V(G | X = M(X))]/V(G)
where G is the goal node, X is the current node, V(G) and V(X) denotes the variance values of G and X respectively, and V(G | X = M(X)) denotes the conditional variance of G given that X is equal to its mean value. Thus, the criticality variance measures the effect of the uncertainty in X on the variance of the goal node. V(G) and M(X) are estimated based on the results in the 窶廴ain simulation窶 phase, while V(Gﾂ |ﾂ Xﾂ = M(X)) is estimated based on the modified goal node values obtained during the 窶廚rit. simulation窶 phase.
Sensitivity
DynRisk provides two measures of the sensitivity of a node with respect to a goal node:
窶｢ Sensitivity mean
窶｢ Sensitivity variance
The sensitivity mean is calculated by using the following formula:
[M(G | S*X) - M(G)]/M(G)
where G is the goal node, X is the current node, S is the specified sensitivity factor, M(G) and M(X) denotes the mean values of G and X respectively, and M(G | S*X) denotes the conditional mean of G given that X is replaced by S*X in all calculations. Thus, the sensitivity mean measures the effect of a change in X on the mean value of the goal node. M(G) is estimated based on the results in the 窶廴ain simulation窶 phase, while M(Gﾂ |ﾂ S*X) is estimated based on the modified goal node values obtained during the 窶廚rit. simulation窶 phase.
The sensitivity variance is calculated by using the following formula:
[V(G | S*X) - V(G)]/V(G)
where G is the goal node, X is the current node, S is the specified sensitivity factor, V(G) and V(X) denotes the variance values of G and X respectively, and V(Gﾂ |ﾂ S*X) denotes the conditional variance of G given that X is replaced by S*X in all calculations. Thus, the sensitivity variance measures the effect of a change in X on the variance value of the goal node. V(G) is estimated based on the results in the 窶廴ain simulation窶 phase, while V(Gﾂ |ﾂ S*X) is estimated based on the modified goal node values obtained during the 窶廚rit. simulation窶 phase.
