# Theory of Faults (ToF): Numerical Quality Management in Complex Systems
## 4 Numerical Experiments
Ergodicity in engineering systems has many implications, such as the vindication of the use of partial [unbiased] datasets and, because all networks are interconnected, the percolation of technologies, _the_ rippling of faults, and the emergence of universal traits [62]. The grid morphology down-estimates the reality of small-world networks. Case Study 2 generated a network that is one cluster with a diameter of 2; therefore, in the Case Study 2 morphology, the whole network may be affected in two iterations. **A.3** Numerical experiment FB loops. In these experiments, signals were delivered through 1 FB and 2 FB loops. The entering signals were generated from eigenvectors of \(\delta\)[n] = 1 with a uniform probability distribution. The signals were scaled by a Figure 3 power function (Figure 10a). The signals were amplified by the filters to generate outgoing signals; these signals were added to the current signal load. Figure 9: Cellular automaton, at time 15: graphical presentation (**a**), tabular presentation (**b**). Legend: Green, zero faults; yellow, up to \(\sim\)10\({}^{4}\) faults; light red, \(\sim\)10\({}^{5}\); red \(\sim\)10\({}^{6}\). The 1 FB loop (Figure 10b) had little effect of magnification, even to an event as big as 0.25. In the Figure 10c simulation run, the 1 FB loop magnification of an extreme event of 0.98 magnitude was not enough to reach IC. In the next experiments, a vector signal of length 5, with uniform probability and power function scaling, was issued into a 2 FB loop. At every time (that is, in every row), a new vector was added to the filter. The results are in Table 2.  
The magnitude of event time = 1, event = 4, highlighted in the red frame, was sufficient to cause an avalanche in a three-time-unit sequence; the other vectors were too small to add to its effect, therefore the outcome would be the same for any combination of this event. The results are that the 1 FB loop adds little to the overload; in processing defects, its effect is negligible. Figure 2 shows that even with high-magnitude events such as 0.253 \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & & & & & & \\ \hline
**Time** & **1** & **2** & **3** & **4** & **5** & **Total** \\ \hline
0 & 0.0013 & 0.007 & 0.0297 & 0.0013 & 0.0135 & 0.0465 \\
1 & 0.0079 & 0.0012 & 0.0302 & 0.253 & 0.0159 & 0.3082 \\
2 & 0.0142 & 0.0027 & 0.0605 & 0.2567 & 0.0717 & 0.4058 \\
3 & 0.0233 & 0.0073 & 0.0915 & 0.5141 & 0.0888 & 0.725 \\
4 & 0.0431 & 0.0113 & 0.15577 & 0.7843 & 0.1625 & 1.15697 \\ \hline \end{tabular}
\end{table} 
Table 2: The 2 FB loop random iterations. Figure 10: A 1 FB loop amplification of extreme events: the entering power function (**a**) and the amplification (**b**); 1 FB loop amplification of an extreme event (**c**). or even 0.98 values, the accumulation rarely causes an avalanche. Yet, this experiment is negligent of the enormity of the number of faults; the noise generated would drown the second IC system. Systems must have a mechanism to dub the noise. The mechanism is suggested in Equation (32) for 1 FB loops; Equation (33) suggests a similar mechanism for 2 FB loops; the first suggestion, for the 1 FB loop, is sustained by expert opinion, but the second one is not. Defects are often ignored. Events of potential high magnitude are not ignored; they may be left untreated owing to system overload, not to neglect [63]. The results of the 2 FB loop experiment stress the importance of treating faults without delay, a justification for a trouble-shooting culture and for the above directive to apply an energetic, rapid response. **A.4** Information net morphology and transformation. In this section, a \"super\" network of a design + construction info-system was simulated. A public project was studied by experts, and an adjacency matrix was generated for 61 of the participants in the design + site information network. The participants are designers introduced by discipline and their site correspondents in the contractor and QC.