# Theory of Faults (ToF): Numerical Quality Management in Complex Systems
## 6 Discussion
In summary of quality-risk relations, there is a correlation between low quality and reduced risk; projects with better quality have lower amounts of faults but of a higher magnitude (Figure 2) The negative correlation between quality and risk and the diminishing effects of faults are \"justifications\" for the neglect of quality in construction. This neglect comes with a \"price\" of high entropy and information loss. Power functions are a measure of risk. The power function exponential \"b\" is a **phase parameter**; it facilitates the transition of networks and the segmentation of the market (Figures 7 and 18c). A range of 1 < \(b\) < 2 implies well-managed projects, such as projects 2 and 3 of Case Study 1. Similarly, 2 < \(b\) < 3 stands for fairly well-managed projects, of which a considerable number are present in the Case Study 1 dataset; in that range, there is a possibility for a second IC; the notion of a second IC was validated in Figure 15. According to [27], in this \"\(b\)\", finite sub-graphs are formed, and in the presence of randomness, the spatial overlap between the subsequent avalanches becomes insignificant, and ultimately, a critical state is not reached. The last part of this statement was proved wrong here (project 23); if at all, the presence of randomness enables overlapping [8]. \"\(b\)\" > 3 mathematically allows a mean and S.D. ; that possibility is meaningless as events are unlimited. It is a fact, though, that insurance companies and big contractors have established largely reliable means; this reliability is for entire market segments or a multitude of projects. \"\(b\)\"\(>\)\(>\) appears in avalanche projects. An avalanche changes the morphology, causing phase transition and aftershocks [23]; such is the transformation from the b = -2 of project 23 to the \(b>>10\) of project 1. The aftershocks of that avalanche are reported below. On a smaller scale of magnitude, the move to the left in Figure 4 or down in Figure 6 within the lifespan of construction projects is common, perhaps indicating that **self-organization** finds an avenue to reduce risk and the load on info-systems through the enlargement of \"b\"; such is the dynamic portrayed in Figure 17. \(b<1\) was found in the degree distributions of design networks and of infrastructure networks; it implies that the whole network forms one cluster [64]; this was validated in Figure 18.  
**Signal processing** is another mechanism that influences info-systems. We investigated the trajectory of control signals in numerical experiments (A.3); we showed that the filters magnify the impact of control signals, 1 FB loops cause incessant noise, and 2 FB loops generate a Fibonacci magnification; simulations showed how filters cause info-system overload. The noise created by 1 FB loops scaled by the enormity of the power function tail would down any system. The effects of 2 FB loops are not confined to the site systems; signals may propagate the info-systems to designers,where they have a convolution effect on information workload (simulated in Figure 6) and a potential to cause psychological effects such as fatigue and resentent [74] and sociological effects such as bridge formation (Figure 12). Small-world interconnected networks facilitate the importation of information overload; thus, one project overload may stall or delay information processing in another project. Site systems act on QC signals as a low-pass filter (LPS). The effect of the noise reduction of LPSs for faults of frequency \(w=w0\) is \(-3\) dB (0.7 scaling); lower frequency signals are practically unaffected. Unlike LTI, sites are non-additive time-variant dissipative systems, and calculating a site transformation function is not feasible for us.