# Theory of Faults (ToF): Numerical Quality Management in Complex Systems
## 6 Discussion
We put universality to use by employing the same paradigm, tools, and procedures in various market sectors and to different systems, from facade management to BIM-based design, from construction project quality management to maintenance in an office park, from power grid analysis to drainage system management. The applicability in these different fields is demonstrated here in the Case Studies. Having been mined, cleansed, and transformed into arrays, the varied **databases** are similar: in this manuscript, we used QC faults logs loaded to a server service, in [35] we used error logs accumulated in a municipal call center, and in [37] a BIM meta database was mined. These are discipline-adjusted solutions to the same information gap. All databases of different origins share the same problems of bias, partiality, and satisfaction. The procedure overcomes those problems all the same. **Power functions** explain the stupendous number of small effect faults (Figures 18a and 19c) and the high magnitude faults of low probability (log \(x<0\)). \(\chi_{\min}\) is not bound toward zero; therefore, the magnitude of faults (\"\(y\)\") is not bound. Power functions are not symmetrical; the distance to the abscise diminishes more rapidly than the distance to the ordinate. The long tail of diminishing effect explains the negligence of quality: there is an overwhelming abundance of faults, the potential damage of defects is small, the cost of quality control is certain, and the damage is mostly calculated in, insured against, and reducible to others downstream. Construction site systems are the pinnacle of this effect; their preference is to adjust to poor quality. This preference is vindicated by the steep diminishing effect of faults (Figure 3) and by system robustness, manifested in a high tolerance to defects, defect insurance [72], compensation and litigation procedures, and a \"start-fail-flee\" strategy that is the subcontractor's recourse to incidents of high-magnitude failures [73]. Figure 6 suggest a risk in that policy: in the low-probability parts of the graph, low-quality projects are more dangerous. The magnitude of a fault with a recurrence of one in ten projects in \(a\) = 1, \(b\) = 3 project of 200 weeks (\(x\) = 1/2000) would be \(\sim\)10\({}^{10}\); for the same conditions, a better managed project of b = 1.5, the max magnitude would be \(\sim\)10\({}^{5}\). This is not what happens in actuality: there are two avenues to collapse: by avalanche or by a single event. When \(b\) > 2, there is a partial overlap of clusters (discussed next); therefore an avalanche may happen on any scale, such as in a single-element collapse, where energy is dissipated locally to the farthest limits of the cluster, not to the whole system, while for well-managed \(b\) < 2 projects, avalanches would be inflated by the magnification of the whole system to the farthest extremes of it. Moreover, avalanches are of different magnitudes: a fault causing the recall of a whole product line is an avalanche; so is a detail change in design that affects the whole design network but can be administered by a keystroke; the difference in magnitude may be decided by chance (in the above example, by the availability of a technology). The other avenue is a mega event. Perturbations must penetrate a high barrier to contest well-protected projects. Therefore, penetrating events are rare, and their magnitude may be as high as the Fukushima disaster. In less well-protected projects, a lesser-magnitude event may penetrate; therefore, smaller effects would cause a collapse before mega events have a chance at exercising the mathematical potential of disaster. Yet in O&M, when physical barriers are in place, high-magnitude and low-probability disasters happen to all. Notably, at the O&M stages, all the systems I researched had a \(b\) < 1 small-world one-cluster morphology, which explains the universality of that outcome.