# Theory of Faults (ToF): Numerical Quality Management in Complex Systems
## 1 Introduction
However, it should be noted that notwithstanding our efforts, these are partial information systems we are deciphering, not the world. In this manuscript, the distinctions between design information systems, subsystems such as site management info-systems, and physical systems are blurred. The data gap stems from limitations in data availability and bias. The **gap** in the availability of reliable **data** is associated in part with an intentional concealment of data due to risks of liability, responsibility allocation, and prestige, and in part it is related to systemic bias [13]. Even the quantity of faults reported in the literature [14] is inconsistent, whether owing to segmentation mismatches or intrinsic unreliability [15]. To address this gap, we used fault databases generated by QC. The second gap is an epistemic **gap** in understanding [16]. The origin and inception of construction faults are poorly understood [17]. The literature suggests an **information**-related epistemological origin to faults [18; 19]. A bank of literature suggests information overload as a cause of faults [20; 21]. These suggestions do not provide an understanding of the mechanisms of the creation, inflation, or propagation of faults. The literature does not offer specific suggestions for operative means [22]. The gap in understanding and the need for implementable operative means motivate ToF and this manuscript. In this manuscript, we develop an information-based theoretical framework to address the second gap and enable the use of fault databases to address the first gap. The conceptual framework emerges from an observation made in the literature: infosystems have a capacity limit (termed here an information constraint, **IC**). The IC is, therefore, a threshold of stability; past that threshold, systems avalanche. Putting it differently, complex systems with an IC are threshold phenomena. This threshold was validated here in Case Study 1. The literature suggests that complex systems self-organize at a threshold of stability (SOC = self-organizing criticality) [23]; in the context of CISs, this suggestion was refuted here. These systems are better modeled as complex dissipative systems [24]; these are open systems that exchange materials, energy, and entropy with the environment; those systems are not at equilibrium but rather seek stability in steady-state dissipative structures [25]. Systems are modeled here as information networks. Networks may be geospatial, model, or logical [26], yet all adjacencies are information adjacencies; the use of info-systems simplifies the exposition; all networks are but different presentations of the same phenomena. Networks with a power function degree distribution morphology are scale-free [27]; therefore, these networks are scale-free. Scale-free networks are a product of preferential attachment and the above-mentioned WBS, recursive and iterative work/rework processes, and social behaviors that generate preferential attachment, such as rank and bridges, portrayed here. Another observation made in the literature is that the influencing factors that direct systems' responses are within Internal Variable Theory (IVT [28]); IVT stipulates that these factors are local variables; some are unknown, some produce only fuzzy information [29], and some are elucidated here by numerical experiments and simulations. Added to this are the effects of control signals that magnify the data load. We applied DSP (digital signal processing) theory to investigate these effects in numerical experiments. **Preventive Means** are the sum effects of barriers: physical and normative protections, such as power breakers and their O&M; QC such as in its capacity of reporting faulty execution; test labs blocking bad materials; praxis such as foreman supervision; and BCBs (building control bodies) blocking design errors. Together, the normative means are here termed \"the **Via Trita**\". Case Study 2 presents events that develop following a stray from the Via Trita. **Corrective means** are applied to barriers.