Weighted dependency trees (WDTs) are used in a multitude of approaches to system analysis, such as fault tree analysis or event tree analysis. In fact, any acyclic graph can be transformed to a WDT. Important decisions are often based on WDT analysis. Common for all WDT-based approaches is the inherent uncertainty due to lack or inaccuracy of the input data. In order to indicate credibility of such WDT analysis, uncertainty handling is essential. There is however, to our knowledge, no comprehensive evaluation of the uncertainty handling approaches in the context of the WDTs. This chapter aims to rectify this. We concentrate on approaches applicable for epistemic uncertainty related to empirical input. The existing and the potentially useful approaches are identified through a systematic literature review. The approaches are then outlined and evaluated at a high-level, before a restricted set undergoes a more detailed evaluation based on a set of pre-defined evaluation criteria. We argue that the epistemic uncertainty is better suited for possibilistic uncertainty representations than the probabilistic ones. The results indicate that precision, expressiveness, predictive accuracy, scalability on real-life systems, and comprehensibility are among the properties which differentiate the approaches. The selection of a preferred approach should depend on the degree of need for certain properties relative to others, given the context. The right trade off is particularly important when the input is based on both expert judgments and measurements. The chapter may serve as a roadmap for examining the uncertainty handling approaches, or as a resource for identifying the adequate one.
TopIntroduction
WDTs are widely used in approaches to system analysis. WDTs are used as a means to understand some artifact, e.g. a system and to make informed decisions regarding its future behaviour. Examples include:
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fault tree analysis (IEC, 2006) – a risk analysis technique based on so-called fault trees;
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event tree analysis (IEC, 1995) – a modeling technique for representing consequences of an event and the probabilities of the respective consequences;
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attack trees (Schneier, 1999) – a notation similar to fault tree analysis for modeling potential attacks on a system with an attack goal as the top node and different ways of achieving that goal as leaf nodes; and
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dependency views in system quality prediction (Omerovic, et al., 2010).
Common for all approaches supported by WDTs is the inherent uncertainty due to lack or inaccuracy of input data. The input data originates from two kinds of sources: expert-judgments-based and measurement-based data acquisition (such as logs, monitoring, experience factories and other measurements). Uncertainty regarding input data (due to for example lack of knowledge, as well as variability or poor quality of the measurement-based data) can lead to errors in relation to both modeling and analysis.
Apart from lack or inaccuracy of input, another source of the uncertainty may be the variability of the system or its usage. However, in this chapter we restrict our attention to artifacts, e.g. systems, whose behavior is deterministic, for which the former type of uncertainty is the only prevailing one. Consequently, we only focus on deterministic uncertainty handling.
Important decisions are made during and after a WDT-based analysis. The ability of explicitly expressing uncertainty in the input and its implications on the rest of the model is crucial due to the consequences of the input uncertainty in the decision making. The uncertain input may have extensive impact on the rest of the WDT-based model. In worst case, decisions involving unacceptable risk may be taken, without the awareness of the analyst. There are numerous approaches to uncertainty handling. Each of them is motivated by a special need not covered by the competing ones. Their properties such as complexity, expressiveness, propagation and generally the practical applicability vary to a high extent. It is however unclear to what degree the existing approaches are suitable for being adopted for use on WDTs. We have not been able to find a comprehensive evaluation of the uncertainty handling approaches in the context of the WDTs.
The overall objective of this chapter is therefore to identify and evaluate the existing and the potentially useful approaches that could, individually or in combination, be adopted for handling the uncertainty in WDTs. This includes:
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identification of the established approaches for uncertainty representation, based on a literature review;
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a high-level evaluation of the identified approaches with respect to the main needs; and
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a low-level evaluation of a restricted set of the approaches which are assessed as potentially useful during the high-level evaluation.
The chapter is structured as follows: “Weighted dependency trees and uncertainty” provides background on the notion of WDT and the issue of uncertainty. The research method is then presented in a section titled “The research method”. Next, a section titled “The evaluation criteria” presents the evaluation criteria, with respect to the practical acceptability of the uncertainty handling approaches. The section titled “The high-level evaluation” reports on the high-level evaluation of the approaches identified, while the section titled “The low-level evaluation” presents the results of a more detailed evaluation of the selected approaches. Finally, we discuss our findings and provide our main conclusions in the section titled “Conclusion”. Furthermore, there are three appendices providing background on the literature review, the detailed deduction of the evaluation criteria, and threats to validity and reliability, respectively.