Causal analysis on chain event graphs for reliability engineering

Various graphical models have been utilised in reliability literature to express the qualitative aspect embedded in certain hypotheses about how a system might fail. There is a wide range of research that translates domain expert beliefs to Bayesian networks (BNs), fault trees and so on [Bedford et al., 2001]. However, many conventional tree-structured analyses designed to demonstrate how systems can fail in reliability theory are not embellished with probabilities and conditional independence statements. Here we apply the Chain Event Graph (CEG) which is a probabilistic graphical model derived from an underlying event tree. This class of model retains the advantages of both events trees and BNs. So a CEG can chronologically represent sequences of events along the paths and model conditional independence. In particular, the CEG model generalises the discrete BNs. A BN can be transformed to an equivalent CEG. Compared with BNs, the class of treebased CEGs have richer semantics for representing context-specific dependencies. For example, given non-extreme weather and temperature, the failure of a system depends on the condition of sub-systems A and B. When having extreme weather, the failure of this system depends only on the temperature. This can be easily represented by a CEG, but it is non-trivial to capture the sample space structure of this scenario by a BN. I show in this thesis that these semantics are rich enough to represent the unfolding of the asymmetric failure processes or deteriorating processes and also to provide a formal framework around which to define the intervention calculus required for this domain. Over the last 40 years statistical analyses which embed causal reasoning have been shown to improve the predictive inference and the efficiency in decision making in various fields, such as economics, medicine, public health and reliability [Langseth and Portinale, 2007]. There is almost no research relevant to such analyses which use probability trees { widely used in reliability { as the foundational structural framework with which to explore putative causal hypotheses and to define appropriate causal algebras. Therefore, in Chapter 2, we demonstrate how an event tree can be customised for modelling causes of system failures. A CEG derived from this tree is then constructed which faithfully represents typical classes of model found in reliability as causal probability models. Causal algebras associated with different domains have already been successfully developed for the CEG. However we find that these are xi not usually suitable for the types of causal interventions appropriate to reliability theory. Our main contribution here is customising causal algebras for two types of domain-specific interventions { the remedial intervention and the routine intervention { with semantics of CEGs. The former is associated with maintenance performed after observing failures which fixes the root causes of the observed failures. The latter is associated with routine maintenance which is scheduled to prolong the system's lifetime and to prevent failures. We show that the manipulations in response to these domain-specific interventions can be imported into CEGs in a simple and transparent way. We can then use the developed causal algebras to study the effects of such interventions. In particular, we have been able to adapt the algorithms originally developed by Pearl [2009] to determine when certain causal effects are identifiable and produce explicit formulae for these effects as a function of these interventions bespoke to this application and the CEG representing the failure processes. Thwaites [2013] has shown that Pearl's back-door theorem [Pearl, 2009] can be extended on CEGs to identify effects of controlling an event. Here, under the two new types of intervention regime, we have more complicated types of manipulations than controlling a single event. We show that the back-door theorem can still be adapted to estimate effects of these new interventions even when data are only partially observed. Although there are confidentiality constraints that have precluded me sharing fully its contents, this thesis is informed by a dataset based on engineer reports of the failure and maintenance of electrical transformers. These documents consist of well-structured ordinary data and free texts. The free texts are informative about how engineers believe a system may fail and how the system can be repaired or restored. So we have available to us documentation of how engineers reason causally where this reasoning is encoded within the natural language descriptions. In order to automate the process of causal discovery from these free texts onto a CEG for this system, it is required to design algorithms which enable us to extract and embed these causal hypotheses from the texts. In Chapter 3, we propose a new sequence of algorithms that are able to perform this extraction and provide an innovative hierarchical framework with two levels which can be used to embed them on a CEG. The surface level registers the extracted causal events while the deeper level can be described by a causal CEG. The complexity of the analysis is increased when data is only partially observed or missing in embedding causal dependencies and making predictive inference about causal e_ects in this domain. However, we show in Chapter 4 that this issue can be successfully addressed with the bespoke causal algebras within the proposed causal framework. In Chapter 5, we show predictive inference can be improved by incorporating the causal algebras established for the remedial intervention and the routine intervention. We also design an algorithm to map free texts onto a CEG using the hierarchical framework developed in Chapter 3 and evaluate the performance of this algorithm using synthetic experimental data. In the last chapter, we give a brief discussion on possible extensions of the current work. xi