# Anticipatory Troubleshooting
## 7 Related Work  
There are several lines of work that are related to this research. We discuss them below. Probing and testing are well-studied diagnostic actions that are often part of the troubleshooting process. Intuitively, one would like to seek for the most informative observations and actions while doing the troubleshooting process. Probes enable one to observe the outputs of internal components, and tests enable further information, such as observing system output. Placing probes and performing tests can be very expensive. The basic idea is that not all probing and test choices are equal. Using this technique requires considerations, such as probe placement and which tests to choose. Those aspects have been studied over the years, and are also known as sequential diagnosis [17; 22; 26; 27; 28]. Most works use techniques such as greedy heuristics and information gain; e.g., measuring  
Figure 9: Long-term costs as a function of the overhead ratio. Evaluating the \(N\text{-}MDP_{RepHeal}\) algorithm. the amount of information that observation \(Y\) tells us about the diagnosis state \(X\). Some researchers present locally optimal solutions that run in linear time [28; 29; 30]. [PERSON] [29] proposes to use active learning techniques in order to achieve a nearly optimal sequence of queries. It should be noted that there are techniques that concentrate on saving system tests (e.g., a test that shows whether the system returned to its healthy state) and therefore consider batch repair in a period of time [6; 31] rather than fix one component in each iteration [3]. Many papers on automated troubleshooting are based on the seminal work of [PERSON] et al. [3] on decision theoretic troubleshooting (DTT). Our paper can be viewed as a generalization of DTT by taking prognosis into consideration. A decision theoretic approach integrates planning and diagnosis to a real-world troubleshooting application [32; 33]. In their setting, a sequence of actions may be needed to perform repairs. For example, a vehicle may need to be disassembled to gain access to its internal parts. To address this problem, they use a Bayesian network for diagnosis and the AO* algorithm [34] as the planner. [PERSON] and [PERSON] [35] propose a troubleshooting algorithm aimed at minimizing the breakdown costs, a concept that corresponds roughly to a penalty incurred for every faulty output in the system and for every time step until the system is fixed. [PERSON] and [PERSON] [32] consider future repair actions using expected cost of repair and heuristic functions. They use a Bayesian network as the MBD and update the current belief state after each iteration. [PERSON] and [PERSON] [36] also used two \"repair\" actions, but they do not use the prognostic information to decide which repair action to perform. Additionally, they did not use survival curves, but rather a dynamic Bayesian network which was unfolded to take time into consideration. The novelty of our work is three-fold. First, none of these previous works incorporated prognosis estimates into the troubleshooting algorithm (as we did in Section 3.2). Second, none of these previous works integrated prognosis estimates into a troubleshooting algorithm that aims at improving decision making when repairing the current fault, as we did. Finally, none of these works considered the dilemmas we present in this paper. Our anticipatory troubleshooting model and algorithm directly attempt to minimize costs incurred due to current and future failures through considering which repair action to take in each time step. Our goal is to minimize repair costs incurred through the lifetime of the system until a time threshold \(T\) is reached. A related line of work is in prognostics, where diagnostic information is used to provide more accurate remaining useful life estimations [37; 38; 39]. In this research we used survival functions to improve the expected costs of repairing future system failures.