The paper describes the task of performing efficient decision-theoretic troubleshooting of electromechanical devices. In general, this task is NP-complete, but under fairly strict assumptions, a greedy approach will yield an optimal sequence of actions, as discussed in the paper. This set of assumptions is weaker than the set proposed by Heckerman et al. (1995). However, the printing system domain, which motivated the research and which is described in detail in the paper, does not meet the requirements for the greedy approach, and a heuristic method is used. The method takes value of identification of the fault into account and it also performs a partial two-step look-ahead analysis. We compare the results of the heuristic method with optimal sequences of actions, and find only minor differences between the two.

Troubleshooting is one of the areas where Bayesian networks are successfully applied [9]. In this paper we show that the generally defined troubleshooting task is NP-hard. We propose a heuristic function that exploits the conditional independence of all actions and questions given the fault of the device. It can be used as a lower bound of the expected cost of repair in heuristic algorithms searching an optimal troubleshooting strategy. In the paper we describe two such algorithms: the depth first search algorithm with pruning and the AO * algorithm.

The goal of troubleshooting is to find an optimal solution strategy consisting of actions and observations for repairing a device. We assume a probabilistic model of dependence between possible faults, actions, and observations; the goal is to minimize the expected cost of repair (ECR). We show that the task of finding an optimal solution strategy is NP hard for various troubleshooting models; therefore, approximate algorithms are necessary.

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Standard methods for solving influence diagrams consist in stepwise elimination of variables, and along with elimination of a variable a set of new potentials over new domains is calculated. It is well known that these methods tend to produce unnecessarily large domains resulting in excessive consumption of time and memory. The lazy evaluation method represents only a partial solution to the problem. In this paper we extend any potential with two graphs over its domain representing the dependencies of variables. When a node A is eliminated, all necessary structural information for establishing the minimal sets of domains for potentials is contained in these graphs. We push lazy evaluation a step further to avoid performing unnecessary multiplications and subsequent division with equivalent potentials.