Diagnosis of Ambiguous Faults in Simple Networks

We propose a theory of how individuals diagnose faults, and we report two experiments that tested its application to the diagnosis of faults in simple Boolean systems. Participants were presented with simple network diagrams in which a signal was transmitted from a set of input nodes to an output node, via a set of connecting nodes. Their task was to detect and diagnose faults. Experiment 1 showed that individuals tend to diagnose events closest to an observed inconsistency as the cause of the fault. Experiment 2 replicated this proximal effect, but also demonstrated that participants tend to target the proximal node most often when it fails to transmit a signal. This phenomenon may occur because individuals construct models of those situations in which a node works, but leave implicit those situations in which it does not work. The present results extend the mental model theory to diagnostic reasoning. How do individuals diagnose faults in simple systems? If something goes wrong, what guides their initial hypotheses about the cause of the fault? In this paper we propose a theory that explains the diagnosis of faults in simple Boolean networks, and we report experimental tests of the theory. The theory assumes that individuals diagnose faults by mentally simulating the network in a dynamic mental model (see Johnson-Laird, 1983). It postulates three main principles for diagnosis. First, individuals assume that causes of faults occur prior to the fault and as close to it as possible. Hence, they should locate faults as close as possible to the output of a network. We refer to this sort of diagnosis as a “proximal” bias, i.e., the proximal cause is the event that occurs nearest to the effect. Second, individuals should be more likely to diagnose faults in the proximal node when it ought to transmit a signal than when it ought not to. Third, individuals assume by default that complex components are more likely to go wrong than simple components. One index of complexity is the ease of understanding how a component works. Prior research has investigated fault finding in network tasks (see e.g., Morrison & Duncan, 1988; Rouse, 1978; Rouse & Rouse, 1979). Participants were presented with a matrix of nodes, connected in a variety of different ways. A set of input nodes was connected by intermediary nodes to a set of output nodes. Typically, the networks consisted of a matrix of about 49 nodes (7 by 7). The input nodes each transmitted a signal through the system, and in the basic form of the task, each connecting node acted as an AND operator, i.e., in order for it to transmit a signal, it had to receive activation from every one of its input nodes. Faults were failures in one or more output nodes to yield a signal. The participants’ task was to locate the cause of a fault by performing tests on single connections between pairs of nodes. They needed to find the single faulty node that accounted for all and only the observed output failures. These studies showed that several factors increased the difficulty of the task, but they did not reveal much about the initial generation of hypotheses to explain the faults. In order to investigate this process, we adopted a modified version of the network task. Our networks were much simpler than those previously investigated: they had only six nodes (Experiment 1) or seven nodes (Experiment 2), and only a single output node. We allowed that the connecting nodes could be one of three sorts of Boolean operator – AND, OR, and OR ELSE. And the participants were not required to determine the cause of the fault definitively, but only to formulate a preliminary hypothesis about what to investigate first in the network in order to find the fault.