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In stopping problems, the decision maker receives a sequence of candidates and decides whether to select the current candidate and thereby stop the search or whether to continue surveying. Some examples include searching for an apartment, selecting an employee for a job, or choosing a new product or service from a sequence of vendors. Most of the literature on stopping problems assumes that the decision maker can perfectly evaluate the candidate when surveyed. We consider practical variations where surveying a candidate may provide no further information or imperfect information about its value. We show how the stopping problem can be considered an extension of the two-action (go/no-go) problem and present threshold optimal policies for the general problem. For the case where surveying candidates provides no further information and the uncertain values of candidates are normally distributed, we present analytical results that highlight how the value of information is affected by the parameters. With the help of an illustrative example, we demonstrate how a model that ignores sequential decisions could potentially severely underestimate the value of information. We also present a data-driven application of our results by studying the value of reports to a potential used car buyer.

Reliability block diagrams (RBDs) depict the functional relationships between components comprising a system, whereas Bayesian networks (BNs) represent probabilistic relationships between uncertain variables. Previous research has described how one can transform an RBD into a BN. In parallel, developments in the artificial intelligence literature have shown how a BN can be transformed into another graphical representation, an arithmetic circuit, which can subsequently be used for efficient inference. In this paper, we introduce a new graphical representation that we call a fault tree circuit, which is a special kind of arithmetic circuit constructed specifically for an RBD. A fault tree circuit can be constructed directly from an RBD and is more efficient than an arithmetic circuit that is compiled from the BN corresponding to that RBD. We develop several methods for fault tree circuits, highlighting how they can aid the analyst in efficient diagnosis, sensitivity analysis, and decision support for many typical reliability problems. The circuit framework can complement tools that are popular in the reliability analysis community. We use a simple pump system example to illustrate the concepts.