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Testing complex systems, such as the ASML TWINSCAN lithographic machine, is expensive and time consuming. In a previous work, a test sequencing method to calculate time-optimal test sequences has been developed. Because complex systems are composed of several subsystems, which are again composed of several modules, there exists a need to hierarchically model test sequencing problems. Such a hierarchical test sequencing problem consists of a high-level model that describes a test sequencing problem at the system level, and one or more low-level models that describe the test sequencing problems at the subsystem or module level. The tests at the system level correspond to the solutions of low-level problems. This paper describes a hierarchical test sequencing model and proposes two algorithms to compute an optimal test sequence. The benefits of hierarchically modeling a problem are less computational effort and less modeling effort, because not all relations are needed. This is illustrated by a small example. The industrial relevance of this method is illustrated on a case study related to a manufacturing testing phase of a lithographic machine. Index Terms--Hierarchical test sequencing, manufacturing systems, semiconductor manufacturing industry, Tangram, test strategy.

In this paper the track initiation problem is formulated as multiple composite hypothesis testing using maximum likelihood estimation with probabilistic data association (ML-PDA). The hypothesis selection is based on the minimum description length (MDL) criterion. We first review some well-known approaches for statistical model selection and the advantage of the MDL criterion. Then we present one-dimensional examples to illustrate the MDL criterion used in multiple composite hypothesis testing and the performance limit of the ML-PDA for track initiation is interpreted in terms of the sharpness of the hypothesis testing. Finally, we apply the MDL approach for the detection and initiation of tracks of incoming tactical ballistic missiles in the exo-atmospheric phase using a surface-based electronically scanned array (ESA) radar. The targets are characterized by low signal-to-noise ratio (SNR), which leads to low detection probability and high false alarm rate. The target acquisition problem is formulated using a batch of radar scans to detect the presence of up to two targets. The ML-PDA estimator is used to initiate the tracks assuming the target trajectories follow a deterministic state propagation. The approximate MDL criterion is used to determine the number of valid tracks in a surveillance region. The detector and estimator are shown to be effective even at 4.4 dB average SNR.

We consider a multilevel hierarchical decision network faced with a distributed binary detection problem with partial information at the individual decisionmaker (DM). The partial information is modeled by different local events at the DM's, and these local events are probabilistically related to one another. Solution to this generalized hypothesis testing problem is obtained using the optimal control approach, where the optimization criterion is the expected decision cost of the network. The impacts of variations in the correlation of events at two communicating nodes on the aggregated expertise of the network and on the overall decision cost are illustrated via a numerical example.

This paper considers a hierarchical team faced with a binary detection problem, wherein decision makers (DM's) have access to different subsets of noise-corrupted information about the true state of the environment. A normative model is developed that aggregates individual expertise of DM's at different levels of hierarchy. The resulting team expertise is characterized in the form of a Team Receiver Operating Characteristic (ROC) curve, thereby replacing the team by an equivalent single decision-making node. The normative model is tested against human teams in a laboratory experiment. The team objective is to minimize the cost of errors in the final decision at the primary DM, where the cost structure and the information structure are treated as independent variables. Discrepancies between normative predictions and experimental results are attributed to inherent limitations and cognitive biases of humans. These human characteristics are quantified and the normative model is augmented with psychologically interpretable (descriptive) factors. The resulting normative-descriptive model yields accurate predictions of both the performance and strategy variables of human teams.

A distributed binary detection problem with multimessage (greater than or equal to 1 bit) communications is considered, wherein the nodes (sensors, decision makers (DMs)) of the system are organized in the form of a tree with multiple root nodes. A numerical algorithm is developed for determining the optimal decision rule at each node assuming monotone cost functions imposed only on the root nodes. It is assumed that the observations of each node are conditionally independent of those of the other nodes. It is shown that the problem is equivalent to solving a nonlinear optimal control problem, and the necessary conditions of optimality using Bayes' risk as the optimization criterion are derived. The optimal control approach provides an interpretation of certain functions of the co-state variables in terms of thresholds, and leads to a computationally efficient min-H algorithm to solve for the optimal decision rule at each node. The numerical algorithm provides a tool to investigate the organizational issues of adaptation, structure, and robustness.

In this paper we present a new technique for data association using multiassignment for tracking a large number of closely spaced (and overlapping) objects. The algorithm is illustrated on a biomedical problem, namely the tracking of a group of fibroblast (tissue) cells from an image sequence, which motivated this work. Because of their proximity to one another and due to the difficulties in segmenting the images accurately from a poor-quality image sequence, the cells are effectively closely spaced objects (CSOs). The algorithm presents a novel dichotomous, iterated approach to multiassignment using successive one-to-one assignments of decreasing size with modified costs. The cost functions, which are adjusted depending on the 'depth' of the current assignment level and on the tracking results, are derived. The resulting assignments are used to form, maintain and terminate tracks with a modified version of the probabilistic data association (PDA) filter, which can handle the contention for a single measurement among multiple tracks in addition to the association of multiple measurements to a single track. Estimation results are given and compared with those of the standard 2-dimensional one-to-one assignment algorithm. It is shown that iterated multiassignment results in superior measurement-to-track association. The algorithms presented here can be used for other general tracking problems, including dense air traffic surveillance and control.