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See detailSequential testing of k-out-of-n systems with imperfect tests
Wenchao, Wei; Coolen, Kris ULg; Talla Nobibon, Fabrice et al

E-print/Working paper (2015)

A k-out-of-n system configuration requires that, for the overall system to be functional, at least k out of the total of n components be working. We consider the problem of sequentially testing the ... [more ▼]

A k-out-of-n system configuration requires that, for the overall system to be functional, at least k out of the total of n components be working. We consider the problem of sequentially testing the components of a k-out-of-n system in order to learn the state of the system, when the tests are costly and when the individual component tests are imperfect, which means that a test can identify a component as working when in reality it is down, and vice versa. Each component is tested at most once. Since tests are imperfect, even when all components are tested the state of the system is not necessarily known with certainty, and so reaching a lower bound on the probability of correctness of the system state is used as a stopping criterion for the inspection. We define different classes of inspection policies and we examine global optimality of each of the classes. We find that a globally optimal policy for diagnosing k-out-of-n systems with imperfect tests can be found in polynomial time when the predictive error probabilities are the same for all the components. Of the three policy classes studied, the dominant policies always contain a global optimum, while elementary policies are compact in representation. The newly introduced class of so-called `interrupted block-walking' policies combines these merits of global optimality and of compactness. [less ▲]

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See detailPROJECT SCHEDULING WITH MODULAR PROJECT COMPLETION ON A BOTTLENECK RESOURCE
Coolen, Kris; Wenchao, Wei; Talla Nobibon, Fabrice ULg et al

Report (2011)

In this paper, we model a research-and-development project as consisting of several modules, with each module containing one or more activities. We examine how to schedule the activities of such a project ... [more ▼]

In this paper, we model a research-and-development project as consisting of several modules, with each module containing one or more activities. We examine how to schedule the activities of such a project in order to maximize the expected profit when the activities have a probability of failure and when an activity’s failure can cause its module and thereby the overall project to fail. A module succeeds when at least one of its constituent activities is successfully executed. All activities are scheduled on a scarce resource that is modeled as a single machine. We describe various policy classes, establish the relationship between the classes, develop exact algorithms to optimize over two different classes (one dynamic program and one branch-and-bound algorithm), and examine the computational performance of the algorithms on two randomly generated instance sets. [less ▲]

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