Testing systems of identical components

We consider the problem of testing sequentially the components of a multi-component reliability system in order to figure out the state of the system via costly tests. In particular, systems with identical components are considered. The notion of lexicographically large binary decision trees is introduced and a heuristic algorithm based on that notion is proposed. The performance of the heuristic algorithm is demonstrated by computational results, for various classes of functions. In particular, in all 200 random cases where the underlying function is a threshold function, the proposed heuristic produces optimal solutions

Testing strategies for k-out-of-n systems under forest type precedence constraints

This thesis investigates diagnosis strategies for k-out-of–n systems under precedence constraints. A k-out-of-n system consists of n independent components whose working probabilities of are known in advance. The system itself functions if at least k components function. The true state of the system is determined by the sequentially inspection of these components. This inspection is costly and the cost of inspection for each component is also known. This study aims to minimize expected cost of determining true state of such a system when there are forest type precedence constraints. Optimal inspection strategies are already known for series and parallel systems. In this study, modifications of these strategies are proposed for k-out-of-n systems. Numerical results are presented to evaluate and compare the proposed strategies

Testing strategies for k-out-of-n systems precedence constraints

This thesis investigates diagnosis strategies for k-out-of-n systems under the general type precedence constraints. Given the testing costs and the prior working probabilities, the problem is to devise strategies that minimizes the total expected cost of finding the correct state of the system. The true state of the system is determined by sequential inspection of these n components. We try to find good strategies for the problem under general type precedence constraints by adapting an optimal algorithm that works when there are no precedence constraints. We refer to this algorithm Intersection-Precedence and represent the strategy that we obtain efficiently by a Block-Walking Diagram structure. Since no computational results are reported in the literature for this particular problem, in order to benchmark the performance of the Intersection-Precedence algorithm, we develop Tabu Search and Simulated Annealing algorithms that find permutation strategies.We conduct an extensive computational study to compare the results obtained by the alternative algorithms and we observe that Intersection- Precedence algorithm, in general, outperforms the other algorithms

Finding Optimal Derivation Strategies in Redundant Knowledge Bases

A backward chaining process uses a collection of rules to reduce a given goal to a sequence of data-base retrievals. A "derivation strategy" is an ordering on these steps, specifying when to use each rule and when to perform each retrieval. Given the costs of reductions and retrievals, and the a priori likelihood that each particular retrieval will succeed, one can compute the expected cost of any strategy, for answering a specific query from a given knowledge base. [Smi89] presents an algorithm that finds the minimal cost strategy in time (essentially) linear in the number of rules, for any disjunctive, irredundant knowledge base. This paper proves that the addition of redundancies renders this task NP-hard. Many Explanation-Based Learning systems work by adding in redundancies; this shows the complexities inherent in their task. 1 Introduction Problem solving is combinatorially expensive. There can be a combinatorial number of potential "solution paths" for a given query --- as ther..