Assumptions, beliefs and probabilities
Artificial Intelligence
Performance and reliability analysis of computer systems: an example-based approach using the SHARPE software package
Mathematical foundations of evidence theory: a theory of reasoning with uncertain arguments
Mathematical models for handling partial knowledge in artificial intelligence
A generalization of the algorithm of Heidtmann to non-monotone formulas
Journal of Computational and Applied Mathematics
Distributed Computing Network Reliability
Distributed Computing Network Reliability
Analysis of Noncoherent Systems and an Architecture for the Computation of the System Reliability
IEEE Transactions on Computers
CAREL: Computer Aided Reliability Evaluator for Distributed Computing Networks
IEEE Transactions on Parallel and Distributed Systems
Temporal Logic Applied to Reliability Modelling of Fault-Tolerant Systems
Proceedings of the Second International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems
An Improved Multiple Variable Inversion Algorithm for Reliability Calculation
TOOLS '98 Proceedings of the 10th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Using probabilistic argumentation for key validation in public-key cryptography
International Journal of Approximate Reasoning
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The evaluation of system reliability and safety is important for the design of new systems and the improvement or further development of existing systems. Especially the probability that a systems operates (safely) using the probabilities that its components operate is a vital system characteristic and its computation is a non-trivial task. The most often used method to solve this problem is to derive disjoint events from the description of the system structure and to sum up the probabilities of these disjoint events to quantify system reliability or safety. To compute disjoint products as logical representation of disjoint events Abraham's algorithm inverts single variables indicating the state of a component and therefor produces a huge number of disjoint products. To avoid this disadvantage Heidtmann developed a new method which inverts multiple variables at once and results in a much smaller number of disjoint products as confirmed by some examples. This paper quantifies this advantage by statistical methods and statistical characteristics for both algorithms presenting measurements of the number of produced disjoint products and the computation time of both algorithms for a large sample of randomly generated systems. These empirical values are used to investigate the efficiency of both algorithms by statistical means showing that the difference between both algorithm grows exponentially with system size and that Heidtmanns method is significantly superior. The results were obtained using our Java tool for system reliability and safety computation which is available in the WWW.