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Statistical Comparison of Two Sum-of-Disjoint-Product Algorithms for Reliability and Safety Evaluation

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Computer Safety, Reliability and Security (SAFECOMP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2434))

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Abstract

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 nontrivial 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.

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Author information

Authors and Affiliations

  1. Departement of Computer Science, Hamburg University, Vogt-Kölln-Str. 30, D-22527, Hamburg, Germany

    Klaus Heidtmann

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  1. Klaus Heidtmann
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Editor information

Editors and Affiliations

  1. LFCS, Division of Informatics, The University of Edinburgh, Mayfield Road, EH9 3JZ, Edinburgh, UK

    Stuart Anderson  & Massimo Felici  & 

  2. ENEA CR Casaccia, Via Anguillarese, 301, 00060, Rome, Italy

    Sandro Bologna

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© 2002 Springer-Verlag Berlin Heidelberg

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Heidtmann, K. (2002). Statistical Comparison of Two Sum-of-Disjoint-Product Algorithms for Reliability and Safety Evaluation. In: Anderson, S., Felici, M., Bologna, S. (eds) Computer Safety, Reliability and Security. SAFECOMP 2002. Lecture Notes in Computer Science, vol 2434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45732-1_9

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  • DOI: https://doi.org/10.1007/3-540-45732-1_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44157-1

  • Online ISBN: 978-3-540-45732-9

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