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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abraham J.A., An improved algorithm for network reliability, IEEE Trans. Reliability Vol. 28,No. 1, 1979 58–61, also in: [RaA90], 89-92
Almasi B., Bolch G., Sztrik J., Modeling Terminal Systems using MOSEL, Proc. Europ. Simulation Symp. ESS’99, Erlangen, Germany, 1999
Anders J.M., Methods for the reliability analysis of complex binary systems, PhD thesis, Dept. Mathematics, Humboldt-University, Berlin, 1992
Barlow R.E., Heidtmann K.D., Computing k-out-of-n system reliability, IEEE Trans. Reliability, 33,3, 1984
Besnard P., Kohlas J., Evidence Theory based on general consequence relations, Intern. J. Foundation of Computer Science 6, 1995, 119–135
Bertschy R., Monney P.A., A generalization of the algorithm of Heidtmann to non-monotone formulas, J. of Computational and Applied Mathematics, Dec 1996, Vol. 76,No. 1–2, 55–76
Chatelet E., Dutuit Y., Rauzy A., Bouhoufani T., An optimized procedure to generate sums of disjoint products, Reliability Engineering and System Safety, Sept. 1999, Vol. 65,No. 3, 289–294
Heidtmann K.D., A class of noncoherent systems and their reliability analysis, Dig. 11th Ann. Intern. Symp. Fault-Tolerant Computing, FTCS 11, Portland/USA, 1981
Heidtmann K.D., Minset splitting for improved reliability computation, IEEE Trans. Reliability 35,5, 1986
Heidtmann K.D., Smaller sums of disjoint products by subproduct inversion, IEEE Trans. Reliability 38,3, 1989, 305–311
Heidtmann K.D., Temporal Logic applied to reliability modeling of fault-tolerant systems, Proc. 2nd Intern. Symp. Formal Techniques in Real-Time and Fault-Tolerant Systems, Nijmegen/Netherlands, 1992, in: Vytopil J., Lecture Notes in Computer Science, No. 571, Springer, Berlin, 1991
Heidtmann K.D., Deterministic reliability modeling of dynamic redundancy, IEEE Trans. Reliability 41,3, 1992, 378–385
Heidtmann K.D., Methoden zur Zuverlässigkeitsanalyse unter besonderer Berücksichtigung von Rechnernetzen (Methods for reliability analysis with special emphasis on computer communication networks), Habilitationsschrift, Dept. Comp. Science, Hamburg University, 1995 (in german)
Heidtmann K.D., Zuverlässigkeitsbewertung technischer Systeme (Reliability analysis of technical systems), Teubner, Stuttgart, 1997 (in german)
Herold H., MOSEL, An Universal Language for Modeling Computer, Communication, and Manufacturing Systems, PhD Thesis, Techn. Faculty, University Eralngen, 2000
Mathematical foundations of evidence theory, in: Coletti G., Dubois D., Scozzafa R., (Eds.), Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, Plenum Press, New York, 1995, 31–64
Kohlas J., Monney P.A., A Mathematical Theory of Hints, An Approach to the Dempster-Shafer Theory of Evidence, Lecture Notes in Economics and Mathematical Systems Vol. 425, Springer, Berlin, 1995
Laskey K.B., Lehner P.E., Assumptions, belief and probabilities, Artificial Intelligence 41, 1989, 65–77
Luo T., Trivedi K.S., An improved multiple variable inversion algorithm for reliability calculation, 10th Intern. Conf. Tools’98, Palma de Mallorca, Spain, Sept. 1998, in: Puigjaner R., Savino N.N., Serra B. (eds.), Computer Performance Evaluation, Modeling Techniques and Tools, Springer, 1998
Luo T., Trivedi K.S., An improved algorithm for coherent-system reliability, IEEE Trans. Reliability, March 1998, Vol. 47,No. 1, 73–78
Luo T., Trivedi K.S., Using Multiple Inversion Techniques to Analyze Fault-trees with Inversion Gates, 28Th Ann. Fault Tolerant Computing Symp., FTCS 98, Munich 1998
Misra K.B., New trends in system reliability evaluation, Elsevier Publishers, 1993
Puliafito A., Tomarchio O, Vita L., Porting SHARPE on the Web, Proc. TOOL’97, Saint Malo, June 1997
Rai S., Agrawal D.P., Distributed Computing Network Reliability, IEEE Computer Society Press, Washington, 1990
Rushdi A.M., Efficient computation of k-to-l-out-of-n systems, Reliability Engineering 17, 1987, 157–163
Rai S., Veeraraghavan, Trivedi K.S., A Survey of Efficient Reliability Computation Using Disjoint Products Approach, Networks 25,3, 1995, 147–163
Soh S., Rai S., CAREL: computer aided reliability estimator for distributed computing networks, IEEE Trans. Parallel and Distributed Systems 2,2, 1991, 199–213
Sahner R., Trivedi K.S., Puliafito A., Performance and Reliability Analysis of Computer Systems — An Example Based Approach Using SHARPE Software Package, Kluwer Academic Publishers, Massachussetts, 1995
Tsuchiya T., Kajikawa T., Kikuno T., Parallelizing SDP (Sum of Disjoint Products) Algorithms for fast reliability analysis, IEICE Trans. Inf. & Syst., Vol. E83,No. 5, May 2000, 1183–1186
Trivedi K.S., Malhotra M., Reliability and Performability Techniques and Tools: A Survey Proc. 7th ITG/GI Conf. Measurement, Modelling and Evaluation of Computer and Communication Systems, Aachen University of Technology, 1993, 27–48
Upadhyaya, Pham, Analysis of a class of noncoherent systems and an architecture for the computation of the system reliability, IEEE Trans. Computers 42,4, 1993
Vahl A. Reliability Assessment of Complex System Structures — A Software Tool for Design Support, Proc. 9th Symp. Quality and Reliability in Electronics, Relectronic’95, Budapest, 1995, 161–166
Vahl A., Interaktive Zuverlässigkeitsanalyse von Flugzeug-Systemarchitekturen, PhD Thesis, Technical University Hamburg-Harburg, Flugzeug-Systemtechnik, VDI-Verlag, Düsseldorf, 1998 (in german)
Veeraraghavan and Trivedi K.S., An improved algorithm for the symbolic reliability Analysis of Networks," IEEE Trans. on Reliability, Vol. 40,No. 3, Aug. 1991, 347–358
Ma Yue, Trivedi K.S., An algorithm for reliability analysis of phased mission systems, Intern. Symposium on Software Reliability Engineering, ISSRE 1998
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-45732-1_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44157-1
Online ISBN: 978-3-540-45732-9
eBook Packages: Springer Book Archive