Abstract
Reliability has always been an important concern in the design of engineering systems. Recently proposed formal reliability analysis techniques have been able to overcome the accuracy limitations of traditional simulation based techniques but can only handle problems involving discrete random variables. In this paper, we extend the capabilities of existing theorem proving based reliability analysis by formalizing several important statistical properties of continuous random variables, for example, the second moment and the variance. We also formalize commonly used reliability theory concepts of survival function and hazard rate. With these extensions, it is now possible to formally reason about important reliability measures associated with the life of a system, for example, the probability of failure and the mean-time-to-failure of the system operating in an uncertain and harsh environment, which is usually continuous in nature. We illustrate the modeling and verification process with the help of an example involving the reliability analysis of electronic system components.
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
Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model Checking Algorithms for Continuous time Markov Chains. IEEE Transactions on Software Engineering 29(4), 524–541 (2003)
Broughton, E.: The Bhopal Disaster and its Aftermath: A Review. Environmental Health 4(6), 1–6 (2005)
Coble, A.: Anonymity, Information and Machine-assisted Proof. PhD Thesis, University of Cambridge, Cambridge, UK (2009)
Dean, S.M.: Considerations involved in making system investments for improved service reliability. EEI Bulletin (6), 491–496 (1938)
U. S. Department of Defence. Reliability Prediction of Electronic Equipment, Military handbook, MIL-HDBK-217B (1974)
U. S. Department of Defense. Reliability-Centered Maintenance (RCM) Requirements for Naval Aircraft, Weapon Systems, and Support Equipment, MIL-HDBK-2173 (1998)
FIDES. Reliability Methodology for Electronic Systems (2009)
Gordon, M.J.C., Melham, T.F.: Introduction to HOL: A Theorem Proving Environment for Higher-Order Logic. Cambridge University Press, Cambridge (1993)
Hasan, O.: Formal Probabilistic Analysis using Theorem Proving. PhD Thesis, Concordia University, Montreal, QC, Canada (2008)
Hasan, O., Abbasi, N., Akbarpour, B., Tahar, S., Akbarpour, R.: Formal Reasoning about Expectation Properties for Continuous Random Variables. In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 435–450. Springer, Heidelberg (2009)
Hasan, O., Tahar, S., Abbasi, N.: Formal Reliability Analysis using Theorem Proving. IEEE Transactions on Computers 59(5), 579–592 (2010)
Hurd, J.: Formal Verification of Probabilistic Algorithms. PhD Thesis, University of Cambridge, Cambridge, UK (2002)
Investigative Documentary on National Geographic Channel. Derailment at Eschede (High Speed Train Wreck), Seconds From Disaster (2007)
Leemis, L.M.: Reliability, Probabilistic Models and Statistical Methods (2009)
Mhamdi, T., Hasan, O., Tahar, S.: On the Formalization of the Lebesgue Integration Theory in HOL. In: Interactive Theorem Proving. LNCS, vol. 6172, pp. 387–402. Springer, Heidelberg (2010)
Myers, R.H., Ball, L.W.: Reliability Engineering for Electronic Systems. Wiley, Chichester (1964)
Institute of Electrical and Electronics Engineers. IEEE Standard Reliability Program for the Development and Production of Electronic Systems and Equipment, IEEE 1332 (1998)
Rogers Commission report, Report of the Presidential Commission on the Space Shuttle Challenger Accident, vol. 1, ch.4. p. 72 (1986), http://history.nasa.gov/rogersrep/v1ch4.htm
Rutten, J., Kwaiatkowska, M., Normal, G., Parker, D.: Mathematical Techniques for Analyzing Concurrent and Probabilisitc Systems. CRM Monograph Series, vol. 23. American Mathematical Society, Providence (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Abbasi, N., Hasan, O., Tahar, S. (2010). Formal Lifetime Reliability Analysis Using Continuous Random Variables. In: Dawar, A., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2010. Lecture Notes in Computer Science(), vol 6188. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13824-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-13824-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13823-2
Online ISBN: 978-3-642-13824-9
eBook Packages: Computer ScienceComputer Science (R0)