Survey of software tools for evaluating reliability, availability, and serviceability
ACM Computing Surveys (CSUR)
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
A compositional approach to performance modelling
A compositional approach to performance modelling
METASAN: a performability evaluation tool based on stochastic activity networks
ACM '86 Proceedings of 1986 ACM Fall joint computer conference
On the accuracy of MANET simulators
Proceedings of the second ACM international workshop on Principles of mobile computing
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Circuit Level Reliability Analysis of Cu Interconnects
ISQED '04 Proceedings of the 5th International Symposium on Quality Electronic Design
Experimental evaluation of wireless simulation assumptions
MSWiM '04 Proceedings of the 7th ACM international symposium on Modeling, analysis and simulation of wireless and mobile systems
Cell Cycle Control in Eukaryotes: A BioSpi model
Electronic Notes in Theoretical Computer Science (ENTCS)
Formalization of Continuous Probability Distributions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Probabilistic Analysis using Theorem Proving
Probabilistic Analysis using Theorem Proving
Formal Reasoning about Expectation Properties for Continuous Random Variables
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Probabilistic Guarded Commands Mechanized in HOL
Electronic Notes in Theoretical Computer Science (ENTCS)
Quantitative Analysis With the Probabilistic Model Checker PRISM
Electronic Notes in Theoretical Computer Science (ENTCS)
Formal Reliability Analysis Using Theorem Proving
IEEE Transactions on Computers
Formal lifetime reliability analysis using continuous random variables
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
On the formalization of the lebesgue integration theory in HOL
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Berkeley reliability tools-BERT
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
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Recently proposed formal reliability analysis techniques have overcome the inaccuracies 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 like the second moment and the variance. We also formalize commonly used concepts about the reliability theory such as survival, hazard, cumulative hazard and fractile functions. With these extensions, it is now possible to formally reason about important measures of reliability (the probabilities of failure, the failure risks and the mean-time-to failure) associated with the life of a system that operates in an uncertain and harsh environment and is usually continuous in nature. We illustrate the modeling and verification process with the help of examples involving the reliability analysis of essential electronic and electrical system components.