Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Formal probabilistic analysis using theorem proving
Formal 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
Formal Reliability Analysis Using Theorem Proving
IEEE Transactions on Computers
On the formalization of the lebesgue integration theory in HOL
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
An approach for lifetime reliability analysis using theorem proving
Journal of Computer and System Sciences
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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.