Formal Lifetime Reliability Analysis Using Continuous Random Variables

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.