Abstract

Traditional techniques used in the reliability analysis of engineering systems have limitations. Paper-and-pencil based analysis is prone to human error and simulation based techniques cannot be computationally one hundred percent accurate.

An alternative to these two traditional approaches is modeling and analysis of reliability of systems using formal methods based techniques such as probabilistic theorem proving. Probabilistic theorem proving using higher-order logic can be used for modeling and analysis of reliability of engineering systems provided a certain reasoning infrastructure is developed. The developed infrastructure can include random variables, their probabilistic and statistical properties, and basic reliability theory concepts such as survival and hazard functions. This thesis describes state-of-the-art research in reliability analysis using theorem proving. It also describes the main contributions of this thesis which include: the formalization of statistical properties of continuous random variables, the formalization of multiple continuous random variables and the formalization of the basic notions of reliability that can be applied to single and multiple component systems. Engineering applications of the formalization are presented that illustrate the usefulness of our formalization infrastructure. These applications include reliability analysis of electronic system components such as a capacitor and an underground power transmission cable. We also present the reliability analysis of an automobile transmission using our higher-order logic formalization.

To the best of our knowledge, for the very first time, the use of theorem proving based infrastructure enables formal reliability analysis of engineering systems that is computationally one hundred percent accurate and sound. The analysis is performed using real and true random variables. We show that the results presented in this thesis are general and can be applied to many reliability engineering problems.