Foundational issues in reliability and risk analysis

We discuss statistical methods for hazard characterization, reliability, and risk analysis. We motivate our development via the scenario of a fault tree and state that 'probability is the only satisfactory way to describe the inherent uncertainty associated with these'. We discuss the various notions of probability, and recommend the one which appears to be the most meaningful for the context under consideration. We also discuss some difficulties in distinguishing between 'real risk' and perceived risk'. We then state the rules of probability and use them as a means of combining the various uncertainties and introduce the notions of a failure model, the parameters of a model and the reliability of an item. The important notion of independence and its relevance to applications is discussed. We introduce the notions of hazard rates, failure rates and the mean time to failure, the meaning of these and several misconceptions about them are pointed out. We discuss statistical models, statistical sampling, inference, parameter estimation, the notion of the likelihood and the likelihood principle. We make some comments about maximum likelihood estimation and confidence limits, and point out some difficulties with their use and interpretatin.