Uncertainty accompanies our lives. Coherent modelling of uncertainties for decision-making is essential in engineering and related disciplines. The important tools have been outlined. It is neither possible nor desirable to attempt to give a recipe that can be used for specific problems. The fun of engineering is to use the tools so as to create a methodology that can be used for a particular problem. Probability is seen as the measure of uncertainty. Decisions are based on an analysis of uncertainties using probability and of desires and aversion using utility. These factors guide our thinking in approaching problems.

In estimating probabilities, the beacon that guides us is the definition of probability as a fair bet. Frequencies can be used only to assist in evaluating probabilities but do not constitute a definition of probability. It is important to address all uncertainties without taking a problem out of reasonable practical proportion. If done in a blind manner without judgement, this can lead to gross overestimation of the uncertainty regarding our quantity of interest. Our estimates of mean values, including variances and other moments, should accord with our judgement, and we should beware of compounding uncertainties that might result in unrealistic engineering judgements.

Flowing from the definition of probability as a fair bet, Bayesian thought should guide our modelling.