The paper introduces a new domain-independent method for improving reliability and reducing risk based on proving algebraic inequalities. The use of algebraic inequalities provides: (i) sharp bounds for the variation of a risk-critical properties and (ii) possibility for ranking systems, processes and decision strategies in the presence of large uncertainty related to key controlling variables. By proving an inequality, the paper shows that if no information about the component reliability characterising the individual suppliers is available, purchasing components from a single supplier or from the smallest possible number of suppliers maximises the probability of a high-reliability assembly. Proving an inequality has also been used to demonstrate that the well-ordered parallel-series systems are characterised by the smallest possible risk of failure. Finally, a method has been proposed for minimising the absolute error in a reliability-critical parameters caused by variations of design variables.