ABSTRACT
This chapter discusses various applications of algebraic inequalities for determining upper and lower bounds of risk-critical parameters. An important application of the upper-bound variance inequality has been used for identifying the source whose removal causes the largest reduction of the worst-case variation. It is also shown how the upper-bound variance inequality can be used for increasing the robustness of electronic devices.
Important applications of convex functions have been considered for determining an upper bound for the equivalent resistance of elements whose resistance is associated with uncertainty.
Applications of the Chebyshev’s inequality have also been considered for determining a tight upper bound for the risk of a faulty assembly. Finally, tight bounds for the fraction of items with a particular property have been determined in the case where the exact number of components in the separate batches is unknown.
