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The paper introduces a powerful method for developing lightweight designs and enhancing the load-bearing capacity of common structures. The method, referred to as the 'method of aggregation', has been derived from reverse engineering of sub-additive and super-additive algebraic inequalities. The essence of the proposed method is consolidating multiple elements loaded in bending into a reduced number of elements with larger cross sections but a smaller total volume of material. This procedure yields a huge reduction in material usage and is the first major contribution of the paper. For instance, when aggregating eight load-carrying beams into two beams supporting the same total load, the material reduction was more than 1.58 times. The second major contribution of the paper is in demonstrating that consolidating multiple elements loaded in bending into a reduced number of elements with larger cross sections but the same total volume of material leads to a big increase in the load-bearing capacity of the structure. For instance, when aggregating eight cantilevered or simply supported beams into two beams with the same volume of material, the load-bearing capacity until a specified tensile stress increased twice. At the same time, the load-bearing capacity until a specified deflection increased four times. [ABSTRACT FROM AUTHOR]

The paper explores the probabilistic interpretations of algebraic inequalities and presents several findings. First, the inequality of the additive ratios can be used to increase the probability of an event occurring within a set of mutually exclusive and exhaustive events. The interpretation of this inequality produced a counter‐intuitive result, that for suppliers delivering the same quantity of reliable products alongside unknown numbers of unreliable products, the probability of purchasing a reliable product from a randomly selected supplier is higher than the probability of purchasing a reliable product from the market formed by all suppliers. Next, the paper discusses how averaging the reliabilities of components from different varieties can lead to a significant overestimation of the calculated system reliability, as demonstrated by another algebraic inequality interpretation. Finally, the paper derives tight bounds for the reliability of demand in a load‐strength interference model by interpreting the Hayashi's inequality. Notably, these bounds do not depend on the shape of the load distribution and only require the strength distribution to be known in relatively small vicinities of the lower and upper bound of the load. [ABSTRACT FROM AUTHOR]

Problems with the current methods for reliability improvement are discussed as well as two generic methods for reliability improvement. The paper argues that reliability improvement is underpinned by common principles that provide key input to the design process. The domain-independent methods change the way engineers and scientists approach reliability improvement. The presented generic methods encourage simple low-cost solutions as opposed to some traditional high-cost solutions based on introducing redundancy, condition monitoring, reinforcement and use of expensive materials. The domain-independent methods allow engineers and scientists in a particular domain to access excellent solutions and practices for eliminating failure modes in other domains. In this way, the constant 'reinventing of the wheel' is avoided. As part of the presented approach, a generic method for increasing reliability by increasing the level of balancing and by substitution have been presented. In addition, a new classification of techniques related to increasing the level of balancing has been introduced and discussed for the first time. The paper also proves rigorously that if two components must be selected from n batches containing reliable and faulty components with unknown proportions, the likelihood that both components will be reliable is maximised by selecting the components from a randomly selected batch. [ABSTRACT FROM AUTHOR]

A method for optimising the design of systems and processes has been introduced that consists of interpreting the left- and the right-hand side of a correct algebraic inequality as the outputs of two alternative design configurations delivering the same required function. In this way, on the basis of an algebraic inequality, the superiority of one of the configurations is established. The proposed method opens wide opportunities for enhancing the performance of systems and processes and is very useful for design in general. The method has been demonstrated on systems and processes from diverse application domains. The meaningful interpretation of an algebraic inequality based on a single-variable sub-additive function led to developing a light-weight design for a supporting structure based on cantilever beams. The interpretation of a new algebraic inequality based on a multivariable sub-additive function led to a method for increasing the kinetic energy absorbing capacity during inelastic impact. The interpretation of a new inequality has been used for maximising the mass of deposited substance during electrolysis. [ABSTRACT FROM AUTHOR]