Risk and Uncertainty Reduction by Using Algebraic Inequalities

Todinov, Michael

doi:10.1201/9781003032502

Cited by 3 publications

(21 citation statements)

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“…In standard reliability textbooks [17][18][19][20] there has been a big gap in applying algebraic inequalities to improve reliability and reduce risk. Recently, this gap has been reduced 35 by demonstrating the use of algebraic inequalities for reliability imrovement and risk reduction.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, by using inequalities, the reliabilities of two systems can be compared in the absence of knowledge about the reliabilities of the separate components or in the presence of partial knowledge only, for example, that a particular type of component is older (less reliable) than another type of component. 35 It needs to be pointed out that algebraic inequalities not only permit ranking two systems in terms of reliability but also identifying the optimal (most reliable) system. 34,35 Algebraic inequalities provide a strong support for risk-critical decisions under deep, unstructured uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…35 It needs to be pointed out that algebraic inequalities not only permit ranking two systems in terms of reliability but also identifying the optimal (most reliable) system. 34,35 Algebraic inequalities provide a strong support for risk-critical decisions under deep, unstructured uncertainty. Despite that the distributions of the risk-critical parameters remain unknown, the method of algebraic inequalities can still establish the intrinsic superiority of one of the competing options.…”

Section: Introductionmentioning

confidence: 99%

“…These advantages of algebraic inequalities have already been demonstrated. [32][33][34][35] Unlike algebraic equalities, which establish that two different configurations of a system or a process are equivalent, an algebraic inequality establishes that one of the compared configurations is superior. In this way, the use of algebraic inequalities opens wide opportunities for enhancing the performance of systems and processes.…”

Section: Introductionmentioning

confidence: 99%

“…The applications of algebraic inequalities discussed earlier [32][33][34][35][36] are based on the forward approach which includes several basic steps: (i) detailed analysis of the system (e.g. by using reliability theory), (ii) conjecturing an inequality about the competing alternatives or an inequality related to the bounds of a risk-critical parameter, (iii) testing the conjectured inequality by using Monte Carlo simulation and (iv) proving the conjectured inequality rigorously.…”

Section: Introductionmentioning

confidence: 99%

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Meaningful interpretation of algebraic inequalities to achieve uncertainty and risk reduction

Todinov

2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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The paper develops an important method related to using algebraic inequalities for uncertainty and risk reduction and enhancing systems performance. The method consists of creating relevant meaning for the variables and different parts of the inequalities and linking them with real physical systems or processes. The paper shows that inequalities based on multivariable sub-additive functions can be interpreted meaningfully and the generated new knowledge used for optimising systems and processes in diverse areas of science and technology. In this respect, an interpretation of the Bergström inequality, which is based on a sub-additive function, has been used to increase the accumulated strain energy in components loaded in tension and bending. The paper also presents an interpretation of the Chebyshev’s sum inequality that can be used to avoid the risk of overestimation of returns from investments and an interpretation of a new algebraic inequality that can be used to construct the most reliable series-parallel system. The meaningful interpretation of other algebraic inequalities yielded a highly counter-intuitive result related to assigning devices of different types to missions composed of identical tasks. In the case where the probabilities of a successful accomplishment of a task, characterising the devices, are unknown, the best strategy for a successful accomplishment of the mission consists of selecting randomly an arrangement including devices of the same type. This strategy is always correct, irrespective of existing uknown interdependencies among the probabilities of successful accomplishment of the tasks characterising the devices.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Meaningful interpretation of algebraic inequalities to achieve uncertainty and risk reduction

Todinov

2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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A general class of algebraic inequalities for generating new knowledge and optimising the design of systems and processes

Todinov¹

2022

Res Eng Design

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A special class of general inequalities has been identified that provides the opportunity for generating new knowledge that can be used for optimising systems and processes in diverse areas of science and technology. It is demonstrated that inequalities belonging to this class can always be interpreted meaningfully if the variables and separate terms of the inequalities represent additive quantities.The meaningful interpretation of a new algebraic inequality based on the proposed general class of inequalities led to developing a light-weight design for a supporting structure based on cantilever beams, reducing the maximum force upon impact, generating new knowledge about the deflection of elastic elements connected in parallel and series and optimising the allocation of resources to maximise the expected benefit. The interpretation of the new inequality yielded the result stating that the deflection of elastic elements connected in parallel is at least 2 n times smaller than the deflection of the same elastic elements connected in series irrespective of the individual stiffness values of the elastic elements.The interpretation of another algebraic inequality from the proposed general class led to a method for decreasing the stiffness of a mechanical assembly by cyclic permutation of the elastic elements building the assembly. The analysis showed that a decrease of stiffness exists only if asymmetry of the stiffness values in the connected elements is present.

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Optimised design of systems and processes using algebraic inequalities

Todinov

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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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.

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Risk and Uncertainty Reduction by Using Algebraic Inequalities

Cited by 3 publications

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Meaningful interpretation of algebraic inequalities to achieve uncertainty and risk reduction

Meaningful interpretation of algebraic inequalities to achieve uncertainty and risk reduction

A general class of algebraic inequalities for generating new knowledge and optimising the design of systems and processes

Optimised design of systems and processes using algebraic inequalities

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