Reducing Risk Through Inversion and Self-Strengthening

Reducing Risk Through Inversion and Self-Strengthening

Michael Todinov (Department of Mechanical Engineering and Mathematical Sciences, Oxford Brookes University, UK)
Copyright: © 2017 |Pages: 29
DOI: 10.4018/IJRCM.2017010102

Abstract

A number of new techniques for reliability improvement and risk reduction based on the inversion method, such as: ‘inverting design variables,' ‘inverting by maintaining an invariant,' ‘inverting resulting in a reinforcing counter-force,' ‘negating basic required functions' and ‘moving backwards to general and specific contributing factors' have been introduced for the first time. By using detailed calculations, it has been demonstrated how the new technique ‘repeated inversion maintaining an invariant' can be applied to reduce the risk of collision for multiple ships travelling at different times and with variable speeds. It has been demonstrated that for pressure vessels, an inversion of the geometric parameters by maintaining an invariant volume could result not only in an increased safety but also in a significantly reduced weight. The method of self-strengthening (self-reinforcement) has been introduced for the first time as a systematic method for improving reliability and reducing risk. The method of self-strengthening by capturing a proportional compensating factor and the method of self-strengthening by creating a positive feedback loop have been proposed for the first time as reliability improvement tools. Finally, classifications have been proposed of methods and techniques for risk reduction based on the methods of inversion and self-strengthening.
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1. Introduction

A systematic classification of generic methods for reducing technical risk is crucial to safe operation, engineering designs and software, yet this very important topic has been overlooked in the reliability and risk literature. Distilling approaches for reliability improvement and risk reduction and formulating new approaches, provides a valuable and much needed support for design-engineers.

The work on formulating principles and methods for improving the reliability of engineering systems was initiated in (Todinov, 2007) and continued in Todinov (2015).

The reverse strategy for reliability improvement and risk reduction, which is in the focus of this work, has always been an important technique in problem solving. It was already known to Pappus of Alexandria about 320 AD, who described it as ‘beginning with the desired outcome and working backwards until something known is reached.’ The famous algebraist Carl Gustav Jacobi, whose favourite maxim was ‘invert, always invert,’ used the reverse strategy with great success in solving many hard mathematical problems. An important example of the reverse strategy in problem solving is the recursion, widely used for solving difficult combinatorial problems (Wirt, 1976). A typical approach in recursion is reducing the initial problem of size n to two or more problems of size n-1, which in turn are reduced to problems of size n-2 and so on, until problems with trivial solutions are reached. Starting from the trivial solutions and moving backwards helps to assemble the solution.

The struggle between the need of reducing the weight of components and systems and the need of high reliability is a constant source of technical and physical contradictions. The reverse strategy has been an important technique for resolving some of these contradictions. It is then no surprise that the reverse strategy features in texts related to creativity and inventive problem solving (Altshuller, 1984; 1996; 1999; Orloff, 2006). The reverse strategy is at the heart of many inventions and Altshuller's TRIZ system (Altshuller, 1984; 1996; 1999) identified a number of useful applications of this technique.

Reverse strategy is often used in planning projects, operations or processes where the success is critically dependent on whether people, equipment and resources are available when and where needed. This is particularly relevant to projects where critical deadlines need to be met. In order to reduce the risk of failure, the planning of the project/process is often started from the desired outcome and progressed backwards. Starting from the desired end result and planning backwards helps to determine what resources are necessary to achieve the goal and to ensure how to make the necessary resources available at the right place and at the right time.

Despite the progress made in using the reverse strategy for problem solving and planning, almost none of the known sources focuses on the application of the reverse strategy for reliability improvement and risk reduction. In addition, the structure needed for applying this technique for reliability improvement and risk reduction is missing.

The reverse strategy is a powerful method for improving the reliability of engineering designs and will be referred to as the method of inversion.

Inverse states based on compressive residual stresses introduced by shot peening and their role in improving the reliability of automotive suspension springs have been discussed in (Todinov, 1999) and Todinov (2000). Recently, Fu et al. (2015) presented a comprehensive review of methods for introducing compressive residual stresses by a cold expansion, to improve the fatigue life of connection holes in aircraft structures.

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