In this paper the axioms, of axiomatic design, are extended to the non-probabilistic and repetitive events. The idea of information, in the classic theories of Fisher andWiener–Shannon, is a measure only of probabilistic and repetitive events. The idea of information is broader than the probability. The Wiener–Shannon’s axioms are extended to the non-probabilistic and repetitiveness events. It is possible the introduction of a theory of information for events not connected to the probability therefore for non-repetitive events. On the basis of the so-called Laplace’s principle of insufficient knowledge, the MaxInf Principle is defined for choose solutions in absence of knowledge. In this paper the value of information, as a measure of equality of data among a set of values, is applied in axiomatic framework for data analysis in such cases in which the number of functional requirements (FRs) is greater than the design parameter’s (DPs) one. As example is studied an application in which the number of DPs is lower then the number of FRs, and the coupled design cannot be satisfied. A typical example in which that happens is in the evaluation of the potential failure mechanisms, failure stresses, failure sites, and failure modes, given a product architecture, the comprising products and materials, and the manufacturing processes. In design analysis it is possible to hypothesise several causes that can affect the normal functionalities of some products/processes’ parts and to individuate several possible effect that those causes can cause. In ideal analysis, each functional requirement (effect) must be linked to one design parameter (cause), and vice versa each design parameter can satisfy one (or more) functional parameter. From the system of equations it turns out that with the number of {FR} < {DP} it is possible to have only approximate solutions. In this situation the number of DPs is insufficient to achieve all the {FR} in exact mode. Respecting the following statements: • In absence of solution is not possible compare anything: is needed at least a solution. • Using mathematical transformations it is possible to obtain a marginal solution. Using the idea of information in metric space, in according with Maximum Entropy Principle of Jaynes it is possible to select as solution the distribution that maximise the Shannon entropy measure and simultaneously is consistent with the values of constraints. So this method allows to solve the Axiomatic framework and to reason for obtain the best design solution.

### Failure mode analysis using Axiomatic Design and Non-Probabilistic Information

#### Abstract

In this paper the axioms, of axiomatic design, are extended to the non-probabilistic and repetitive events. The idea of information, in the classic theories of Fisher andWiener–Shannon, is a measure only of probabilistic and repetitive events. The idea of information is broader than the probability. The Wiener–Shannon’s axioms are extended to the non-probabilistic and repetitiveness events. It is possible the introduction of a theory of information for events not connected to the probability therefore for non-repetitive events. On the basis of the so-called Laplace’s principle of insufficient knowledge, the MaxInf Principle is defined for choose solutions in absence of knowledge. In this paper the value of information, as a measure of equality of data among a set of values, is applied in axiomatic framework for data analysis in such cases in which the number of functional requirements (FRs) is greater than the design parameter’s (DPs) one. As example is studied an application in which the number of DPs is lower then the number of FRs, and the coupled design cannot be satisfied. A typical example in which that happens is in the evaluation of the potential failure mechanisms, failure stresses, failure sites, and failure modes, given a product architecture, the comprising products and materials, and the manufacturing processes. In design analysis it is possible to hypothesise several causes that can affect the normal functionalities of some products/processes’ parts and to individuate several possible effect that those causes can cause. In ideal analysis, each functional requirement (effect) must be linked to one design parameter (cause), and vice versa each design parameter can satisfy one (or more) functional parameter. From the system of equations it turns out that with the number of {FR} < {DP} it is possible to have only approximate solutions. In this situation the number of DPs is insufficient to achieve all the {FR} in exact mode. Respecting the following statements: • In absence of solution is not possible compare anything: is needed at least a solution. • Using mathematical transformations it is possible to obtain a marginal solution. Using the idea of information in metric space, in according with Maximum Entropy Principle of Jaynes it is possible to select as solution the distribution that maximise the Shannon entropy measure and simultaneously is consistent with the values of constraints. So this method allows to solve the Axiomatic framework and to reason for obtain the best design solution.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11386/1060453`
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