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The Paradigm of Complex Probability and Prognostic Using FORM

London Journal of Research in Science: Natural and Formal
Volume | Issue | Compilation
Authored by Dr. Abdo Abou Jaoude , NA
Classification: NA
Keywords: Degradation, Remaining Useful Lifetime, Complex Probability, First-Order Reliability Method (FORM), Failure Probability, Young Modulus, Prognostic.
Language: English

The imaginary set of numbers is incorporated by extending the probability system of five axioms of Andrey Nikolaevich Kolmogorov set up in 1933 and this by adding three supplementaryaxioms. Therefore, any random experiment can thus be performed in the extended complex probability set C which is the sum of the real set R of real probabilities and the imaginary set M of imaginary probabilities. The aim here is to determine the complex probabilities by taking into consideration additional new imaginary dimensions to the event that occurs in the “real” laboratory. The outcome of the stochastic phenomenon in C can be foretold perfectly whatever the probability distribution of the input random variable in R is since the corresponding probability in the whole set C is permanently and constantly equal to one. Therefore, the consequence that follows indicates that randomness and chance in R is substituted now by absolute determinism in C. This novel complex probability paradigm will be implemented to the field of prognostic based on reliability, hence to the concepts of the system remaining useful lifetime (RUL) and degradation. Additionally, the First-Order Reliability Method (FORM) analysis will be applied to Young’s modulus to illustrate my original and innovative paradigm.


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