Abstract
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 supplementary axioms. 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 maginary 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, theconsequence that follows indicates that randomness and chance in R is substituted now by absolute determinism in C. This novel complex probability paradigm will be mplemented to the field of prognostic based on reliability, hence to the concepts of the system remaining usefu 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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