COMPLEX PROBABILITY THEORY AND PROGNOSTIC

The Kolmogorov’s system of axioms can be extended to encompass the imaginary set of numbers and this b y adding to the original five axioms an additional th ree axioms. Hence, any experiment can thus be executed in what is now the complex set C (Real set R with real probability + Imaginary set M with imaginary probability). The objective here is to evaluate the complex probabilities by considering supplementary new imaginary dimensions to the event occurring in the “real” laboratory. Whatever the probability distrib ution of the input random variable in R is, the correspondin g probability in the whole set C is always one, so the outcome of the random experiment in C can be predicted totally. The result indicates that chance and l uck in R is replaced now by total determinism in C. This new complex probability model will be applied to the c oncepts of degradation and the Remaining Useful Lifetime (RUL), thus to the field of prognostic.

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