Abstract
ABSTRACTAndrey Kolmogorov put forward in 1933 the five fundamental axioms of classical probability theory. The original idea in my complex probability paradigm (CPP) is to add new imaginary dimensions to the experiment real dimensions which will make the work in the complex probability set totally predictable and with a probability permanently equal to one. Therefore, adding to the real set of probabilities the contributions of the imaginary set of probabilities will make the event in absolutely deterministic. It is of great importance that stochastic systems become totally predictable since we will be perfectly knowledgeable to foretell the outcome of all random events that occur in nature. Hence, my purpose is to link my CPP to unburied petrochemical pipelines’ analytic prognostic in the linear damage accumulation case. Consequently, by calculating the parameters of the novel prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of knowledge, the complex probability, the system failure and survival probabilities, and the remaining useful lifetime probability, after a pressure time t has been applied to the pipeline, and which are all functions of the system degradation subject to random effects.
Highlights
In this introductory section an overview of probability interpretations will be done
By calculating the parameters of the novel prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of knowledge, the complex probability, the system failure and survival probabilities, and the remaining useful lifetime probability, after that a pressure time t has been applied to the pipeline and which are all functions of the system degradation subject to random effects
By calculating the parameters of the new prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of our knowledge, the complex probability, the system failure and survival probabilities, and the Remaining Useful Lifetime (RUL) probability, after that a pressure cycles time t has been applied to the unburied pipeline and which are all functions of the system degradation subject to chaos and random effects
Summary
In this introductory section an overview of probability interpretations will be done. Previous specialized prognostic studies belong generally to three types of technical approaches (Figure 1): the first type is the ‘Experience-based prognostic’ (Vasile, 2008) (based on measurements taken from health monitoring of machine like for example those based on expert judgment, stochastic model, Markovian process, Bayesian approach, Reliability analysis, Optimization of preventive maintenance, etc.). Their prognostic methodology proves to be simple but inflexible toward changes in system behaviour and environment.
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