Probability of an Intermediate (Reduced Operational) State

Paweł SZCZEPAŃSKI; Paweł SZCZEPAŃSKI

Pobierz

Ta publikacja jest chroniona prawem autorskim. Dostęp do jej cyfrowej wersji jest możliwy po zalogowaniu.

Tytuł: Probability of an Intermediate (Reduced Operational) State ; Probability of an Intermediate (Reduced Operational) State

Abstrakt:

This work examines with the form of the well-known sum: p + q = 1 – which is the sum of the probabilities of opposite events, in particular: the sum of the probabilities of the operational and non-operational (failure) states of a single element (a creation characterised by one output and any number of inputs). It was found that without significantly compromising the accuracy of the previous analyses, it was possible to introduce an additional component to the sum: iiipq3, a component that embodies the probability of an intermediate state, or a reduced operational state. With a constant value of the sum of the components in question, their variation as a function of probability q was determined, following which in the function of the same variable the variation of the entropy of an element's i state was examined using Chapman–Kolmogorov equations; here the focus was on investigating the intensity of the transition from the operational state to the non-operational state or an intermediate state, and from an intermediate state to the non-operational state. The meaning of intermediate probability was also referenced to the object: its diagnostic program, the entropy of structure, the full set of discriminable states, and the relevant transition intensities. It became indispensable in this respect to describe the object using the language of graph theory, in which the basic concepts are layers and an availability matrix. It should be noted that the subject object is an entity that comprises a set of individual elements, with a number and structure of connections that are consistent with the purpose of this entity.
; This work examines with the form of the well-known sum: p + q = 1 – which is the sum of the probabilities of opposite events, in particular: the sum of the probabilities of the operational and non-operational (failure) states of a single element (a creation characterised by one output and any number of inputs). It was found that without significantly compromising the accuracy of the previous analyses, it was possible to introduce an additional component to the sum: iiipq3, a component that embodies the probability of an intermediate state, or a reduced operational state. With a constant value of the sum of the components in question, their variation as a function of probability q was determined, following which in the function of the same variable the variation of the entropy of an element's i state was examined using Chapman–Kolmogorov equations; here the focus was on investigating the intensity of the transition from the operational state to the non-operational state or an intermediate state, and from an intermediate state to the non-operational state. The meaning of intermediate probability was also referenced to the object: its diagnostic program, the entropy of structure, the full set of discriminable states, and the relevant transition intensities. It became indispensable in this respect to describe the object using the language of graph theory, in which the basic concepts are layers and an availability matrix. It should be noted that the subject object is an entity that comprises a set of individual elements, with a number and structure of connections that are consistent with the purpose of this entity.