Open AccessChapman-Kolmogorov Equations for a Complete Set of Distinct Reliability States of an Object
Author(s) -
Paweł Szczepański,
J. Żurek
Publication year - 2018
Publication title -
problemy mechatroniki
Language(s) - English
Resource type - Journals
eISSN - 2720-5266
pISSN - 2081-5891
DOI - 10.5604/01.3001.0012.7332
Subject(s) - computer science , reliability (semiconductor) , object (grammar) , theoretical computer science , reliability theory , set (abstract data type) , entropy (arrow of time) , graph theory , reliability block diagram , interdependence , data mining , mathematics , failure rate , reliability engineering , artificial intelligence , statistics , fault tree analysis , programming language , combinatorics , engineering , power (physics) , physics , quantum mechanics , law , political science
The Chapman-Kolmogorov equations indicated in the title are a pretext to demonstrate a mathematically unrecognised truth about the effect of the reliability states of elements (which are generally understood as “subjects”) on the reliability states of a complete set of the same elements, which is called an object. Of importance here are not just the reliability characteristics of individual elements, but the independencies, dependencies and interdependencies between the elements. The relations were described in the language of graph theory. The availability matrix of the language of graph theory was translated to determine the size and probabilities of distinct reliability states of the object, the derivatives of their similarities, and the transition rates adequate to those derivatives. This article continues the research work which identifies the relationship of the properties of a complete set of distinct reliability states of an object with a widely understood theory of systems. The previous papers referred, among others, to: risk, safety, structure entropy, the reliability of the results of checks, and – most of all – technical diagnostics, both in the area of its algorithms and of its optimisation. The object’s serial reliability structure was not assumed in any of those papers, recognising that it would be a serious abuse. The research results were referred to all possible structures of a three-element object. It is believed that by virtue of the block diagrams appropriate to those structures, the readers hereof are provided with a realistic opportunity to practically (and inexpensively) verify the ideas presented here.