What About Non-Coherent Systems?

Non‐coherent systems do not follow the monotony principle of their structure function. This is often the case of systems involving feedback control. The calculus methods based on the knowledge of minimal tie‐or cut‐sets are therefore improper because in the state diagram, a node associated with a ti...

Full description

Saved in:
Bibliographic Details
Published inSystems Dependability Assessment pp. 61 - 74
Main Authors Brinzei, Nicolae, Aubry, Jean-François
Format Book Chapter
LanguageEnglish
Published United States Wiley 2015
John Wiley & Sons, Inc
Subjects
Boolean function
calculus methods
non‐coherent systems
Shannon theorem
state diagram
Online AccessGet full text

Cover

More Information
Summary:Non‐coherent systems do not follow the monotony principle of their structure function. This is often the case of systems involving feedback control. The calculus methods based on the knowledge of minimal tie‐or cut‐sets are therefore improper because in the state diagram, a node associated with a tie‐set may be, according to the order relation, upper‐bounded by a node associated with a cut‐set. The concepts of minimal cut‐ or tie‐sets no longer make sense. It is often recommended to discuss the problem as an ordinary Boolean function reduction to obtain a minimal Boolean sum of disjoint monomials. In the general case of a system that is highly non‐coherent, many paths may present multiple‐state alternations of the system state. It is possible to process these by successive applications of the Shannon theorem to obtain a decomposition of the structure function as monotone subfunctions.
ISBN:9781848217652
184821765X
DOI:10.1002/9781119053996.ch3