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Research on the system function-structure analysis based on its implicit relation

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Abstract

To understand the system function-structure under different background relations, two analysis methods are proposed based on space fault tree and factor space theory. They are the system function-structure minimal disjunctive formula and the system function-structure simplest formula. The former establishes the axiom system of system function-structure analysis based on factor logic, and proves that the system function-structure obtained by function-structure analysis method is a minimal disjunction formula. The latter gives a more detailed analysis steps based on the former idea, which is mainly used to determine the implicit relation between system function and component function. The background sets consisting of the 16 and 32 background relations are studied with these two methods. The results show that the complete background relations can obtain a certain system function-structure uniquely; the incomplete background relations can obtain a family of certain system function-structures. If the incomplete background relations are a subset of the complete background relations, then the incomplete background relations must has a linear relation between functions to complement the incomplete background relations. At the same time, the system function equivalent and replacement relation are obtained. It is also proved that the system function-structure obtained from several subsets of the background sets is the simplest and the condition required for the simplest structure of the background set is strict. At present, the above methods are mainly used for system reliability analysis in safety system engineering.

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Abbreviations

SFSA:

System function-structure analysis

R/B:

Background relation

MDF:

Minimal disjunctive formula

SFSSF:

System function-structure simplest formula

SFS:

System function-structure

FFSAT:

Factor function-structure analysis table

SFT:

Space Fault Tree

FS:

Factor Space

f i :

iTh structure factor

g :

Function factor

U :

Universe

F :

Set of factors

X(f i):

Phase set(space) of fi

X(g):

Phase set(space) of g

b K :

Last one phase in the X(g)

a n ( j ) j :

Phase of fj

u i :

A sample point

[a]:

A decision class for factor fj

h :

Number of rows of fj in FFSAT

m :

Number of rows of fj in

d :

Decision d = h/m

L f :

Factor logic system

S :

Symbol set

x ij :

Phase value, called word

footmark ij :

Word xij is the ith phase of factor fj

F(S):

Formula set

∧:

Conjunction

x i (1) j (1),…,x i ( k ) j ( k ) :

A word set

∨:

Disjunction

r 1 + … + r t :

Disjunctive normal formula

p :

Tautology

X(f i) = {x 1 j,…, x m ( i ) j}:

Words in jth family

W2 :

Binary Boolean algebra

(p, x) ∈ F(S) × S :

A proposition

T :

Normal state of a system or component

F :

Abnormal state of a system or component

K :

Length of word set

Z :

Switching system

Z 1,…,Z 4 :

Four components

x j :

Zj On

x j :

Zj Off

M :

Number um of objects

N :

Number of structure factors

x n|m :

Phase string

λ :

Length of the phase set(string)

Λ :

Phase(λ = 1) or phase set(λ > 1)

ξ(T):

SFSSF of the class T

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Acknowledgements

The authors wish to thank all his friends for their valuable critics, comments and assistances on this paper. This study was partially supported by the grants (Grant nos. 51704141, 2017YFC1503102, 61350003) from the Natural Science Foundation of China. In particular, the authors would like to express the gratitude to Pro. Wang P. Z., Zhou H. J. and Wang K. Y. for their factorial logic and their related scholars for their research in the field of factor space.

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Authors and Affiliations

  1. School of Business Administration, Liaoning Technical University, Huludao, 125000, Liaoning, China

    Shasha Li

  2. College of Safety Science and Engineering, Liaoning Technical University, Fuxin, 123000, Liaoning, China

    Tiejun Cui

  3. Tunnel and Underground Structure Engineering Center of Liaoning, Dalian Jiaotong University, Dalian, 116028, Liaoning, China

    Tiejun Cui

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  1. Shasha Li
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Correspondence to Tiejun Cui.

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Li, S., Cui, T. Research on the system function-structure analysis based on its implicit relation. J Ambient Intell Human Comput 12, 755–767 (2021). https://doi.org/10.1007/s12652-020-02058-z

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