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A method for exact reliability of consecutive2‐out‐of‐(r, r)‐from‐(n, n):F systems
Author(s) -
Higashiyama Y.
Publication year - 2004
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/j.1475-3995.2004.00453.x
Subject(s) - reliability (semiconductor) , square (algebra) , square tiling , function (biology) , combinatorics , mathematics , grid , computer science , physics , thermodynamics , power (physics) , geometry , evolutionary biology , biology
A new reliability model, consecutive 2‐out‐of‐( r , r )‐from‐( n , n ):F model, is proposed. The consecutive 2‐out‐of‐( r , r )‐from‐( n , n ):F system consists of a square grid of side n (containing n 2 components) such that the system fails if and only if there is at least one square of side r which includes among them at least two failed components. For i.i.d. case an algorithm is given for computing the reliability of the system. The reliability function can be expressed by the number of 0–1 matrices having no two or more 0s at any square of side r .