SYSTEM RELIABILITY AND WEIGHTED LATTICE POLYNOMIALS
نویسندگان
چکیده
منابع مشابه
System Reliability and Weighted Lattice Polynomials
The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y defined by a weighted lattice polynomial of (lattice-valued) random variables is considered in general and in some special cases. The central object of inte...
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We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We also show that these functions include the class of discrete Sugeno integrals and that they are characterized by a remarkable median based decomposition formula.
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We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include ordinary lattice polynomial functions and, particularly, order statistics, our results encompass the corresponding formulas for these particular functions. We also ...
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In lattice theory, lattice polynomials have been defined as well-formed expressions involving variables linked by the lattice operations ∧ and ∨ in an arbitrary combination of parentheses. In turn, such expressions naturally define lattice polynomial functions. For instance, p(x1, x2, x3) = (x1 ∧ x2) ∨ x3 is a 3-ary lattice polynomial function. The concept of lattice polynomial function can be ...
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X iv :m at h/ 06 10 33 0v 1 [ m at h. C V ] 1 0 O ct 2 00 6 From miranda Tue Oct 10 09:42:48 2006 Return-Path: ¡[email protected]¿ Received: miranda@localhost) by coxeter.math.toronto.edu (AIX5.2/8.11.6p2/8.11.0/UTMath 1.0) id k9ADgmn118742; Tue, 10 Oct 2006 09:42:48 -0400 Date: Tue, 10 Oct 2006 09:42:48 -0400 From: Miranda Tang ¡[email protected] Message-Id: ¡200610101342.k9ADgmn118742...
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ژورنال
عنوان ژورنال: Probability in the Engineering and Informational Sciences
سال: 2008
ISSN: 0269-9648,1469-8951
DOI: 10.1017/s0269964808000223