Patent ID: 6560584
Filing Date: 2003-05-06
Classification: H04L

Abstract:
A method for prediction of system reliability of a system having n components, wherein n is greater than one and each component has a reliability pi associated therewith, the system having identifiable minimal path sets and an identifiable total number of minimal path sets, the method comprising the steps of:(a) identifying the minimal path sets of the system and the total number of minimal path sets m; (b) constructing a minimal path set matrix of nÃ—m dimension, where each element of the matrix is a 1 if the component represented belongs to the minimal path sets or is a zero otherwise; (c) constructing a design matrix, the design matrix comprising the minimal path set matrix if the total number of path sets is one, or if the total number of path sets is greater than one, the design matrix is constructed according to the following steps: (1) initializing a set size K to two where the set size represents a number of sets of columns of the minimal path set matrix, (2) selecting each set of size K all possible sets of size K, performing an OR operation on the rows of the selected set, and appending the ORed result as an additional column to the matrix, (3) repeating step (2) until all possible sets of size K have been selected, (4) incrementing the size of K by one, and (5) if the size K is not greater than m, repeating step (2); (d) constructing a vector of ones of dimension 2mâˆ’1 where the first m elements are â€œ1â€ s, and each set of &AutoLeftMatch;(â€ƒ&it;mi&it;â€ƒ)â€ƒelements have the sign (âˆ’1)iâˆ’1, where i ranges from 2 to m; and (e) determining the system reliability by h&it;(p~)=â€ƒ&it;â€ƒj=12m-1&it;1~&it;(j)&CenterDot;&it;&SubsetEqual;ni=1&it;piD&it;(i,j)&it;â€ƒ&it;0<pi<1â€ƒwhere D(i,j) is the (i,j)th element of the design matrix.