Computation of k-out-of-n System Reliability via Reduced Ordered Binary Decision Diagrams

Abstract

A prominent reliability model is that of the partially-redundant (k-out-of-n) system. We use algebraic as well as signal-flow-graph methods to explore and expose the AR algorithm for computing k-out-of-n reliability. We demonstrate that the AR algorithm is, in fact, both a recursive and an iterative implementation of the strategy of Reduced Ordered Binary Decision Diagrams (ROBDDs). The underlying ROBDD for the AR recursive algorithm is represented by a compact Signal Flow Graph (SFG) that is used to deduce AR iterative algorithms of quadratic temporal complexity and linear spatial complexity. Extensions of the AR algorithm for (single or scalar) threshold, double-threshold, vectorthreshold, and k-to-lout of -n systems have similar ROBDD interpretations.

Reliability Evaluation of Rooftop Solar Photovoltaics Using Coherent Threshold Systems

“…The technique is illustrated by a probability map and an acyclic signal flow graph that resembles a reduced ordered binary decision diagram (ROBDD) [7,8,[24][25][26][27]. Similar ROBDD-like SFGs were earlier employed for handling related systems [28][29][30][31][32]. The recursive algorithm has two different implementations that stand for two distinct strategies.…”

Recursively-Defined Combinatorial Functions: The Case of Binomial and Multinomial Coefficients and Probabilities

“…Many combinatorial functions can be characterized by a general framework based on simple twodimensional or multi-dimensional recursion [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Four prominent cases among these combinatorial functions are the functions of binomial coefficients [6,10,15,[20][21][22] and binomial probabilities [1,6,10,23,24], as well as their extensions to multinomial coefficients [21,22,[25][26][27][28][29][30][31][32] and multinomial probabilities [21,22,33,34].…”