סמינר מחלקתי - המחלקה להנדסת תעשייה

Approximate Reliability Calculations Based  on System Combinatorial Invariants

Prof. Ilya Gertsbakh, Ben Gurion University

Abstract:

We consider network-type systems having independent   components subject to failure ( edges or nodes).  Typically,  network failure (the DOWN state) is defined as the loss of  terminal connectivity or disintegration into several isolated  connected components (clusters).  System combinatorial invariant is a parameter ( a vector,

a set or a distribution) that depends only on system  structure function  φ(x) and does not depend on component probabilistic properties.

If all network components have equal failure probability q, network reliability can be computed using the network first combinatorial invariant, so-called D-spectrum or signature (also known as system internal distribution).  This computation is based on the fact that the cumulative D-spectrum allows easy calculation of the number of  system failure sets. The D-spectrum can be estimated by means of a Monte Carlo algorithm.

The second combinatorial invariant is  Birnbaum  Importance Spectrum which allows an easy calculation of  component Birnbaum Important Measure (BIM) . BIM

of component j equals the partial derivative of system reliability function R(p) with respect to p_j. Using this  fact and the Taylor expansion of  R(p), it is possible to obtain an approximation to system reliability for the  general case of arbitrary component  failure probabilities. The BIM spectrum is calculated  using a modification of  the Monte Carlo algorithm  for the D-spectrum.

The third invariant are network border states (BS) defined as the system DOWN states having Manhattan distance 1 from the system UP state.  We describe briefly  the use of BS for  network synthesis problems and for computing so-called system flow for a network with renewable components.

In this talk we avoid detailed proofs and the description of  algorithms and will

concentrate  mainly on the modus operandi of reliability calculations.

This is joint  research with Yoseph Shpungin, Shamoon College of Engineering.

ההרצאה תתקיים ביום ג', 8/5/12 בשעה 14:00 בחדר 206, בנין וולפסון הנדסה, הפקולטה להנדסה, אוניברסיטת תל-אביב.