### Abstract

The evaluation of the reliability of general networks is
based on a few principles coming from the basic
probability theory. The complexity of the networks
inevitably requires the use of a computerised approach.
Discussion leads to the long Boolean expressions (Boolean
sum-of-products) which can include hundreds of product
terms for fairly small networks.
In this study a new binary vector method is presented for
the computerised search of minimum ties of a general
network. The resolved minimum ties are utilised in
generating a network's probability space, i.e. set of
points of success and points of failure. The data file of
these points is interpreted as the network's Boolean
system function. It provides basic information for the
new minimisation algorithm of the Boolean SOP-expression
which is discussed in detail. In addition to these
computer algorithms a short reliability calculation
program is presented for the verification of the former
results.
The developed methods are each, in turn, applied to
several sample networks, and the results are compared and
studied to ascertain the new algorithms.

Original language | English |
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Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 103 |

ISBN (Print) | 951-38-3298-8 |

Publication status | Published - 1988 |

MoE publication type | D4 Published development or research report or study |

### Publication series

Series | Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports |
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Number | 571 |

ISSN | 0358-5077 |

### Keywords

- reliability analysis
- networks
- probability theory
- computer programs
- algorithms
- Boolean functions
- telecommunication

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## Cite this

Nevalainen, S. (1988).

*Minimization of boolean sum of products with applications to the computation of reliability of general networks*. VTT Technical Research Centre of Finland. Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports, No. 571