Novel representations for a coherent threshold reliability system: a tale of eight  signal   ow graphs

ALI MUHAMMAD RUSHDI; ALAA MOHAMMAD ALTURKI

Makale detayları

Novel representations for a coherent threshold reliability system: a tale of eight signal ow graphs

Yazarlar:

ALI MUHAMMAD RUSHDI | ALAA MOHAMMAD ALTURKI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Electrical Engineering and Computer Science 2018 Vol.26 Issue 1, pp.257-269

Belge Tipi:

Makale

Yayın Tarihi:

1/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000735447

Sıklık:

İki Aylık

eISSN:

1303-6203

pISSN:

1300-0632

Özet:

 

A threshold system is a reliability system whose success/failure is a threshold switching function in the  successes/failures of its components. A coherent system (CS) is one that is causal, monotone, and with relevant  components. The coherent threshold system (CTS), typically called the weighted k-out-of-n system, is consequently  described by strictly positive weights and threshold. This paper presents recursive relations as well as boundary conditions  for eight entities pertaining to a CTS. These are (a) expressions of monoform literals as well as disjoint or probability-  ready expressions for either system success or failure, and (b) all-additive formulas as well as inclusion-exclusion ones  for either system reliability or unreliability. These entities are obtained according to the best policy of implementing the  Boole{Shannon expansion with respect to a higher-weight component before it is made with respect to a lower-weight  one. With this best policy, the success and failure expressions with monoform literals are both minimal and shellable.  Each of the eight entities considered is represented by an acyclic (loopless) signal   ow graph (SFG). The SFG for system  success or failure is isomorphic to a reduced ordered binary decision diagram, which is the optimal data structure for  a Boolean function. The interrelations between the SFGs demonstrate optimal procedures for implementing (a) the  probability (real) transform of a Boolean function, (b) inversion or complementation of a Boolean function, and (c)  disjointing or orthogonalization of a sum-of-products expression of a Boolean function. The SFGs discussed herein for a  CT can be extended to a general coherent system. They reduce to elegant symmetric regular graphs for the special case  of a partially redundant system (k-out-of-n system).

Makale detayları

Novel representations for a coherent threshold reliability system: a tale of eight signal ow graphs

Yazarlar: ALI MUHAMMAD RUSHDI | ALAA MOHAMMAD ALTURKI

Yayıncı: TUBITAK

Dergi: Turkish Journal of Electrical Engineering and Computer Science 2018 Vol.26 Issue 1, pp.257-269

Belge Tipi: Makale

Yayın Tarihi: 1/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000735447

Sıklık: İki Aylık

eISSN: 1303-6203

pISSN: 1300-0632

Sayı

Yazarlar:

ALI MUHAMMAD RUSHDI | ALAA MOHAMMAD ALTURKI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Electrical Engineering and Computer Science 2018 Vol.26 Issue 1, pp.257-269

Belge Tipi:

Makale

Yayın Tarihi:

1/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000735447

Sıklık:

İki Aylık

eISSN:

1303-6203

pISSN:

1300-0632