Multi-dimensional recursion relations and mathematical induction techniques : the case of failure frequency of k-out-of-n systems
Other Title(s)
علاقات المعاودة و أساليب الاستقراء الرياضي متعددة الأبعاد : حالة تردد الفشل لنظم ك-من-بين-ن
Joint Authors
Rushdi, Mahmud Ali Muhammad
Barukab, Umar Muhammad
Rushdi, Ali Muhammad Ali
Source
Journal of King Abdulaziz University : Engineering Sciences
Issue
Vol. 27, Issue 2 (31 Dec. 2016), pp.15-31, 17 p.
Publisher
King Abdulaziz University Scientific Publishing Center
Publication Date
2016-12-31
Country of Publication
Saudi Arabia
No. of Pages
17
Main Subjects
Information Technology and Computer Science
Topics
Abstract EN
The probabilities of exactly and at least k successes out of n trials represent respectively the probability mass function (pmf) and the Complementary Cumulative Distribution Function (CCDF) of the generalized Binomial distribution.
These two probabilities obey the same two-dimensional recursive relations (or signal-flow-graph structure), albeit with different boundary conditions (sources) and almost identical regions of validity that cover approximately an octant of the k-n plane.
Related to these is the failure frequency of a non-repairable k-out-of-n system, which equals the probability density function (pdf) for the time to failure of this system.
This failure frequency is represented herein by a two-dimensional signal flow graph (SFG) whose sources emanate from one of the SFGs of the aforementioned probabilities.
Therefore, the recursive relations of this failure frequency take the shape of a three-dimensional loopless or acyclic graph.
Closed-form symbolic expressions for this failure frequency are obtained via Mason gain formula, i.e., simply via path enumeration.
Such expressions are also deduced herein via a two-dimensional strong version of mathematical induction.
An offshoot contribution of this paper is to derive expressions for the k-out-of-n failure frequency via Markov-chain modeling, and to demonstrate that the resulting expressions are equivalent to those obtained via recursive relations.
American Psychological Association (APA)
Rushdi, Mahmud Ali Muhammad& Barukab, Umar Muhammad& Rushdi, Ali Muhammad Ali. 2016. Multi-dimensional recursion relations and mathematical induction techniques : the case of failure frequency of k-out-of-n systems. Journal of King Abdulaziz University : Engineering Sciences،Vol. 27, no. 2, pp.15-31.
https://search.emarefa.net/detail/BIM-791454
Modern Language Association (MLA)
Rushdi, Mahmud Ali Muhammad…[et al.]. Multi-dimensional recursion relations and mathematical induction techniques : the case of failure frequency of k-out-of-n systems. Journal of King Abdulaziz University : Engineering Sciences Vol. 27, no. 2 (Dec. 2016), pp.15-31.
https://search.emarefa.net/detail/BIM-791454
American Medical Association (AMA)
Rushdi, Mahmud Ali Muhammad& Barukab, Umar Muhammad& Rushdi, Ali Muhammad Ali. Multi-dimensional recursion relations and mathematical induction techniques : the case of failure frequency of k-out-of-n systems. Journal of King Abdulaziz University : Engineering Sciences. 2016. Vol. 27, no. 2, pp.15-31.
https://search.emarefa.net/detail/BIM-791454
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 27-30
Record ID
BIM-791454