Some exact and approximate methods for large scale systems steady-state availability analysis.

Persistent Link:
http://hdl.handle.net/10150/187066
Title:
Some exact and approximate methods for large scale systems steady-state availability analysis.
Author:
Chien, Ying-Che
Issue Date:
1995
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
System availability is the probability of the system being operable at instant t. Markov chains are a model used for system availability analysis. The exact analytical solution in terms of component failure rates and repair rates for steady-state system availability is complex to find solving the large numbers of simultaneous linear equations that result from the model. Although exact analytical solutions have been developed for series and parallel systems and for some other small size systems, they have not been developed for large scale general systems with n distinct components. Some methods for approximate analytical solutions have been suggested, but limitations on network types, over simplified states merge conditions and lack of predictions of approximation errors make these methods difficult to use. Markov state transition graphs can be classified as symmetric or asymmetric. A symmetric Markov graph has two-way transitions between each pair of communicating nodes. An asymmetric Markov graph has some pair(s) of communicating nodes with only one-way transitions. In this research, failure rates and repair rates are assumed to be component dependent only. Exact analytical solutions are developed for systems with symmetric Markov graphs. Pure series systems, pure parallel systems and general k out of n systems are examples of systems with symmetric Markov graphs. Instead of solving a large number of linear equations from the Markov model to find the steady-state system availability, it is shown that only algebraic operations on component failure rates and repair rates are necessary. In fact, for the above class of systems, the exact analytical solutions are relatively easy to obtain. Approximate analytical solutions for systems with asymmetric Markov graphs are also developed based on the exact solutions for the corresponding symmetric Markov graphs. The approximate solutions are shown to be close to the exact solutions for large scale and complex systems. Also, they are shown to be lower bounds for the exact solutions. Design principles to improve systems availability are derived from the analytical solutions for systems availability. Important components can be found easily with the iteration procedure and computer programs provided in this research.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Large scale systems; Industrial engineering.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems and Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Dietrich, D. L.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleSome exact and approximate methods for large scale systems steady-state availability analysis.en_US
dc.creatorChien, Ying-Cheen_US
dc.contributor.authorChien, Ying-Cheen_US
dc.date.issued1995en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractSystem availability is the probability of the system being operable at instant t. Markov chains are a model used for system availability analysis. The exact analytical solution in terms of component failure rates and repair rates for steady-state system availability is complex to find solving the large numbers of simultaneous linear equations that result from the model. Although exact analytical solutions have been developed for series and parallel systems and for some other small size systems, they have not been developed for large scale general systems with n distinct components. Some methods for approximate analytical solutions have been suggested, but limitations on network types, over simplified states merge conditions and lack of predictions of approximation errors make these methods difficult to use. Markov state transition graphs can be classified as symmetric or asymmetric. A symmetric Markov graph has two-way transitions between each pair of communicating nodes. An asymmetric Markov graph has some pair(s) of communicating nodes with only one-way transitions. In this research, failure rates and repair rates are assumed to be component dependent only. Exact analytical solutions are developed for systems with symmetric Markov graphs. Pure series systems, pure parallel systems and general k out of n systems are examples of systems with symmetric Markov graphs. Instead of solving a large number of linear equations from the Markov model to find the steady-state system availability, it is shown that only algebraic operations on component failure rates and repair rates are necessary. In fact, for the above class of systems, the exact analytical solutions are relatively easy to obtain. Approximate analytical solutions for systems with asymmetric Markov graphs are also developed based on the exact solutions for the corresponding symmetric Markov graphs. The approximate solutions are shown to be close to the exact solutions for large scale and complex systems. Also, they are shown to be lower bounds for the exact solutions. Design principles to improve systems availability are derived from the analytical solutions for systems availability. Important components can be found easily with the iteration procedure and computer programs provided in this research.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectLarge scale systemsen_US
dc.subjectIndustrial engineering.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairDietrich, D. L.en_US
dc.contributor.committeememberSzidarovszky, Ferencen_US
dc.contributor.committeememberFernandez, Emmanuelen_US
dc.contributor.committeememberKececioglu, Dimitri B.en_US
dc.contributor.committeememberAskin, Ronald G.en_US
dc.identifier.proquest9531089en_US
dc.identifier.oclc700298006en_US
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