skip to content
Mathematical models for systems reliability Preview this item
ClosePreview this item
Checking...

Mathematical models for systems reliability

Author: Benjamin Epstein; Ishay Weissman
Publisher: Boca Raton : CRC Press, ©2008.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Covers the required probability background for understanding reliability theory. This book shows how certain techniques can be applied to a range of reliability problems. It explores statistical  Read more...

Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Benjamin Epstein; Ishay Weissman
ISBN: 9781420080827 1420080822
OCLC Number: 213375865
Notes: "A Chapman & Hall book."
Description: 253 pages : illustrations ; 25 cm
Contents: 1.1 The Poisson process and distribution 1 --
1.2 Waiting time distributions for a Poisson process 6 --
1.3 Statistical estimation theory 8 --
1.3.1 Basic ingredients 8 --
1.3.2 Methods of estimation 9 --
1.3.3 Consistency 11 --
1.3.4 Sufficiency 12 --
1.3.5 Rao-Blackwell improved estimator 13 --
1.3.6 Complete statistic 14 --
1.3.7 Confidence intervals 14 --
1.3.8 Order statistics 16 --
1.4 Generating a Poisson process 18 --
1.5 Nonhomogeneous Poisson process 19 --
1.6 Three important discrete distributions 22 --
1.7 Problems and comments 24 --
2 Statistical life length distributions 39 --
2.1 Stochastic life length models 39 --
2.1.1 Constant risk parameters 39 --
2.1.2 Time-dependent risk parameters 41 --
2.1.3 Generalizations 42 --
2.2 Models based on the hazard rate 45 --
2.2.1 IFR and DFR 48 --
2.3 General remarks on large systems 50 --
2.4 Problems and comments 53 --
3 Reliability of various arrangements of units 63 --
3.1 Series and parallel arrangements 63 --
3.1.1 Series systems 63 --
3.1.2 Parallel systems 64 --
3.1.3 The k out of n system 66 --
3.2 Series-parallel and parallel-series systems 67 --
3.3 Various arrangements of switches 70 --
3.3.1 Series arrangement 71 --
3.3.2 Parallel arrangement 72 --
3.3.3 Series-parallel arrangement 72 --
3.3.4 Parallel-series arrangement 72 --
3.3.5 Simplifications 73 --
3.4 Standby redundancy 76 --
3.5 Problems and comments 77 --
4 Reliability of a one-unit repairable system 91 --
4.1 Exponential times to failure and repair 91 --
4.2 Generalizations 97 --
4.3 Problems and comments 98 --
5 Reliability of a two-unit repairable system 101 --
5.1 Steady-state analysis 101 --
5.2 Time-dependent analysis via Laplace transform 105 --
5.2.1 Laplace transform method 105 --
5.2.2 A numerical example 111 --
5.3 On Model 2(c) 113 --
5.4 Problems and Comments 114 --
6 Continuous-time Markov chains 117 --
6.1 The general case 117 --
6.1.1 Definition and notation 117 --
6.1.2 The transition probabilities 119 --
6.1.3 Computation of the matrix P(t) 120 --
6.1.4 A numerical example (continued) 122 --
6.1.5 Multiplicity of roots 126 --
6.1.6 Steady-state analysis 127 --
6.2 Reliability of three-unit repairable systems 128 --
6.2.1 Steady-state analysis 128 --
6.3 Steady-state results for the n-unit repairable system 130 --
6.3.1 Example 1 --
Case 3(e) 131 --
6.3.3 Example 3 131 --
6.3.4 Example 4 132 --
6.4 Pure birth and death processes 133 --
6.4.3 Example 3 134 --
6.4.4 Example 4 134 --
6.5 Some statistical considerations 135 --
6.5.1 Estimating the rates 136 --
6.5.2 Estimation in a parametric structure 137 --
6.6 Problems and comments 138 --
7 First passage time for systems reliability 143 --
7.1 Two-unit repairable systems 143 --
7.1.1 Case 2(a) of Section 5.1 143 --
7.1.2 Case 2(b) of Section 5.1 148 --
7.2 Repairable systems with three (or more) units 150 --
7.2.1 Three units 150 --
7.2.2 Mean first passage times 152 --
7.2.3 Other initial states 154 --
7.3 Repair time follows a general distribution 160 --
7.3.1 First passage time 160 --
7.3.3 Steady-state probabilities 165 --
7.4 Problems and comments 167 --
8 Embedded Markov chains and systems reliability 173 --
8.1 Computations of steady-state probabilities 173 --
8.1.1 Example 1: One-unit repairable system 174 --
8.1.2 Example 2: Two-unit repairable system 175 --
8.1.3 Example 3: n-unit repairable system 177 --
8.1.4 Example 4: One out of n repairable systems 183 --
8.1.5 Example 5: Periodic maintenance 184 --
8.1.6 Example 6: Section 7.3 revisited 189 --
8.1.7 Example 7: One-unit repairable system with prescribed on-off cycle 192 --
8.2 Mean first passage times 194 --
8.2.1 Example 1: A two-unit repairable system 194 --
8.2.2 Example 2: General repair distribution 195 --
8.2.3 Example 3: Three-unit repairable system 195 --
8.2.4 Computations based on s[subscript jk] 197 --
8.3 Problems and comments 200 --
9 Integral equations in reliability theory 207 --
9.2 Example 1: Renewal process 208 --
9.2.1 Some basic facts 208 --
9.2.2 Some asymptotic results 210 --
9.2.3 More basic facts 212 --
9.3 Example 2: One-unit repairable system 213 --
9.4 Example 3: Preventive replacements or maintenance 215 --
9.5 Example 4: Two-unit repairable system 218 --
9.6 Example 5: One out of n repairable systems 219 --
9.7 Example 6: Section 7.3 revisited 220 --
9.8 Example 7: First passage time distribution 223 --
9.9 Problems and comments 224.
Responsibility: Benjamin Epstein, Ishay Weissman.
More information:

Reviews

Editorial reviews

Publisher Synopsis

... The material presented in the book is classic material, but is also timeless because the basic theory, probability and statistical rigor and applications to system reliability are still relevant Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/213375865> # Mathematical models for systems reliability
    a schema:Book, schema:CreativeWork ;
   library:oclcnum "213375865" ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/131346331#Place/boca_raton> ; # Boca Raton
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/flu> ;
   schema:about <http://id.worldcat.org/fast/1093656> ; # Reliability (Engineering)--Mathematics
   schema:about <http://dewey.info/class/620.00452015118/e22/> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/131346331#Topic/fiabilite_mathematiques> ; # Fiabilité--Mathématiques
   schema:about <http://experiment.worldcat.org/entity/work/data/131346331#Topic/reliability_engineering_mathematics> ; # Reliability (Engineering)--Mathematics
   schema:about <http://experiment.worldcat.org/entity/work/data/131346331#Topic/fiabilite_methodes_statistiques> ; # Fiabilité--Méthodes statistiques
   schema:about <http://id.worldcat.org/fast/1141415> ; # System failures (Engineering)--Mathematical models
   schema:about <http://experiment.worldcat.org/entity/work/data/131346331#Topic/system_failures_engineering_mathematical_models> ; # System failures (Engineering)--Mathematical models
   schema:bookFormat bgn:PrintBook ;
   schema:contributor <http://viaf.org/viaf/48695093> ; # Ishay Weissman
   schema:copyrightYear "2008" ;
   schema:creator <http://experiment.worldcat.org/entity/work/data/131346331#Person/epstein_benjamin_1918> ; # Benjamin Epstein
   schema:datePublished "2008" ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/131346331> ;
   schema:inLanguage "en" ;
   schema:name "Mathematical models for systems reliability"@en ;
   schema:productID "213375865" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/213375865#PublicationEvent/boca_raton_crc_press_2008> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/131346331#Agent/crc_press> ; # CRC Press
   schema:url <http://catdir.loc.gov/catdir/toc/ecip0813/2008010874.html> ;
   schema:workExample <http://worldcat.org/isbn/9781420080827> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/213375865> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/131346331#Person/epstein_benjamin_1918> # Benjamin Epstein
    a schema:Person ;
   schema:birthDate "1918" ;
   schema:familyName "Epstein" ;
   schema:givenName "Benjamin" ;
   schema:name "Benjamin Epstein" ;
    .

<http://experiment.worldcat.org/entity/work/data/131346331#Topic/fiabilite_mathematiques> # Fiabilité--Mathématiques
    a schema:Intangible ;
   schema:name "Fiabilité--Mathématiques"@fr ;
    .

<http://experiment.worldcat.org/entity/work/data/131346331#Topic/fiabilite_methodes_statistiques> # Fiabilité--Méthodes statistiques
    a schema:Intangible ;
   schema:name "Fiabilité--Méthodes statistiques"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/131346331#Topic/system_failures_engineering_mathematical_models> # System failures (Engineering)--Mathematical models
    a schema:Intangible ;
   schema:hasPart <http://id.loc.gov/authorities/subjects/sh85131738> ;
   schema:name "System failures (Engineering)--Mathematical models"@en ;
    .

<http://id.worldcat.org/fast/1093656> # Reliability (Engineering)--Mathematics
    a schema:Intangible ;
   schema:name "Reliability (Engineering)--Mathematics"@en ;
    .

<http://id.worldcat.org/fast/1141415> # System failures (Engineering)--Mathematical models
    a schema:Intangible ;
   schema:name "System failures (Engineering)--Mathematical models"@en ;
    .

<http://viaf.org/viaf/48695093> # Ishay Weissman
    a schema:Person ;
   schema:birthDate "1940" ;
   schema:familyName "Weissman" ;
   schema:givenName "Ishay" ;
   schema:name "Ishay Weissman" ;
    .

<http://worldcat.org/isbn/9781420080827>
    a schema:ProductModel ;
   schema:isbn "1420080822" ;
   schema:isbn "9781420080827" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.