Statistical analysis of some reliability models: Parametrics, semi-parametrics and nonparametrics
An useful survey and unified treatment of the following four statistical reliability problems are considered: (i) bundle strength of filaments, (ii) k-component system — in series, (iii) k-component system — in parallel, and (iv) system availability under spare and repair. Along with the usual param...
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| Vydáno v: | Journal of statistical planning and inference Ročník 43; číslo 1; s. 41 - 66 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
Lausanne
Elsevier B.V
1995
New York,NY Elsevier Science Amsterdam |
| Témata: | |
| ISSN: | 0378-3758, 1873-1171 |
| On-line přístup: | Získat plný text |
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| Abstract | An useful survey and unified treatment of the following four statistical reliability problems are considered: (i) bundle strength of filaments, (ii)
k-component system — in series, (iii)
k-component system — in parallel, and (iv) system availability under spare and repair. Along with the usual parametric solutions, some nonparametric and semi-parametric formulations are presented, and the role of some resampling plans in this context is discussed briefly. |
|---|---|
| AbstractList | An useful survey and unified treatment of the following four statistical reliability problems are considered: (i) bundle strength of filaments, (ii)
k-component system — in series, (iii)
k-component system — in parallel, and (iv) system availability under spare and repair. Along with the usual parametric solutions, some nonparametric and semi-parametric formulations are presented, and the role of some resampling plans in this context is discussed briefly. |
| Author | Sen, Pranab Kumar |
| Author_xml | – sequence: 1 givenname: Pranab Kumar surname: Sen fullname: Sen, Pranab Kumar organization: Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599-7400, USA |
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| Cites_doi | 10.1177/0008068319600101 10.1214/aos/1176342418 10.1214/aos/1176350714 10.1111/j.2517-6161.1972.tb00899.x 10.1214/aos/1176343797 10.1214/aos/1176342367 10.1214/aoms/1177730196 |
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| Copyright | 1995 1995 INIST-CNRS |
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| Keywords | Bootstrapping Extrema of sample functions 62N05 Jackknifing Failure (hazard) rate Systems availability 62G99 Components in parallel Components in series Bundle strength of filaments Delta method Proportional hazard model Parameter estimation Cox model Extreme value Bootstrap Non parametric estimation Reliability Failure rate Semiparametric model |
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| PublicationDate | 1995 1995-1-00 |
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| References | Sen (BIB7) 1977; 5 Sen (BIB11) 1988; 50 Sen, Bhattacharyya, Suh (BIB14) 1973; 1 Cox (BIB2) 1972; 34 Daniels (BIB3) 1945; 183 Sen (BIB12) 1992 Sen (BIB5) 1960; 10 Sen (BIB9) 1986 Sen (BIB10) 1988; 16 Hoeffding (BIB4) 1948; 19 Sen (BIB6) 1973; 1 Sen (BIB8) 1981 Barlow, Proschan (BIB1) 1975 Sen, Bhattacharjee (BIB13) 1986 Daniels (10.1016/0378-3758(94)00007-I_BIB3) 1945; 183 Hoeffding (10.1016/0378-3758(94)00007-I_BIB4) 1948; 19 Sen (10.1016/0378-3758(94)00007-I_BIB10) 1988; 16 Sen (10.1016/0378-3758(94)00007-I_BIB6) 1973; 1 Sen (10.1016/0378-3758(94)00007-I_BIB12) 1992 Sen (10.1016/0378-3758(94)00007-I_BIB5) 1960; 10 Sen (10.1016/0378-3758(94)00007-I_BIB8) 1981 Sen (10.1016/0378-3758(94)00007-I_BIB14) 1973; 1 Sen (10.1016/0378-3758(94)00007-I_BIB7) 1977; 5 Sen (10.1016/0378-3758(94)00007-I_BIB9) 1986 Sen (10.1016/0378-3758(94)00007-I_BIB13) 1986 Cox (10.1016/0378-3758(94)00007-I_BIB2) 1972; 34 Barlow (10.1016/0378-3758(94)00007-I_BIB1) 1975 Sen (10.1016/0378-3758(94)00007-I_BIB11) 1988; 50 |
| References_xml | – start-page: 281 year: 1986 end-page: 296 ident: BIB13 article-title: Nonparametric estimators of availability under provisions of spare and repair, I publication-title: Reliability and Quality Control – year: 1975 ident: BIB1 article-title: Statistical Theory of Reliability and Life Testing: Probability Models – volume: 5 start-page: 315 year: 1977 end-page: 329 ident: BIB7 article-title: Some invariance principles relating to jackknifing and their role in sequential analysis publication-title: Ann. Statist. – start-page: 66 year: 1992 end-page: 79 ident: BIB12 article-title: Resampling methods for the extrema of certain sample functions publication-title: Probability and Statistics: Proc. Calcutta Triennial Internat. Conf. Statist – volume: 183 start-page: 405 year: 1945 end-page: 435 ident: BIB3 article-title: The statistical theory of the strength of bundles of threads publication-title: Proc. Roy. Soc. Ser. A – volume: 19 start-page: 293 year: 1948 end-page: 325 ident: BIB4 article-title: A class of statistics with asymptotically normal distribution publication-title: Ann. Math. Statist. – volume: 50 start-page: 394 year: 1988 end-page: 435 ident: BIB11 article-title: Functional approaches in resampling plans: A review of some recent developments publication-title: Sankhya, Ser. A – year: 1981 ident: BIB8 article-title: Sequential Nonparametric: Invariance Principles and Statistical Inference – volume: 34 start-page: 187 year: 1972 end-page: 220 ident: BIB2 article-title: Regression models and life tables (with discussion) publication-title: J. Roy. Statist. Soc. Ser. B – start-page: 297 year: 1986 end-page: 308 ident: BIB9 article-title: Nonparametric estimators of availability under provisions of spare and repair, II publication-title: Reliability and Quality Control – volume: 16 start-page: 450 year: 1988 end-page: 469 ident: BIB10 article-title: Functional jackknifing: Rationality and general asymptotics publication-title: Ann. Statist. – volume: 1 start-page: 297 year: 1973 end-page: 311 ident: BIB14 article-title: Limiting behavior of the extrema of certain sample functions publication-title: Ann. Statist. – volume: 10 start-page: 1 year: 1960 end-page: 18 ident: BIB5 article-title: On some convergence properties of U-statistics publication-title: Calcutta Statist. Assoc. Bull. – volume: 1 start-page: 526 year: 1973 end-page: 537 ident: BIB6 article-title: On fixed-size confidence bands for the bundle strength of filaments publication-title: Ann. Statist. – start-page: 66 year: 1992 ident: 10.1016/0378-3758(94)00007-I_BIB12 article-title: Resampling methods for the extrema of certain sample functions – volume: 10 start-page: 1 year: 1960 ident: 10.1016/0378-3758(94)00007-I_BIB5 article-title: On some convergence properties of U-statistics publication-title: Calcutta Statist. Assoc. Bull. doi: 10.1177/0008068319600101 – volume: 183 start-page: 405 year: 1945 ident: 10.1016/0378-3758(94)00007-I_BIB3 article-title: The statistical theory of the strength of bundles of threads – year: 1975 ident: 10.1016/0378-3758(94)00007-I_BIB1 – volume: 1 start-page: 526 year: 1973 ident: 10.1016/0378-3758(94)00007-I_BIB6 article-title: On fixed-size confidence bands for the bundle strength of filaments publication-title: Ann. Statist. doi: 10.1214/aos/1176342418 – volume: 16 start-page: 450 year: 1988 ident: 10.1016/0378-3758(94)00007-I_BIB10 article-title: Functional jackknifing: Rationality and general asymptotics publication-title: Ann. Statist. doi: 10.1214/aos/1176350714 – volume: 34 start-page: 187 year: 1972 ident: 10.1016/0378-3758(94)00007-I_BIB2 article-title: Regression models and life tables (with discussion) publication-title: J. Roy. Statist. Soc. Ser. B doi: 10.1111/j.2517-6161.1972.tb00899.x – start-page: 297 year: 1986 ident: 10.1016/0378-3758(94)00007-I_BIB9 article-title: Nonparametric estimators of availability under provisions of spare and repair, II – volume: 5 start-page: 315 year: 1977 ident: 10.1016/0378-3758(94)00007-I_BIB7 article-title: Some invariance principles relating to jackknifing and their role in sequential analysis publication-title: Ann. Statist. doi: 10.1214/aos/1176343797 – volume: 1 start-page: 297 year: 1973 ident: 10.1016/0378-3758(94)00007-I_BIB14 article-title: Limiting behavior of the extrema of certain sample functions publication-title: Ann. Statist. doi: 10.1214/aos/1176342367 – volume: 19 start-page: 293 year: 1948 ident: 10.1016/0378-3758(94)00007-I_BIB4 article-title: A class of statistics with asymptotically normal distribution publication-title: Ann. Math. Statist. doi: 10.1214/aoms/1177730196 – start-page: 281 year: 1986 ident: 10.1016/0378-3758(94)00007-I_BIB13 article-title: Nonparametric estimators of availability under provisions of spare and repair, I – year: 1981 ident: 10.1016/0378-3758(94)00007-I_BIB8 – volume: 50 start-page: 394 year: 1988 ident: 10.1016/0378-3758(94)00007-I_BIB11 article-title: Functional approaches in resampling plans: A review of some recent developments publication-title: Sankhya, Ser. A |
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| SubjectTerms | 62G99 62N05 Applications Biology, psychology, social sciences Bootstrapping Bundle strength of filaments Components in parallel Components in series Delta method Exact sciences and technology Extrema of sample functions Failure (hazard) rate Insurance, economics, finance Jackknifing Mathematics Medical sciences Probability and statistics Proportional hazard model Reliability, life testing, quality control Sciences and techniques of general use Statistics Systems availability |
| Title | Statistical analysis of some reliability models: Parametrics, semi-parametrics and nonparametrics |
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