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Statistical Reliability with Applications

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Springer Handbook of Engineering Statistics

Part of the book series: Springer Handbooks ((SHB))

Abstract

This chapter reviews fundamental ideas in reliability theory and inference. The first part of the chapter accounts for lifetime distributions that are used in engineering reliability analysis, including general properties of reliability distributions that pertain to lifetime for manufactured products. Certain distributions are formulated on the basis of simple physical properties, and other are more or less empirical. The first part of the chapter ends with a description of graphical and analytical methods to find appropriate lifetime distributions for a set of failure data.

The second part of the chapter describes statistical methods for analyzing reliability data, including maximum likelihood estimation and likelihood ratio testing. Degradation data are more prevalent in experiments in which failure is rare and test time is limited. Special regression techniques for degradation data can be used to draw inference on the underlying lifetime distribution, even if failures are rarely observed.

The last part of the chapter discusses reliability for systems. Along with the components that comprise the system, reliability analysis must take account of the system configuration and (stochastic) component dependencies. System reliability is illustrated with an analysis of logistics systems (e.g., moving goods in a system of product sources and retail outlets). Robust reliability design can be used to construct a supply chain that runs with maximum efficiency or minimum cost.

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References

  1. Z. W. Birnbaum, S. C. Saunders: A new family of life distributions, J. Appl. Probab. 6, 319–327 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  2. R. E. Barlow, F. Proschan: Statisitcal Theory of Reliability and Life Testing (Holt, Rinehart, Austin 1975)

    Google Scholar 

  3. J. I. Ansell, M. J. Phillips: Practical Methods for Reliability Data Analysis (Oxford Univ. Press, Oxford 1994)

    MATH  Google Scholar 

  4. L. Leemis: Reliability: Probabilistic Models and Statistical Methods (Prentice Hall, Englewood 1995)

    MATH  Google Scholar 

  5. P. A. Tobias, D. C. Trindade: Applied Reliability (CRC, Boca Raton 1995)

    Google Scholar 

  6. R. E. Barlow: Engineering Reliability (Society for Industrial and Applied Mathematics, Alexandria 1998)

    Book  MATH  Google Scholar 

  7. P. Kales: Reliability for Technology, Engineering and Management (Prentice-Hall, Englewood 1998)

    Google Scholar 

  8. W. Q. Meeker, L. A. Escobar: Statistical Methods for Reliability Data (Wiley, New York 1998)

    MATH  Google Scholar 

  9. W. R. Blischke, D. N. P. Murthy: Reliability Modeling, Prediction, and Optimization (Wiley, New York 2000)

    MATH  Google Scholar 

  10. S. E. Rigdon, A. P. Basu: Statistical Methods for the Reliability of Repairable Systems (Wiley-Interscience, New York 2000)

    MATH  Google Scholar 

  11. V. E. Johnson, M. Hamada, H. Martz, S. Reese, A. Wilson: Modern Reliability Analysis: A Bayesian Perspective (Springer, Berlin Heidelberg New York 2005)

    Google Scholar 

  12. J. L. Bogdanoff, F. Kozin: Probabilistic Models of Cumulative Damage (Wiley, New York 1985)

    Google Scholar 

  13. K. Sobczyk, B. F. Spencer: Random Fatigue From Data to Theory (Academic, Boston 1992)

    MATH  Google Scholar 

  14. M. R. Lyu: Handbook of Software Reliability Engineering (McGraw Hill, New York 1996)

    Google Scholar 

  15. N. D. Singpurwalla, S. P. Wilson: Statistical Methods in Software Engineering (Springer, Heidelberg Berlin New York 1999)

    MATH  Google Scholar 

  16. T. Bedford, R. Cooke: Probabilistic Risk Analysis: Foundations and Methods (Cambridge Univ. Press, London 2001)

    MATH  Google Scholar 

  17. G. Baecher, J. Christian: Reliability and Statistics in Geotechnical Engineering (Wiley, New York 2003)

    Google Scholar 

  18. M. Ohring: Reliability & Failure of Electronic Materials & Devices (Academic, Boston 1998)

    Google Scholar 

  19. R. E. Melchers: Structural Reliability Analysis and Prediction (Wiley, New York 1999)

    Google Scholar 

  20. M. Shaked, J. G. Shanthikumar: Stochastic Orders and their Applications (Academic, Boston 1994)

    MATH  Google Scholar 

  21. W. Weibull: A statistical theory of the strength of material, Ingeniors Vetenskaps Akademiens Handligar, Stockholm 151, 5–45 (1939)

    Google Scholar 

  22. H. A. David: Order Statistics (Wiley, New York 1981)

    MATH  Google Scholar 

  23. G. S. Mudholkar, D. K. Srivastava, G. D. Kollia: A generalization of the Weibull distribution with application to the analysis of survival data, J. Am. Stat. Assoc. 91, 1575–1583 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  24. A. Høyland, M. Rausand: System Reliability Theory Models and Statistical Methods (Wiley, New York 1994)

    Google Scholar 

  25. W. Q. Meeker: SPLIDA (S-PLUS Life Data Analysis) Version 6.5, http://www.public.iastate.edu/∼splida/

  26. S. J. Bae, P. H. Kvam: A nonlinear random coefficients model for degration testing, Technometrics 46(4), 460–469 (2004)

    Article  MathSciNet  Google Scholar 

  27. S. J. Bae, P. H. Kvam: A change-point analysis for modeling incomplete burn-in for light displays, IEEE Trans. , to appear (2006)

    Google Scholar 

  28. A. C. Atkinson: Plots, Transformations, and Regression: An Introduction to Graphical Methods of Diagnostic Regression Analysis, Oxford Statistical Science Series (Oxford Univ. Press, Oxford 1992)

    Google Scholar 

  29. L. A. Waller, B. W. Turnbull: Probability Plotting with censored data, Am. Stat. 46, 5–12 (1992)

    Article  Google Scholar 

  30. A. Owen: Empirical Likelihood (Chapman and Hall, CRC, Boca Raton 2001)

    Book  MATH  Google Scholar 

  31. B. Efron, R. Tibshirani: An Introduction to the Bootstrap (Chapman and Hall, CRC Press, Boca Raton 1993)

    MATH  Google Scholar 

  32. P. H. Kvam, F. J. Samaniego: Nonparametric maximum likelihood estimation based on ranked set samples, J. Am. Stat. Assoc. 89, 526–537 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  33. J. Huang: Asymptotic of the NPMLE of a distribution function based on ranked set samples, Ann. Stat. 25(3), 1026–1049 (1997)

    Article  Google Scholar 

  34. Z. Chen: Component reliability analysis of k-out-of-n systems with censored data, J. Stat. Plan. Inference. 116, 305–316 (2003)

    Article  MATH  Google Scholar 

  35. K. Takahasi, K. Wakimoto: On unbiased estimates of the population mean beased on samples stratified by meand of ordering, Ann. Inst. Stat. Math. 20, 1–31 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  36. P. H. Kvam, F. J. Samaniego: On estimating distribution functions using nomination samples, J. Am. Stat. Assoc. 88, 1317–1322 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  37. A. W. Marshall, I. Olkin: A multivariate exponential distribution, J. Am. Stat. Assoc. 62, 30–44 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  38. H. E. Daniels: The statistical theory of the strength of bundles of threads, Proc. R. Soc. Lond. A 183, 405–435 (1945)

    Article  MathSciNet  MATH  Google Scholar 

  39. P. H. Kvam, E. Peña: Estimating load-sharing properties in a dynamic reliability system, J. Am. Stat. Assoc. 100(469), 262–272 (2004)

    Article  Google Scholar 

  40. M. O. Ball: Computing Network Reliability, Oper Res 27, 823–838 (1979)

    Article  MATH  Google Scholar 

  41. B. Sanso, F. Soumis: Communication and Transportation Network Reliability Using Routing Models, IEEE Trans. Reliability 40, 29–37 (1991)

    Article  MATH  Google Scholar 

  42. V. Shi: Evaluating the performability of tactical communications network, IEEE Trans. Vehicular Technol. 53, 253–260 (2004)

    Article  Google Scholar 

  43. A. Chen, H. Yang, H. Lo, W. H. Tang: A capacity related reliability for transportation networks, J. Adv. Transport. 33(2), 183–200 (1999)

    Article  Google Scholar 

  44. S. Dandamudi, J.-C. Lu: Competition Driving Logistics Design with Continuous Approximation Methods, Technical Report can be seen in http://www.isye.gatech.edu/apps/research-papers/

  45. W. Ni, J.-C. Lu, P. Kvam: Multi-scale Spatial Modeling for Logistics System Reliability, Technical Report can be seen in http://www.isye.gatech.edu/apps/research-papers/

  46. C. F. J. Wu, M. Hamada: Experiments: Planning, Analysis, and Parameter Design Optimization (Wiley, New York 2000) p. 503

    MATH  Google Scholar 

  47. D. Fudenberg, J. Tirole: Game Theory (MIT Press, Cambridge 2000)

    Google Scholar 

  48. W. Chen, K. Lewis: Robust design approach for achieving flexibility in multidisciplinary design, AIAA J. 37(8), 982–989 (1999)

    Article  Google Scholar 

  49. C. Charoensiriwath, J.-C. Lu: Competition Under Retail Price and Manufacturing Service, Technical Report can be seen in http://www.isye.gatech.edu/apps/research-papers/

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Author information

Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, 755 Ferst Drive, 30332-0205, Atlanta, GA, USA

    Paul Kvam

  2. Georgia Institute of Technology, The School of Industrial and Systems Engineering, 765 Ferst Drive, Campus Box 0205, 30332, Atlanta, GA, USA

    Jye-Chyi Lu

Authors
  1. Paul Kvam
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  2. Jye-Chyi Lu
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Corresponding authors

Correspondence to Paul Kvam or Jye-Chyi Lu .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Engineering, Rutgers the State University of New Jersey, 96 Frelinghuysen Road, 08854, Piscataway, NJ, USA

    Hoang Pham Prof.

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© 2006 Springer-Verlag

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Kvam, P., Lu, JC. (2006). Statistical Reliability with Applications. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-84628-288-1_2

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  • DOI: https://doi.org/10.1007/978-1-84628-288-1_2

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-806-0

  • Online ISBN: 978-1-84628-288-1

  • eBook Packages: EngineeringEngineering (R0)

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