Basic Statistical Inference

  • Wallace R. Blischke
  • M. Rezaul Karim
  • D. N. Prabhakar Murthy
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


Once data are collected, edited, summarized and otherwise prepared for detailed analysis, basic methods of statistical inference are applied to address stated experimental and management objectives. In this chapter, we look at several key statistical techniques that are used in inference, particularly in the context of reliability and warranty analysis. These include (1) estimation, including maximum likelihood, several other methods of point estimation, and confidence intervals; (2) hypothesis testing, including comparison of two population means; (3) nonparametric methods for comparing populations; (4) tolerance intervals for estimating population fractiles; and (5) rank correlation for measuring data relationships.


Likelihood Function Exponential Distribution Weibull Distribution Maximum Likelihood Estimator Asymptotic Variance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abramowitz M, Stegun IA (1964) Handbook of mathematical functions with formulas, graphs and mathematical tables. U.S. Government Printing Office, WashingtonGoogle Scholar
  2. 2.
    Blischke WR, Murthy DNP (2000) Reliability. Wiley, New YorkMATHCrossRefGoogle Scholar
  3. 3.
    Dixon WJ, Massey FJ Jr (1969) Introduction to Statistical Analysis, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  4. 4.
    Govindarajulu Z (1964) A supplement to Mendenhall’s bibliography on life testing and related topics. J Am Statist Assoc 59:1231ᾢ1291MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Hirose H, Lai TL (1997) Inference from grouped data in three-parameter Weibull models with applications to breakdown-voltage experiments. Technometrics 39:199ᾢ210MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Hogg RV, Craig A, McKean JW (2004) Introduction to mathematical statistics, 6th Edition edn. Prentice Hall, New YorkGoogle Scholar
  7. 7.
    Hollander M, Wolfe DA (1999) Nonparametric statistical methods, 2nd Edition edn. Wiley, New YorkMATHGoogle Scholar
  8. 8.
    Høyland A, Raussand M (1994) System reliability theory. Wiley Interscience, New YorkGoogle Scholar
  9. 9.
    Johnson NL, Kotz S (1970) Distribution in statistics: continuous univariate distributionsᾢI. Wiley, New YorkGoogle Scholar
  10. 10.
    Kruskal W, Wallis A (1952) Use of ranks in one-criterion variance analysis. J Am Statist Assoc 47:583ᾢ621MATHCrossRefGoogle Scholar
  11. 11.
    Lawless JF (1982) Statistical models and methods for lifetime data. Wiley, New YorkMATHGoogle Scholar
  12. 12.
    Martz HF, Waller RA (1982) Bayesian reliability analysis. Wiley, New YorkMATHGoogle Scholar
  13. 13.
    Moore DS, McCabe GP, Craig B (2007) Introduction to the practice of statistics. W H Freeman, New YorkGoogle Scholar
  14. 14.
    Murthy DNP, Xie M, Jiang R (2004) Weibull models. Wiley, New YorkMATHGoogle Scholar
  15. 15.
    Nelson W (1982) Applied life data analysis. Wiley, New YorkMATHCrossRefGoogle Scholar
  16. 16.
    Owen DB (1962) Handbook of statistical tables. Addison-Wesley, Reading, MAMATHGoogle Scholar
  17. 17.
    Ryan TP (2007) Modern engineering statistics. John Wiley, New YorkMATHCrossRefGoogle Scholar
  18. 18.
    Somerville P (1958) Tables for obtaining non-parametric tolerance limits. Ann of Math Statist 29:599ᾢ601MATHCrossRefGoogle Scholar
  19. 19.
    Stuart A, Ord JK (1991) Kendall’s advanced theory of statistics, vol. 2, 5th Edition edn. Oxford University Press, New YorkMATHGoogle Scholar
  20. 20.
    Wackerly D, Mendenhall W, Scheaffer RL (2007) Mathematical statistics with applications, Duxbury, New York 2007Google Scholar
  21. 21.
    Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1:80ᾢ83CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Wallace R. Blischke
    • 1
  • M. Rezaul Karim
    • 2
  • D. N. Prabhakar Murthy
    • 3
  1. 1.Sherman Oaks, Los AngelesUSA
  2. 2.Department of StatisticsRajshahi UniversityRajshahiBangladesh
  3. 3.School of Mechanical and Mining EngineeringThe University of QueenslandBrisbaneAustralia

Personalised recommendations