References

Mathematics

ANTON, Howard (1988) Calculus with Analytic Geometry, 3rd edition, Wiley.
SADLER, A. J. and THORNING, D. W. S. (1987) Understanding Pure Mathematics, Oxford University Press.

Basic Probability Concepts

MILLER, Irwin and MILLER, Marylees (1999) John E. Freunds Mathematical Statistics, 6th ed. Prentice Hall.
ROSS, Sheldon (2002) A First Course in Probability, 6th ed. Prentice Hall.

Continuous Lifetime Distributions 1

O'CONNER, P. D. T. (1995) Practical Reliability Engineering, 3rd revised ed. Wiley.
  Contains the data on testing electrical relays against the Weibull reliability function on page 79 and the data on testing the breaking strengths of 15 equal length wires on page 82.

Continuous Lifetime Distributions 2

COX, D. and OAKES, D. (1984) Analysis of survival data. Chapman and Hall, p.169.
COX, S. and TAIT, R. (1998) Safety, Reliability & Risk Management, 2nd ed. Oxford: Butterworth-Heinemann, p.16.
  This data (shown on screen 6) in turn was taken from "An analysis of some failure data" David Journal of the American Statistical Association 1952, volume 47, page 113.
WANG, W. and KECECIOGLU, D. B. (2000) Fitting the Weibull log-linear model to accelerated life-test data. IEEE Transactions on Reliability, June 2000, 49(2), 217 - 223.

Model Selection

BAKER, R. D. (1993) A nonparametric estimator of the renewal function. Computers and Operational Research, pp. 167-178.
BURNHAM, K. P. and ANDERSON, D. R. (2002) Model Selection and multimodel inference: a practical information-theoretic approach. New York: Springer.
  Discusses the corrected Akaike Information Criterion (AIC).
COX, D. R. and OAKES, D. (1984) Analysis of Survival data, London: Chapman and Hall.
LAWLESS, J. F. (1982) Statistical models and methods for lifetime data. New York: Wiley.
STONE, G. C. (1978) Statistical analysis of accelerated ageing tests on solid electrical insulation. University of Waterloo, MSc thesis.
SAKAMOTO, Y., ISHIGURO, M. and KITAGAWA, G. (1986) Akaike Information Criterion Statistics. Tokyo: KTK Publishing House.

Testing Model Fitness

LEITCH, R. D. (1995) Reliability Analysis for Engineers. New York: Oxford University Press.
NEAVE, H. R. (1985) Elementary Satistics Tables. London: George Allen and Unwin.
PEARSON, E. S. and HARTLEY, H. O. (1972) Biometrika Tables for Satistics, 2, Cambridge University Press.
SHAPIRO, S. S. and WILK, M. B. (1965) An analysis of variance test for normality (complete samples). Biometrika, 22, 591.
STEPHENS, M. A. (1997) Goodness of fit for the extreme value distribution. Biometrika, 62, 467 - 475.
WOLSTENHOLME L. C. (1995) A non-parametric test of the weakest-link property. Technometrics, 37, 169 - 175.
WOLSTENHOLME L. C. (1999) Reliability Modelling: A Statistical Approach. London: Chapman and Hall.

Regression Modelling

BENNET, S. (1983) Analysis of Survival Data by the Proportional Odds Model. Statistics in Medicine, 2, 273 - 77.
COX, D. R. and OAKES, D. (1984) Analysis of Survival Data. London: Chapman and Hall.
CROWDER, M. J., KIMBER, A. C., SMITH, R. L. and SWEENY, T, J. (2000) Statistical Analysis of reliability data. Chapman and Hall/CRC.
NETER, J., KUTNER,, M. H., NACHTSHEIM, C. J. and WASSERMAN, W. (1996) Applied Linear Statistical Models. WCB McGraw Hill.
LAWLESS, J. F. (1986) A note on lifetime regression models. Biometrika, 73, 509-12.
LINDGREN, G. And ROOTZEN, H. (1987) Extreme values: theory and technical applications. Scand. J. Statist., 14, 241-79.
WATSON, A. S. and SMITH, R. L. (1985) An examination of statistical theories for fibrous materials in the light of experimental data. J. Meter. Sci., 20, 3260-70.

Proportional Hazards and Accelerated Life Models

COX D. R. (1972) Regression Models and Life Tables (with discussion). J.R. Statistics. Soc. B, 34, 187-202.
CROWDER, M. J., KIMBER, A. C., SMITH, R. L. and SWEETING, T. J. (1991) Statistical Analysis of Reliability Data. London: Chapman & Hall.
KALBFLEISCH, J. D. and PRENTICE, R. (1980) The Statistical Analysis of Failure Time Data. New York: John Wiley & Sons.
LAWLESS, J. F. (1982) Statistical Models and Methods for Lifetime Data. New York: John Wiley & Sons.
NELSON, W. B. (1972) Theory and applications of hazard plotting for censored failure data. Technometrics, 14, 945-65.
PRENTICE, R. L. (1973) Exponential survival with censoring and explanatory variables. Biometika, 60, 279-288.
WOLSTENHOLME, L. C. (1999) Reliability Modelling, a Statistical Approach. London: Chapman & Hall.

Repairable Systems

ASCHER, H. and FEINGOLD, H. (1984) Repairable systems reliability. New York: Marcel Dekker.
CROWDER, M. J., KIMBER, A. C., SMITH, R. L. and SWEETING, T. J. (1991) Statistical analysis of reliability data. London: Chapman & Hall.
WOLSTENHOLME, L. C. (1999) Reliability Modelling, a Statistical Approach. London: Chapman & Hall.

Renewal Processes

BAKER, R. D. (1993) A nonparametric estimator of the renewal function. Computers and Operational Research, 167-178.
COX, D. R. (1962) Renewal Theory. London: Chapman & Hall.
DUFFY, D. G. (1993) On the numerical inversion of Laplace transforms: comparison of three new methods on characteristic problems from applications. ACM transactions on mathematical software, 333-359.
MURLI, A. and RIZZARDI, M. (1990) Algorithm 682: Talbot's method for the Laplace inversion problem. ACM transactions on mathematical software, 158-168.
TAYLOR, H. M. and KARLIN, S. (1994) An introduction to stochastic modelling. San Diego: Academic Press.
TIJMS, H. C. (1994) Stochastic models: an algorithmic approach. New York: Wiley.
XIE, M. (1989) On the solution of renewal-type integral equations. Commun. Statist. B, 281-293.

The Bayesian Approach

BERNARDO, J. M., and SMITH, A. F. M. (2000) Bayesian Theory, 2nd ed. Chichester: Wiley.
BERRY (1996) Statistics: a Bayesian Perspective.
GELMAN (1995) Carlin, Stern and Rubin, Bayesian Data Analysis.
O'HAGAN, A. (2004) Kendall's Advanced Theory of Statistics Volume 2B: Bayesian Inference, 2nd ed. London: Arnold.
JEFFREYS (1998) Theory of Probability.
LEE, P. M. (2004) Bayesian Statistics: an Introduction, 3rd ed. London: Arnold.
MIGON and GAMERMAN (1999) Statistical Inference: an Integrated Approach.
PRESS (1989) Bayesian Statistics - Principles, Models and Applications.