On successful completion of this module students should be able to

Derive the structure function from the structure diagram of a system;

Prove results on system reliability in terms of the reliability of their components;

Define and interpret the failure rate and derive the survival function from it;

Fit lifetime distibutions to data, including censored data;

Calculate non-parametric estimates of the survival function;

Calculate various exceedances and the distribution of the maxima and minima of a sequence of random variables;

State the extreme value theorem and apply it to derive approximate distributions of extremes;

Use the bootstrap (both parametic and non-parameteric) and jacknife to derive approximate confidence intervals and bias of estimates;

State the advantages and disadvantages of the bootstrap and jacknife;

Module Content

Survival Analysis: systems of components, reliability of systems, failure rate, lifetime distributions, inference, censoring;

Extreme Value Theory: modelling extrema, extreme value theorem, inference, extrema under non-random and random censoring;

The Bootstrap: review of Monte Carlo simulation, the jacknife, the simple bootstrap, extensions;

Module Prerequisite

ST2351

Recommended Reading

Barlow, R.E. and Proschan, F. (1981), Statistical Theory of Reliability and Life Testing, 2nd edition. To Begin With.

Crowder, M.J., Kimber, A.C., Smith, R.L. and Sweeting, T.J. (1991), Statistical Analysis of Reliability Data. Chapman & Hall

Reiss, R-D and thomas, M. (1991), Statistical Analysis of Extreme Values.

Efron, B. and Tibshirani, R. (1994), An Introduction to The Bootstrap, Chapman & Hall

Tanner, M. (1997), Tools For Statistical Inference. Springer

Assessment Detail

This module will be examined jointly with ST3455
in a 3-hour examination in Trinity term,
except that those taking just one of the
two modules will have a 2 hour examination.