Reliability and Survival Analysis

Syllabus Details

• Unit I: Reliability concepts and measures, components and systems, coherent systems, reliability of coherent systems. Life-distributions, reliability function, hazard rate, Mean residual life, common univariate life distributions exponential, weibull, gamma, etc.. Bivariate exponential.
• Unit II: Structure function, coherent structure Reliability and their bonds, the notion of aging; failure rate, classes of life time distributions and their relationships, Availability, maintenances through repairs and spares, multi state systems, multivariate monotone failure distributions.
• Unit III: Estimation and testing under censoring for parametric models, testing for class properties, nonparametric models. Kaplan Meier estimation of reliability curve, Greenwood formula, Non parametric methods for comparison of several reliability curves, Log rank tests.
• Unit IV: Regression models in reliability, Cox PH and Accelerated failure time models; Estimation of parameters and diagnostics. conditional and partial likelihoods, asymptotic normality of estimators.

Course Learning Objective

1. Discuss various statistical lifetime models.
2. Discuss various classes and their interrelations.
3. Apply non-parametric estimation in lifetime data.

Recommended Books

1. Barlow, R. E. and Proschan, F., Statistical Theory of Reliability and Life Testing, Holt, Renehart and Winston Inc., 1975
2. Miller, R. G., Survival Analysis, John Wiley, NY, 1981
3. Deshpande, J. V. and Purohit, S. G., Life Time Data - Statistical Models and Methods, World Scientific, 2005