## Presentation

Censored or truncated data,  instantaneous hazard rate, ageing models, parametric and nonparametric (Kaplan-Meier and Nelson-Aalen) estimation, models with covariates (regression models of Cox and of Aalen), bayesian approach.

System structure and Reliability:

reliability diagram, series system, parallel system, k/n or mixed system, structure function.

Reliability of repairable systems:

Reliability and Availability, Markov models, failure intensity process, homogenous and non homogeneous Poisson process models, renewal process, corrective and préventive maintenance, imperfect maintenance models, dégradation models and maintenance policy.

## Objectives

At the end of this module, the student will be able to drive the following process and to explain the obtained conclusions:

• Using the Reliability database in order to estimate the functions of interest
• Analyzing and exploiting the  structure of a system to derive its reliability from the characteristics of its components
• Modeling the recursive occurrences of the failures on a system. Modeling the évolution of the system-state with time.
• Modeling the effect of maintenance and its planning according to the observations made on the system (dégradation process in particular)

## Needed prerequisite

• Markov chains and applications (MIC3)
• Inferential Statistics (I3MIMT41)
• Statistical Modelling (I4MMMS71)
• Poisson processes, applications in Insurance and Reliability (I4MMSP81)

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

## Bibliography

• William Q. Meeker, Luis A. Escobar. Statistical Methods for Reliability Data, Wiley (1998)
• Patrick O'Connor & Andre Kleyner. Practical Reliability Engineering, 5th Edition, Wiley (2012)
• Marvin Rausand & Arnljot Høyland. System Reliability Theory: Models, Statistical Methods, and Applications, 2nd Edition, Wiley (2004).