This paper examines practical issues in the statistical analysis of component aging data. These issues center on the stochastic process chosen to model component failures. However, the paper also discusses practical issues related to parameter estimation and model validation. The two stochastic processes examined are repair same as new, leading to a renewal process, and repair same as old, leading to a nonhomogeneous Poisson process. Under the first assumption, times between failures can treated as statistically independent observations from a stationary process. The common distribution of the times between failures is called the renewal distribution. Under the second process, the times between failures will not be independently and identically distributed, and one cannot simply fit a renewal distribution to the cumulative failure times or the times between failures. The paper illustrates how the assumption made regarding the repair process is crucial to the analysis. The paper uses modern Bayesian computational techniques, based on Markov chain Monte Carlo sampling and freely available open-source software packages. Besides the choice of stochastic process, other issues that are discussed include qualitative graphical analysis and simple nonparametric hypothesis tests to help judge which process appears more appropriate, quantitative parameter estimation for both processes, and Bayesian model validation using the posterior predictive distribution. Numerical examples are presented to illustrate the issues discussed in the paper.

KELLY Dana;  RODIONOV Andriy;  KLUGEL Jens-Uwe; 

2008-11-04

American Nuclear Society

JRC45389

https://publications.jrc.ec.europa.eu/repository/handle/JRC45389,