A shock model for assessing component aging reliability
A. Rodionov, G. Celeux,
ESReDA seminar, Madrid, Spain, 27-28 May 2002,
In this communication we present a competing risk model applicable for observed failures, which can be classified into two types. The first type is "accidental" failure. It does not depend on the component age and can occur at any time with the same intensity. The second type of failure is "cumulative degradation" failure, which can occur on demand or during the startup, and is caused by the accumulation of an unknown number of shocks. Thus, this second type of failure depends on the component age.
We assume that "accidental" failures arise from an exponential distribution with a failure rate l and that the shocks are independent and arise from a Poisson distribution with a known intensity w. Consequently, the number of shocks until the equipment "cumulative degradation" failure follows a Gamma distribution with parameters N and w, where N denotes the number of shocks causing a failure.
The competing risk model we propose is a two parameters (l, N) model. These parameters have to be estimated from operating experience data for which the failure cause is generally unknown. Moreover, there are strongly right-censored data.
We have developed several algorithms to estimate the parameters of this masked risk model
* a maximum likelihood estimation via the EM (expectation maximization) algorithm;
* a stochastic version of EM;
* a Bayesian estimation using an importance sampling technique.
Moreover, an extension of this model is presented taking into account data concerning component replacement due to preventive maintenance for which our algorithms have been adapted.
This model appears to be useful:
* for aging reliability assessment of safety components with multiple operating modes (periodically tested components, rarely loaded equipment, etc.);
* for interpreting the failure rate parameter as a function of component age ;
* for combining non aging component failures and aging degradations due to the normal and abnormal operational stresses;
* for providing some idea about component lifetime.