by Wendt, Heide.

**Series:** 1998-11, Preprints

- MSC:
- 60G55 Point processes
- 62F10 Point estimation
- 62F12 Asymptotic properties of estimators

**Abstract:**

The system reliability for a shock model with accumulating

damages will be described by marked point processes

where the sequence of jump times is a doubly stochastic

Poisson process. The intact probability of the system is

determined for different distributions of damages.

Likelihood functions are depended on observed history.

The several resulting maximum likelihood estimates for

parameters in the distribution of the system failure time are

derived.

**Keywords:**

point process, doubly stochastic Poisson process, history, compensator, independent right-censoring