Hnbue property in a shock model with cumulative damage threshold
A device subjected to shocks occurring randomly according to a general counting process and that fails when the cu~nulative damage exceeds a fixed threshold is considered. Sufficient conditions for the lifetime of an HNBTJE class device are given and it is shown that the HNBUE property for the shock model depends only on the arrival process. A means of obtaining distribution functions of the HNBUE class in parametric form is given and the characteristic function of the accumulated damage process is obtained.