A component is subjected to a sequence of shocks. Shocks are of two types, namely effective shocks and non-effective shocks. Damages due to effective shocks are exponential random variables. If the accumulated damage exceeds the threshold of the component, the component fails. The threshold of the component is also an exponential random variable. The survival probability of the component with

(known) shocks is derived. The maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the survival probability are obtained.

survival probability, shock model, life testing experiment, MLE, UMVUE.