The paper categorizes shocks as major (Type A) and minor (Type B). While a major shock can become fatal to the system, minor shocks have been taken as non-fatal. Given that the rth order of a major shock is fatal (where r is a random variable; r = 0,1, 2,.), an attempt has been made to predict the survival time by the method of factorial moments. The main feature of this work is that the parameters that are usually unobservable or about which it is difficult to gain information, are estimable from the time-of-death data of the system or the patient. A second type of probability model with an accelerated failure rate for shocks in general has been developed to predict the residual survival time of the system (or the patient) given that the system (or the patient) has just received a major shock (of order r, say). A comparison of the residual survival time under an accelerated failure rate shows that by taking a constant hazard rate (while the real hazard rate is time-dependent and accelerated), the residual survival time is often overestimated. The second probability model has been developed by employing the technique of Palm probability.