  In this paper, a new reliability model has been developed for a single system
degrading stochastically which experiences soft and hard failure. Soft failure
occurs when the physical deterioration level of the system is greater than a
predefined failure threshold, and hard failure occurs when the instantaneous
stress caused by a shock process is greater than a critical threshold. It is
considered that the degradation and shock process are mutually dependent. In
fact, each arriving shock accelerates the degradation process by adding abrupt
additional damages to the degradation path and changing the degradation rate
according to specific magnitude; also, the cumulative degradation changes the
occurrence intensity of shock process. A gamma process is used as a stochastic
process to model the degradation path. A realistic numerical example is
presented to illustrate the proposed reliability.
