The present paper deals with two time-shifted density models for wear out failure period of a single unit system. The study, considered the time-shifted Gamma and Normal distributions. Wear out failures occur as a result of deterioration processes or mechanical wear and its probability of occurrence increases with time. A failure rate as a function of time deceases in an early failure period and it increases in wear out period. Failure rates for time shifted distributions and expression for mean time to system are also obtained. Finally, the graphically representation of all the measures of reliability are shown. So we can say from the study that in the wear out period the reliability of the system increases and failure rates of the system decreases.