Abstract: In this study, a new family of continuous distributions based on [0, 1] truncated Frechet distribution is introduced. Special cases of [0, 1] truncated Frechet Power distribution ([0, 1] TFP_ower) is argued. The cumulative distribution function, the rth moment and central moment the mean, the variance, the skewness, the kurtosis, the mode, the median, the characteristic function, the reliability function and the hazard rate function are obtained for the distributions under consideration. It is well known that an item fails when a stress to which it is subjected exceeds the corresponding strength. In this sense, strength can be viewed as “resistance to failure”. Good design practice is such that the strength is almost greater than the predicted stress. The safety factor can be defined in terms of strength and stress as strength/stress. Consequently, the [0, 1] TFP_ower strength-stress will the Shannon entropy and Kullback-Leibler and Renyi entropy will be derived also.