Ayandegan Institute of Higher Education, IranInternational Journal of Research in Industrial Engineering2783-13377120180401[0,1] Truncated Fréchet-Weibull and Fréchet Distributions1061355571410.22105/riej.2018.100865.1020ENS.AbidDepartment of mathematics, Education College, University of Mustansiriyah, Baghdad, Iraq.0000-0003-3617-6908R.AbdulrazakDepartment of mathematics, Education College, University of Mustansiriyah, Baghdad, Iraq.Journal Article20171012In this paper, we introduce a new family of continuous distributions based on [0, 1] Truncated Fréchet distribution. [0, 1] Truncated Fréchet Weibull ([0, 1] ) and [0, 1] Truncated Fréchet ([0, 1] ) distributions are discussed as special cases. The cumulative distribution function, the rth 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 always greater than the expected stress. The safety factor can be defined in terms of strength and stress as strength/stress. So, the [0, 1] strength-stress and the [0, 1] strength-stress models with different parameters will be derived here. The Shannon entropy and Relative entropy will be derived also.http://www.riejournal.com/article_55714_0459bc5cae3ec76f7da643445319dbe2.pdf