Coexistence of fuzziness and the randomness has become an intrinsic character in modern manufacturing environments. Accordingly, it is necessary to introduce a new random fuzzy reliability concept and regression models to facilitate the random and fuzzy uncertainties. In this article, we propose the average chance reliability as a measure of quality index under random fuzzy uncertainty, which can be regarded as a counterpart of conventional reliability under probability theory. Furthermore, we extend the probabilistic location-scale family, which is actually a non-normal regression model, into a random fuzzy location-scale family, which is developed for the facilitation of the covariate modeling under random fuzzy environments. We will particularly focus our development on a random fuzzy location-scale family, in which the location function is a fuzzy regression model with each fuzzy exploratory variable being piecewise linear credibility distributed.