Purpose – The purpose of this paper is to analyze mathematical aspects of the q‐Weibull model and explore the influence of the parameter q.Design/methodology/approach – The paper uses analytical developments with graph illustrations and an application to a practical example.Findings – The q‐Weibull distribution function is able to reproduce the bathtub shape curve for the failure rate function with a single set of parameters. Moments of the distribution are also presented.Practical implications – The generalized q‐Weibull distribution unifies various possible descriptions for the failure rate function: monotonically decreasing, monotonically increasing, unimodal and U‐shaped (bathtub) curves. It recovers the usual Weibull distribution as a particular case. It represents a unification of models usually found in reliability analysis. Q‐Weibull model has its inspiration in nonextensive statistics, used to describe complex systems with long‐range interactions and/or long‐term memory. This theoretical backgrou...