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Fundamental engineering considerations may result in the need for using a statistical distribution with a failure-free life (FFL) parameter. These include failure-time models as well as specialized repair-time models (for maintenance planning) and breakdown-voltage models used for voltage-endurance studies of electrical insulations. In this paper, some commonly encountered statistical distributions with FFL are described together with a review of their engineering applications. From the literature, the three-parameter Weibull distribution has been found to be the most common statistical distribution used when FFL is considered. Some estimation procedures for the three-parameter Weibull distribution are discussed and a new modified maximum-likelihood-estimation approach which leverages on the empirical cumulative distribution function is proposed. Two case examples considering complete and censored data are described.