A systematic approach to defining margin in a manner that incorporates statistical information and accommodates data uncertainty but does not require assumptions about specific forms of the tails of distributions is developed. A margin that is insensitive to the character of the tails of the relevant distributions (tail insensitive margin, TIM) is defined. This is complemented by the calculation of probability of failure (PoF) where the load distribution is augmented by a quantity equal to the TIM. This approach avoids some of the perplexing results common to traditional reliability theory where, on the basis of very small amounts of data, one is led to extraordinary claims of infinitesimal probability of failure. Additionally, this approach permits a more meaningful separation of statistical and engineering issues.