This paper addresses a common problem associated with data analysis when a 1st failure in n, Weibull analysis is used. This is known among Weibull practitioners as the method of “sudden death”. Weibull analysis is a widely used reliability assessment and prediction technique. The “sudden death” method was initially developed to help reduce test time. In a “sudden death” test, k groups of n parts each are tested. In each test group testing is halted when the first failure occurs. This is referred to as the “first failure in n” and is usually detected by periodic inspection or by automatic/electronic test shut-off when the first failure occurs. It may happen that the first failure is not detected and there are two or more failures found upon inspection. In such cases the first failure time is lost since there are now 2 or more failures. If the second or third failure time is used as if it were the first failure time, overestimation of the reliability will result.This paper offers a set of correction factors that can be used to estimate the first failure time when 2 or more failures have occurred in a test group of size n. This is shown theoretically and then demonstrated using simulation.