For the needs of the life scatter factors under different conditions to assess the engine component lives

in this paper

the theoretical formulas of the life scatter factors based on the arbitrary kth order experimental life of a small sample with logarithm normal distribution were deduced.Life scatter factors were given with the confidence of 0.95

the reliability of 0.9987 and the standard deviation of logarithm normal distribution 0.13.The life scatter factors based on the worst experimental lives fit well with those in the published literatures.The life scatter factors based on the best experimental lives are more reasonable than those in the literatures.Using the formulae given in the paper

the life scatter factors can be obtained with any given confidence

reliability and standard deviation of the logarithm normal distribution

which can be used to assess component lives in engineering application.