Probability of infancy problems for space launch vehicles

This paper addresses the treatment of ‘infancy problems’ in the reliability analysis of space launch systems. To that effect, we analyze the probability of failure of launch vehicles in their first five launches. We present methods and results based on a combination of Bayesian probability and frequentist statistics designed to estimate the systemʹs reliability before the realization of a large number of launches. We show that while both approaches are beneficial, the Bayesian method is particularly useful when the experience base is small (i.e. for a new rocket). We define reliability as the probability of success based on a binary failure/no failure event. We conclude that the mean failure rates appear to be higher in the first and second flights (≈1/3 and 1/4, respectively) than in subsequent ones (third, fourth and fifth), and Bayesian methods do suggest that there is indeed some difference in launch risk over the first five launches. Yet, based on a classical frequentist analysis, we find that for these first few flights, the differences in the mean failure rates over successive launches or over successive generations of vehicles, are not statistically significant (i.e. do not meet a 95% confidence level). This is true because the frequentist analysis is based on a fixed confidence level (here: 95%), whereas the Bayesian one allows more flexibility in the conclusions based on a full probability density distribution of the failure rate and therefore, permits better interpretation of the information contained in a small sample. The approach also gives more insight into the considerable uncertainty in failure rate estimates based on small sample sizes.