The historical success and failure record of launch vehicles clearly demonstrates the presence of reliability growth over successive launches. The reality of reliability growth is critical to decisions on ground and flight testing programs, and is a much greater driver of the expected number of failures over a campaign, than the best analysis of mature reliability can ever be. While mathematical models exist that match the reliability growth demonstrated by historical systems, the space industry is still lacking a practical method to develop forecasts of reliability growth for new systems, update those forecasts on the basis of early tests and flight results, and accurately estimate integrated campaign metrics over several launches. Modeling the failure probability as originating from potential "defects" in the system, each with a probability of trigger, a conditional probability of causing loss of mission, and a probability of detection and correction, provides a starting place to address this need. The method provides a model of reliability growth that is mathematically sound, matches historical results, is directly amenable to system engineering inputs, clearly identifies and quantifies the drivers of reliability growth, and provides a clear basis for uncertainty analysis and Bayesian updating. Nomenclature p min = irreducible (mature) probability of failure of the system D = number of defect types defined in the model d k = initial number of defects of type k present in the system λ k = given presence of a defect of type k, probability of defect trigger at any given flight τ k = given presence and trigger of defect of type k, conditional probability of loss of mission ω = given loss of mission, conditional probability of loss of crew ( = 1−ΑΕ) ν k = after defect of type k caused partial anomaly, conditional probability that it is observable ϕ k = after triggered defect of type k is observable, conditional probability that it is noticed and reported γ k = after a defect of type k is uncovered, conditional probability to eliminate the defect N = index of flight (or test) number p k = λ k τ k = probability of system failure from a defect of type k, if the defect is present in the system ρ k = ν k ϕ k γ k = after defect of type k caused partial anomaly, conditional probability to eliminate it η k = 1/ τ k = mean number of triggers of a defect of type k for one trigger to cause loss of mission α k = (η k -1)ρ k = measure of the potential to eliminate a defect of type k before it causes loss of mission ζ k = (η k -1) ν k ϕ k = measure of the potential to report a defect of type k before it causes loss of mission δ k (N) = probability that a given defect of type k is still present in the system at flight number N ε k = 'test effectiveness' for defects of type k = probability of defect elimination at each flight (or test) P k (N) = probability of loss of mission at flight number N from a single defect of type k R(N)= system reliability at flight number N Δ k (N) = probability to not have any loss of mission in the fi...

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This paper addresses the importance of considering the initial reliability and reliability growth as opposed to only the mature risk estimate when making relative comparisons among developmental launch vehicle (LV) alternatives and introduces the current model used to perform this type of analysis.Probabilistic risk assessments (PRA) often focus on modeling the mature state of a system under consideration; however, in the aerospace field of LV design such an assessment can be dangerously misleading. Due to the low flight rate, a given LV may never reach maturity prior to retirement and will fly mostly in an immature state. The historical record of early LV flights suggests a risk posture well above the mature estimate predicted through the standard PRA approach. Thus, any decision based upon the mature estimates may be significantly different than a decision based upon the predicted risk during the bulk of its useful life while it is still maturing. In order to make an informed decision about the relative merits of competing LV architectures, decision makers must consider not only the mature system risk, but also the reliability growth for the system along the path to maturity.The current model described in this paper uses a reliability growth methodology, which has expanded the scope of risk influencing factors and has been able to provided Loss of Mission (LOM) and Loss of Crew (LOC) risk estimates for over 20 LVs in a period of less than two months. The advantage of employing such a methodology to conceptual LV designs is that it enables a more realistic estimate of campaign success during early flights without the need for detailed design information. This model captures the reality that element heritage and maturity are more important to early flight success than first order component reliability calculations while yielding valuable insights for designers of future vehicles.

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