Reliability as an Independent Variable Applied to Liquid Rocket Engine Hot Fire Test Plans

Abstract

Manufacturers lack an adequate method to balance performance, reliability, and affordability. The reliability-asan-independent-variable methodology is the solution proposed by expressing quantitatively the reliability trade space as ranges of a number of hardware sets and a number of hot-fire tests necessary to develop and qualify/certify a liquid rocket engine against a stated reliability requirement. Therefore, reliability-as-an-independent-variable becomes one of the key decision parameters in early tradeoff studies for liquid rocket engines because the reliability trade space directly influences the performance requirements and, as a result, the affordability. The overall solution strategy of reliability-as-an-independent-variable is based on the Bayesian statistical framework using either the planned or actual number of hot-fire tests. The planned hot-fire test results may include test failures to simulate the typical design-fail-fix-test cycles present in liquid rocket engine development programs in order to provide the schedule and cost risk impacts for early tradeoff studies. The reliability-as-an-independent-variable methodology is exemplarily applied to the actual hot-fire test history of the F-1, the space shuttle main engine, and the RS-68 liquid rocket engine, showing adequate agreement between computed results and actual flight engine reliability.Nomenclature Beta = Beta probability density function Bi = Binomial probability density function C = level of confidence (credibility bound) c = number of cycles CTD = cumulated test duration, s F X = cumulative density function HW = number of hardware L = likelihood function n = number of trials, i.e., hot-fire tests p = probability of success q = failure fraction q ind = candidate probability density function R = reliability r = number of failures t = hardware life, s tp = hot-fire test proportion T 50 = median lifetime, s w = weighting factor x = number of successes, i.e., hot-fire tests = shape parameter 1 , 2 = weighting factors = shape parameter = median regression coefficients = integration domain = parameters to be estimated = acceptance rate = Gamma function = parameter of Poisson probability mass function = probability of success of a functional node = posterior probability 0 = prior probability = standard deviation