University of Maryland

Image: The Space Shuttle Main Engine during a test firing. Source: (via Wikipedia).

Improving Liquid Rocket Engine Program Decision-Making

This work was done by Richard Strunz for his dissertation. Jeffrey W. Herrmann, Department of Mechanical Engineering and Institute for Systems Research, University of Maryland, was the dissertation advisor.


This research developed a multiobjective decision-making methodology to support design selection, hot-fire test planning, and reliability growth planning during the development of a liquid rocket engine.


Manufacturers lack an adequate method to balance performance, reliability, and affordability. The reliability-as-an-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.

The hot fire test strategy for liquid rocket engines has always been a concern of space industry and agency alike because no recognized standard exists. Previous hot fire test plans focused on the verification of performance requirements but did not explicitly include reliability as a dimensioning variable. The stakeholders are, however, concerned about a hot fire test strategy that balances reliability, schedule, and affordability. A multiple criteria test planning model is presented that provides a framework to optimize the hot fire test strategy with respect to stakeholder concerns. The Staged Combustion Rocket Engine Demonstrator, a program of the European Space Agency, is used as example to provide the quantitative answer to the claim that a reduced thrust scale demonstrator is cost beneficial for a subsequent flight engine development. Scalability aspects of major subsystems are considered in the prior information definition inside the Bayesian framework. The model is also applied to assess the impact of an increase of the demonstrated reliability level on schedule and affordability.

Liquid rocket engine reliability growth modeling is a blend of art and science because of data scarcity and heterogeneity, which result from the limited number of engine development programs as well as testing profiles that are much different from the actual mission profile. In particular, hot fire tests are shorter than full mission duration due to test facility limitations and some of them are performed at extreme load points to demonstrate robustness and design margin.

The well-known empirical Duane and analytical Crow/AMSAA models are therefore no longer best practice because the reliability growth rate is calculated using a MTBF estimate that is simply the total accumulated test time divided by the total number of failures. Therefore, we propose a new, fully Bayesian estimation based methodology that estimates the system reliability while taking into account the test profile characteristics and aggregating component, subsystem, and system level hot fire test data.

The methodology is applied to planning, tracking, and projecting reliability growth and illustrated using an example. In the example, a system reliability target must be demonstrated in a TAAF program. The system reliability target defines the scope of the hot fire test plan for the reliability growth planning using pseudo numbers for the planned hot fire tests. At each occurrence of a failure, the methodology is used in the context of reliability growth tracking, i.e. the attained system level reliability is estimated. The test plan is updated to reflect the need for additional tests to meet the system reliability target. Reliability growth projection is easily performed using either specific projection models or the prior distribution that features a knowledge factor to model the specified level of fix effectiveness.

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Last updated on April 8, 2013, by Jeffrey W. Herrmann.