Planning, tracking, and projecting reliability growth a Bayesian approach

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.