Bayesian parameter estimation for compartmental models in biology and physics

We demonstrated that the use of Bayes\u27 Theorem, with the Box and Draper likelihood, to estimate the parameters of compartmental models is an improvement over current ad hoc parameter estimation methods. This method has several novel features that are useful in parameter estimation. First, the remaining parameter uncertainty is described by the posterior density, which cannot be obtained with classical regression methods. Second, highest posterior density contours can be used to illustrate uncertainty of parameter pairs, and their shape changes can be used to describe the influence of reduced data sets and/or different models on the estimation uncertainty. Third, information from other experiments and sources can be incorporated using appropriate prior distribution. Two areas of application for this technique are biology and physics. Three biokinetic models were studied: the exchange of calcium at bone surfaces in beagles, human cerebral glucose metabolism, and the exchange of serum albumin in human. In physics, we estimated the half-lives of 226Ra, 222Rn and 218Po from simulated decay data. In addition, different reduced data sets were also examined for each model to show their influence on parameter uncertainty. We applied the Bayesian method to two and three-compartment models. The presence of bimodality and divergent behavior in the posterior densities is new and unexpected. They are due to the likelihood and can be changed using prior information and/or the amount of data used. For example, the use of Normal priors stopped the divergence in the bone calcium study. However, it also introduced bimodality for all three parameters. Interestingly, the omission of the extravascular space data in the serum albumin analysis did not diminish the estimation accuracy. Instead, estimation precision was increased for three of the four parameters, as indicated by smaller contours. When open contours are present, the estimation variances are large and can be infinite. Finally, we showed that radioactive decay can be described using compartmental models and that half-lives can be estimated using Box and Draper\u27s method. As always, the most precise estimates were obtained using data for individual compartments

Probabilistic Design Analysis (PDA) Approach to Determine the Probability of Cross-System Failures for a Space Launch Vehicle

Quantifying the probability of significant launch vehicle failure scenarios for a given design, while still in the design process, is critical to mission success and to the safety of the astronauts. Probabilistic risk assessment (PRA) is chosen from many system safety and reliability tools to verify the loss of mission (LOM) and loss of crew (LOC) requirements set by the NASA Program Office. To support the integrated vehicle PRA, probabilistic design analysis (PDA) models are developed by using vehicle design and operation data to better quantify failure probabilities and to better understand the characteristics of a failure and its outcome. This PDA approach uses a physics-based model to describe the system behavior and response for a given failure scenario. Each driving parameter in the model is treated as a random variable with a distribution function. Monte Carlo simulation is used to perform probabilistic calculations to statistically obtain the failure probability. Sensitivity analyses are performed to show how input parameters affect the predicted failure probability, providing insight for potential design improvements to mitigate the risk. The paper discusses the application of the PDA approach in determining the probability of failure for two scenarios from the NASA Ares I projec

Application of Fault Management Theory to the Quantitative Selection of a Launch Vehicle Abort Trigger Suite

This paper describes the quantitative application of the theory of System Health Management and its operational subset, Fault Management, to the selection of abort triggers for a human-rated launch vehicle, the United States' National Aeronautics and Space Administration's (NASA) Space Launch System (SLS). The results demonstrate the efficacy of the theory to assess the effectiveness of candidate failure detection and response mechanisms to protect humans from time-critical and severe hazards. The quantitative method was successfully used on the SLS to aid selection of its suite of abort triggers

Abort Trigger False Positive and False Negative Analysis Methodology for Threshold-Based Abort Detection

This paper describes a quantitative methodology for bounding the false positive (FP) and false negative (FN) probabilities associated with a human-rated launch vehicle abort trigger (AT) that includes sensor data qualification (SDQ). In this context, an AT is a hardware and software mechanism designed to detect the existence of a specific abort condition. Also, SDQ is an algorithmic approach used to identify sensor data suspected of being corrupt so that suspect data does not adversely affect an AT's detection capability. The FP and FN methodologies presented here were developed to support estimation of the probabilities of loss of crew and loss of mission for the Space Launch System (SLS) which is being developed by the National Aeronautics and Space Administration (NASA). The paper provides a brief overview of system health management as being an extension of control theory; and describes how ATs and the calculation of FP and FN probabilities relate to this theory. The discussion leads to a detailed presentation of the FP and FN methodology and an example showing how the FP and FN calculations are performed. This detailed presentation includes a methodology for calculating the change in FP and FN probabilities that result from including SDQ in the AT architecture. To avoid proprietary and sensitive data issues, the example incorporates a mixture of open literature and fictitious reliability data. Results presented in the paper demonstrate the effectiveness of the approach in providing quantitative estimates that bound the probability of a FP or FN abort determination

Application of Fault Management Theory to the Quantitive Selection of a Launch Vehicle Abort Trigger Suite

SHM/FM theory has been successfully applied to the selection of the baseline set Abort Triggers for the NASA SLS center dot Quantitative assessment played a useful role in the decision process M&FM, which is new within NASA MSFC, required the most "new" work, as this quantitative analysis had never been done before center dot Required development of the methodology and tool to mechanize the process center dot Established new relationships to the other groups The process is now an accepted part of the SLS design process, and will likely be applied to similar programs in the future at NASA MSFC Future improvements center dot Improve technical accuracy Differentiate crew survivability due to an abort, vs. survivability even no immediate abort occurs (small explosion with little debris) Account for contingent dependence of secondary triggers on primary triggers Allocate " LOC Benefit" of each trigger when added to the previously selected triggers. center dot Reduce future costs through the development of a specialized tool Methodology can be applied to any manned/unmanned vehicle, in space or terrestria

Application of Probabilistic Risk Assessment (PRA) During Conceptual Design for the NASA Orbital Space Plane (OSP)

In order to meet the space transportation needs for a new century, America's National Aeronautics and Space Administration (NASA) has implemented an Integrated Space Transportation Plan to produce safe, economical, and reliable access to space. One near term objective of this initiative is the design and development of a next-generation vehicle and launch system that will transport crew and cargo to and from the International Space Station (ISS), the Orbital Space Plane (OSP). The OSP system is composed of a manned launch vehicle by an existing Evolved Expendable Launch Vehicle (EELV). The OSP will provide emergency crew rescue from the ISS by 2008, and provide crew and limited cargo transfer to and from the ISS by 2012. A key requirement is for the OSP to be safer and more reliable than the Soyuz and Space Shuttle, which currently provide these capabilities