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NASA NTRS2009

DSN Simulator

The DSN Simulator (wherein DSN signifies NASA's Deep Space Network) is an updated version of the software described in DSN Array Simulator (NPO-44506), Software Tech Briefs (Special supplement to NASA Tech Briefs), Vol. 32, No. 9 (September 2008), page 26. To recapitulate: This software is used for computational modeling of proposed DSN facilities comprising arrays of antennas and transmitting and receiving equipment for microwave communication with spacecraft on interplanetary missions. Such modeling is performed to estimate facility performance, evaluate requirements that govern facility design, and evaluate proposed improvements in hardware and/or software. The software includes a Monte Carlo simulation component that enables rapid generation of key mission-set metrics (e.g., numbers of links, data rates, and data volumes), and statistical distributions thereof as functions of time. The prior version of the software could model only one DSN facility at a time and included hard-coded, unconfigurable metrics. The present updated version is capable of modeling the entire DSN and provides for configurable metrics, making it possible to perform loading analyses for alternative future DSN architectures and mission-set scenarios. The present version also features an improved user interface and interfaces for exchange of data with other DSN software and with a DSN mission model database.

Fijany, Amir↗

NASA NTRS2009

Regression Model Optimization for the Analysis of Experimental Data

A candidate math model search algorithm was developed at Ames Research Center that determines a recommended math model for the multivariate regression analysis of experimental data. The search algorithm is applicable to classical regression analysis problems as well as wind tunnel strain gage balance calibration analysis applications. The algorithm compares the predictive capability of different regression models using the standard deviation of the PRESS residuals of the responses as a search metric. This search metric is minimized during the search. Singular value decomposition is used during the search to reject math models that lead to a singular solution of the regression analysis problem. Two threshold dependent constraints are also applied. The first constraint rejects math models with insignificant terms. The second constraint rejects math models with near-linear dependencies between terms. The math term hierarchy rule may also be applied as an optional constraint during or after the candidate math model search. The final term selection of the recommended math model depends on the regressor and response values of the data set, the user s function class combination choice, the user s constraint selections, and the result of the search metric minimization. A frequently used regression analysis example from the literature is used to illustrate the application of the search algorithm to experimental data.

Ulbrich, N.↗

NASA NTRS2009

First International Diagnosis Competition - DXC'09

A framework to compare and evaluate diagnosis algorithms (DAs) has been created jointly by NASA Ames Research Center and PARC. In this paper, we present the first concrete implementation of this framework as a competition called DXC 09. The goal of this competition was to evaluate and compare DAs in a common platform and to determine a winner based on diagnosis results. 12 DAs (model-based and otherwise) competed in this first year of the competition in 3 tracks that included industrial and synthetic systems. Specifically, the participants provided algorithms that communicated with the run-time architecture to receive scenario data and return diagnostic results. These algorithms were run on extended scenario data sets (different from sample set) to compute a set of pre-defined metrics. A ranking scheme based on weighted metrics was used to declare winners. This paper presents the systems used in DXC 09, description of faults and data sets, a listing of participating DAs, the metrics and results computed from running the DAs, and a superficial analysis of the results.

Kurtoglu, tolga↗

NASA NTRS2010

The Role and Quality of Software Safety in the NASA Constellation Program

In this study, we examine software safety risk in the early design phase of the NASA Constellation spaceflight program. Obtaining an accurate, program-wide picture of software safety risk is difficult across multiple, independently-developing systems. We leverage one source of safety information, hazard analysis, to provide NASA quality assurance managers with information regarding the ongoing state of software safety across the program. The goal of this research is two-fold: 1) to quantify the relative importance of software with respect to system safety; and 2) to quantify the level of risk presented by software in the hazard analysis. We examined 154 hazard reports created during the preliminary design phase of three major flight hardware systems within the Constellation program. To quantify the importance of software, we collected metrics based on the number of software-related causes and controls of hazardous conditions. To quantify the level of risk presented by software, we created a metric scheme to measure the specificity of these software causes. We found that from 49-70% of hazardous conditions in the three systems could be caused by software or software was involved in the prevention of the hazardous condition. We also found that 12-17% of the 2013 hazard causes involved software, and that 23-29% of all causes had a software control. Furthermore, 10-12% of all controls were software-based. There is potential for inaccuracy in these counts, however, as software causes are not consistently scoped, and the presence of software in a cause or control is not always clear. The application of our software specificity metrics also identified risks in the hazard reporting process. In particular, we found a number of traceability risks in the hazard reports may impede verification of software and system safety.

Layman, Lucas↗

NASA NTRS2010

Improving Separation Assurance Stability Through Trajectory Flexibility Preservation

New information and automation technologies are enabling the distribution of tasks and decisions from the service providers to the users of the air traffic system, with potential capacity and cost benefits. This distribution of tasks and decisions raises the concern that independent user actions will decrease the predictability and increase the complexity of the traffic system, hence inhibiting and possibly reversing any potential benefits. One such concern is the adverse impact of uncoordinated actions by individual aircraft on the stability of separation assurance. For example, individual aircraft performing self-separation may resolve predicted losses of separation or conflicts with some traffic, only to result in secondary conflicts with other traffic or with the same traffic later in time. In answer to this concern, this paper proposes metrics for preserving user trajectory flexibility to be used in self-separation along with other objectives. The hypothesis is that preserving trajectory flexibility will naturally reduce the creation of secondary conflicts by bringing about implicit coordination between aircraft. The impact of using these metrics on improving self-separation stability is investigated by measuring the impact on secondary conflicts. The scenarios analyzed include aircraft in en route airspace with each aircraft meeting a required time of arrival in a twenty minute time horizon while maintaining separation from the surrounding traffic and using trajectory flexibility metrics to mitigate the risk of secondary conflicts. Preliminary experiments showed promising results in that the trajectory flexibility preservation reduced the potential for secondary conflicts.

Idris, Husni↗

NASA NTRS2010

Evaluation of Dual Pressurized Rover Operations During Simulated Planetary Surface Exploration

Introduction: A pair of small pressurized rovers (Space Exploration Vehicles, or SEVs) is at the center of the Global Point-of-Departure architecture for future human planetary exploration. Simultaneous operation of multiple crewed surface assets should maximize productive crew time, minimize overhead, and preserve contingency return paths. Methods: A 14-day mission simulation was conducted in the Arizona desert as part of NASA?s 2010 Desert Research and Technology Studies (DRATS). The simulation involved two SEV concept vehicles performing geological exploration under varied operational modes affecting both the extent to which the SEVs must maintain real-time communications with mission control ("Continuous" vs. "Twice-a-Day") and their proximity to each other ("Lead-and-Follow" vs. "Divide-and-Conquer"). As part of a minimalist lunar architecture, no communications relay satellites were assumed. Two-person crews consisting of an astronaut and a field geologist operated each SEV, day and night, throughout the entire 14-day mission, only leaving via the suit ports to perform simulated extravehicular activities. Standard metrics enabled quantification of the habitability and usability of all aspects of the SEV concept vehicles throughout the mission, as well as comparison of the extent to which the operating modes affected crew productivity and performance. Practically significant differences in the relevant metrics were prospectively defined for the testing of all hypotheses. Results and Discussion: Data showed a significant 14% increase in available science time (AST) during Lead-and-Follow mode compared with Divide-and-Conquer, primarily because of the minimal overhead required to maintain communications during Lead-and-Follow. In Lead-and-Follow mode, there was a non-significant 2% increase in AST during Twice-a-Day vs. Continuous communications. Situational awareness of the other vehicle?s location, activities, and contingency return constraints were enhanced during Lead-and-Follow and Twice-a-Day communications modes due to line-of-sight and direct SEV-to-SEV communication. Preliminary analysis of Scientific Data Quality and Observation Quality metrics showed no significant differences between modes.

Abercromby, Andrew F. J.↗

NASA NTRS2010

Propulsion Technology Lifecycle Operational Analysis

The paper presents the results of a focused effort performed by the members of the Space Propulsion Synergy Team (SPST) Functional Requirements Sub-team to develop propulsion data to support Advanced Technology Lifecycle Analysis System (ATLAS). This is a spreadsheet application to analyze the impact of technology decisions at a system-of-systems level. Results are summarized in an Excel workbook we call the Technology Tool Box (TTB). The TTB provides data for technology performance, operations, and programmatic parameters in the form of a library of technical information to support analysis tools and/or models. The lifecycle of technologies can be analyzed from this data and particularly useful for system operations involving long running missions. The propulsion technologies in this paper are listed against Chemical Rocket Engines in a Work Breakdown Structure (WBS) format. The overall effort involved establishing four elements: (1) A general purpose Functional System Breakdown Structure (FSBS). (2) Operational Requirements for Rocket Engines. (3) Technology Metric Values associated with Operating Systems (4) Work Breakdown Structure (WBS) of Chemical Rocket Engines The list of Chemical Rocket Engines identified in the WBS is by no means complete. It is planned to update the TTB with a more complete list of available Chemical Rocket Engines for United States (US) engines and add the Foreign rocket engines to the WBS which are available to NASA and the Aerospace Industry. The Operational Technology Metric Values were derived by the SPST Sub-team in the form of the TTB and establishes a database for users to help evaluate and establish the technology level of each Chemical Rocket Engine in the database. The Technology Metric Values will serve as a guide to help determine which rocket engine to invest technology money in for future development.

Robinson, John W.↗

NASA NTRS2009

Shuttle Wing Leading Edge Root Cause NDE Team Findings and Implementation of Quantitative Flash Infrared Thermography

Comparison metrics can be established to reliably and repeatedly establish the health of the joggle region of the Orbiter Wing Leading Edge reinforced carbon carbon (RCC) panels. Using these metrics can greatly reduced the man hours needed to perform, wing leading edge scanning for service induced damage. These time savings have allowed for more thorough inspections to be preformed in the necessary areas with out affecting orbiter flow schedule. Using specialized local inspections allows for a larger margin of safety by allowing for more complete characterizations of panel defects. The presence of the t-seal during thermographic inspection can have adverse masking affects on ability properly characterize defects that exist in the joggle region of the RCC panels. This masking affect dictates the final specialized inspection should be preformed with the t-seal removed. Removal of the t-seal and use of the higher magnification optics has lead to the most effective and repeatable inspection method for characterizing and tracking defects in the wing leading edge. Through this study some inadequacies in the main health monitoring system for the orbiter wing leading edge have been identified and corrected. The use of metrics and local specialized inspection have lead to a greatly increased reliability and repeatable inspection of the shuttle wing leading edge.

Burke, Eric R.↗

NASA NTRS2010

Impact of Conflict Avoidance Responsibility Allocation on Pilot Workload in a Distributed Air Traffic Management System

Pilot workload was examined during simulated flights requiring flight deck-based merging and spacing while avoiding weather. Pilots used flight deck tools to avoid convective weather and space behind a lead aircraft during an arrival into Louisville International airport. Three conflict avoidance management concepts were studied: pilot, controller or automation primarily responsible. A modified Air Traffic Workload Input Technique (ATWIT) metric showed highest workload during the approach phase of flight and lowest during the en-route phase of flight (before deviating for weather). In general, the modified ATWIT was shown to be a valid and reliable workload measure, providing more detailed information than post-run subjective workload metrics. The trend across multiple workload metrics revealed lowest workload when pilots had both conflict alerting and responsibility of the three concepts, while all objective and subjective measures showed highest workload when pilots had no conflict alerting or responsibility. This suggests that pilot workload was not tied primarily to responsibility for resolving conflicts, but to gaining and/or maintaining situation awareness when conflict alerting is unavailable.

Ligda, Sarah V.↗

NASA NTRS2011

Safe, Advanced, Adaptable Isolation System Eliminates the Need for Critical Lifts

The Starr Soft Support isolation system incorporates an automatically reconfigurable aircraft jack into NASA's existing 1-Hertz isolators. This enables an aircraft to float in mid-air without the need for a critical lift during ground vibration testing (GVT), significantly reducing testing risk, time, and costs. Currently incorporating the most advanced technology available, the 60,000-poundcapacity (27-metric-ton) isolation system is used for weight and measurement tests, control-surface free-play tests, and structural mode interaction tests without the need for any major reconfiguration, often saving days of time and significantly reducing labor costs. The Starr Soft Support isolation system consists of an aircraft-jacking device with three jacking points, each of which has an individual motor and accommodates up to 20,000 pounds (9 metric tons) for a total 60,000-pound (27-metric-ton) capacity. The system can be transported to the aircraft by forklift and placed at its jacking points using a pallet jack. The motors power the electric actuators, raising the aircraft above the ground until the landing gear can retract. Inflatable isolators then deploy, enabling the aircraft to float in mid-air, simulating a 1-Hertz free-free boundary condition. Inflatable isolators have been in use at NASA for years, enabling aircraft to literally float unsupported for highly accurate GVT. These isolators must be placed underneath the aircraft for this to occur. Traditionally, this is achieved by a critical lift a high-risk procedure in which a crane and flexible cord system are used to lift the aircraft. In contrast, the Starr Soft Support isolation system eliminates the need for critical lift by integrating the inflatable isolators into an aircraft jacking system. The system maintains vertical and horizontal isolating capabilities. The aircraft can be rolled onto the system, jacked up, and then the isolators can be inflated and positioned without any personnel needing to work underneath the aircraft. Also, the system accommodates changes in aircraft configuration, automatically adapting to changes in mass, and it can adjust the height of the isolators in one basic setup. Dryden personnel used the Starr Soft Support system to successfully perform a GVT on an F-15 being structurally modified by Gulfstream, Dryden's Gulfstream III used for science research and the crew exploration module and adaptor cone assembly.

Ginn, Starr↗

NASA NTRS2011

Uncertainty Assessments of 2D and Axisymmetric Hypersonic Shock Wave - Turbulent Boundary Layer Interaction Simulations at Compression Corners

This paper is one of a series of five papers in a special session organized by the NASA Fundamental Aeronautics Program that addresses uncertainty assessments for CFD simulations in hypersonic flow. Simulations of a shock emanating from a compression corner and interacting with a fully developed turbulent boundary layer are evaluated herein. Mission relevant conditions at Mach 7 and Mach 14 are defined for a pre-compression ramp of a scramjet powered vehicle. Three compression angles are defined, the smallest to avoid separation losses and the largest to force a separated flow engaging more complicated flow physics. The Baldwin-Lomax and the Cebeci-Smith algebraic models, the one-equation Spalart-Allmaras model with the Catrix-Aupoix compressibility modification and two-equation models including Menter SST, Wilcox k-omega 98, and Wilcox k-omega 06 turbulence models are evaluated. Each model is fully defined herein to preclude any ambiguity regarding model implementation. Comparisons are made to existing experimental data and Van Driest theory to provide preliminary assessment of model form uncertainty. A set of coarse grained uncertainty metrics are defined to capture essential differences among turbulence models. Except for the inability of algebraic models to converge for some separated flows there is no clearly superior model as judged by these metrics. A preliminary metric for the numerical component of uncertainty in shock-turbulent-boundary-layer interactions at compression corners sufficiently steep to cause separation is defined as 55%. This value is a median of differences with experimental data averaged for peak pressure and heating and for extent of separation captured in new, grid-converged solutions presented here. This value is consistent with existing results in a literature review of hypersonic shock-turbulent-boundary-layer interactions by Roy and Blottner and with more recent computations of MacLean.

Gnoffo, Peter A.↗

NASA NTRS2006

Equations for Scoring Rules When Data Are Missing

A document presents equations for scoring rules in a diagnostic and/or prognostic artificial-intelligence software system of the rule-based inference-engine type. The equations define a set of metrics that characterize the evaluation of a rule when data required for the antecedence clause(s) of the rule are missing. The metrics include a primary measure denoted the rule completeness metric (RCM) plus a number of subsidiary measures that contribute to the RCM. The RCM is derived from an analysis of a rule with respect to its truth and a measure of the completeness of its input data. The derivation is such that the truth value of an antecedent is independent of the measure of its completeness. The RCM can be used to compare the degree of completeness of two or more rules with respect to a given set of data. Hence, the RCM can be used as a guide to choosing among rules during the rule-selection phase of operation of the artificial-intelligence system..

James, Mark↗

NASA NTRS2011

Finding Every Root of a Broad Class of Real, Continuous Functions in a Given Interval

One of the most pervasive needs within the Deep Space Network (DSN) Metric Prediction Generator (MPG) view period event generation is that of finding solutions to given occurrence conditions. While the general form of an equation expresses equivalence between its left-hand and right-hand expressions, the traditional treatment of the subject subtracts the two sides, leaving an expression of the form Integral of(x) = 0. Values of the independent variable x satisfying this condition are roots, or solutions. Generally speaking, there may be no solutions, a unique solution, multiple solutions, or a continuum of solutions to a given equation. In particular, all view period events are modeled as zero crossings of various metrics; for example, the time at which the elevation of a spacecraft reaches its maximum value, as viewed from a Deep Space Station (DSS), is found by locating that point at which the derivative of the elevation function becomes zero. Moreover, each event type may have several occurrences within a given time interval of interest. For example, a spacecraft in a low Moon orbit will experience several possible occultations per day, each of which must be located in time. The MPG is charged with finding all specified event occurrences that take place within a given time interval (or pass ), without any special clues from operators as to when they may occur, for the entire spectrum of missions undertaken by the DSN. For each event type, the event metric function is a known form that can be computed for any instant within the interval. A method has been created for a mathematical root finder to be capable of finding all roots of an arbitrary continuous function, within a given interval, to be subject to very lenient, parameterized assumptions. One assumption is that adjacent roots are separated at least by a given amount, xGuard. Any point whose function value is less than ef in magnitude is considered to be a root, and the function values at distances xGuard away from a root are larger than ef, unless there is another root located in this vicinity. A root is considered found if, during iteration, two root candidates differ by less than a pre-specified ex, and the optimum cubic polynomial matching the function at the end and at two interval points (that is within a relative error fraction L at its midpoint) is reliable in indicating whether the function has extrema within the interval. The robustness of this method depends solely on choosing these four parameters that control the search. The roots of discontinuous functions were also found, but at degraded performance.

Tausworthe, Robert C.↗

NASA NTRS2012

Uncertainty Quantification for Polynomial Systems via Bernstein Expansions

This paper presents a unifying framework to uncertainty quantification for systems having polynomial response metrics that depend on both aleatory and epistemic uncertainties. The approach proposed, which is based on the Bernstein expansions of polynomials, enables bounding the range of moments and failure probabilities of response metrics as well as finding supersets of the extreme epistemic realizations where the limits of such ranges occur. These bounds and supersets, whose analytical structure renders them free of approximation error, can be made arbitrarily tight with additional computational effort. Furthermore, this framework enables determining the importance of particular uncertain parameters according to the extent to which they affect the first two moments of response metrics and failure probabilities. This analysis enables determining the parameters that should be considered uncertain as well as those that can be assumed to be constants without incurring significant error. The analytical nature of the approach eliminates the numerical error that characterizes the sampling-based techniques commonly used to propagate aleatory uncertainties as well as the possibility of under predicting the range of the statistic of interest that may result from searching for the best- and worstcase epistemic values via nonlinear optimization or sampling.

Crespo, Luis G.↗

NASA NTRS2012

Dig Hazard Assessment Using a Stereo Pair of Cameras

This software evaluates the terrain within reach of a lander s robotic arm for dig hazards using a stereo pair of cameras that are part of the lander s sensor system. A relative level of risk is calculated for a set of dig sectors. There are two versions of this software; one is designed to run onboard a lander as part of the flight software, and the other runs on a PC under Linux as a ground tool that produces the same results generated on the lander, given stereo images acquired by the lander and downlinked to Earth. Onboard dig hazard assessment is accomplished by executing a workspace panorama command sequence. This sequence acquires a set of stereo pairs of images of the terrain the arm can reach, generates a set of candidate dig sectors, and assesses the dig hazard of each candidate dig sector. The 3D perimeter points of candidate dig sectors are generated using configurable parameters. A 3D reconstruction of the terrain in front of the lander is generated using a set of stereo images acquired from the mast cameras. The 3D reconstruction is used to evaluate the dig goodness of each candidate dig sector based on a set of eight metrics. The eight metrics are: 1. The maximum change in elevation in each sector, 2. The elevation standard deviation in each sector, 3. The forward tilt of each sector with respect to the payload frame, 4. The side tilt of each sector with respect to the payload frame, 5. The maximum size of missing data regions in each sector, 6. The percentage of a sector that has missing data, 7. The roughness of each sector, and 8. Monochrome intensity standard deviation of each sector. Each of the eight metrics forms a goodness image layer where the goodness value of each sector ranges from 0 to 1. Goodness values of 0 and 1 correspond to high and low risk, respectively. For each dig sector, the eight goodness values are merged by selecting the lowest one. Including the merged goodness image layer, there are nine goodness image layers for each stereo pair of mast images.

Rankin, Arturo L.↗

NASA NTRS2012

Space Launch System Accelerated Booster Development Cycle

With the retirement of the Space Shuttle, NASA is seeking to reinvigorate the national space program and recapture the public s interest in human space exploration by developing missions to the Moon, near-earth asteroids, Lagrange points, Mars, and beyond. The would-be successor to the Space Shuttle, NASA s Constellation Program, planned to take humans back to the Moon by 2020, but due to budgetary constraints was cancelled in 2010 in search of a more "affordable, sustainable, and realistic" concept2. Following a number of studies, the much anticipated Space Launch System (SLS) was unveiled in September of 2011. The SLS core architecture consists of a cryogenic first stage with five Space Shuttle Main Engines (SSMEs), and a cryogenic second stage using a new J-2X engine3. The baseline configuration employs two 5-segment solid rocket boosters to achieve a 70 metric ton payload capability, but a new, more capable booster system will be required to attain the goal of 130 metric tons to orbit. To this end, NASA s Marshall Space Flight Center recently released a NASA Research Announcement (NRA) entitled "Space Launch System (SLS) Advanced Booster Engineering Demonstration and/or Risk Reduction." The increased emphasis on affordability is evident in the language used in the NRA, which is focused on risk reduction "leading to an affordable Advanced Booster that meets the evolved capabilities of SLS" and "enabling competition" to "enhance SLS affordability. The purpose of the work presented in this paper is to perform an independent assessment of the elements that make up an affordable and realistic path forward for the SLS booster system, utilizing advanced design methods and technology evaluation techniques. The goal is to identify elements that will enable a more sustainable development program by exploring the trade space of heavy lift booster systems and focusing on affordability, operability, and reliability at the system and subsystem levels5. For this study, affordability is defined as lifecycle cost, which includes design, development, test, and engineering (DDT&E), production and operational costs (P&O). For this study, the system objectives include reducing DDT&E schedule by a factor of three, showing 99.9% reliability, flying up to four times per year, serving both crew and cargo missions, and evolving to a lift capability of 130 metric tons.3 After identifying gaps in the current system s capabilities, this study seeks to identify non-traditional and innovative technologies and processes that may improve performance in these areas and assess their impacts on booster system development. The DDT&E phase may be improved by incorporating incremental development testing and integrated demonstrations to mitigate risk. To further reduce DDT&E, this study will also consider how aspects of the booster system may have commonality with other users, such as the Department of Defense, commercial applications, or international partners; by sharing some of the risk and investment, the overall development cost may be reduced. Consideration is not limited to solid and liquid rocket boosters. A set of functional performance characteristics, such as engine thrust, specific impulse (Isp), mixture ratio, and throttle range are identified and their impacts on the system are evaluated. This study also identifies how such characteristics affect overall life cycle cost, including DDT&E and fixed and variable P&O.

Arockiam, Nicole↗

NASA NTRS2013

An Approach for the Assessment of System Upset Resilience

This report describes an approach for the assessment of upset resilience that is applicable to systems in general, including safety-critical, real-time systems. For this work, resilience is defined as the ability to preserve and restore service availability and integrity under stated conditions of configuration, functional inputs and environmental conditions. To enable a quantitative approach, we define novel system service degradation metrics and propose a new mathematical definition of resilience. These behavioral-level metrics are based on the fundamental service classification criteria of correctness, detectability, symmetry and persistence. This approach consists of a Monte-Carlo-based stimulus injection experiment, on a physical implementation or an error-propagation model of a system, to generate a system response set that can be characterized in terms of dimensional error metrics and integrated to form an overall measure of resilience. We expect this approach to be helpful in gaining insight into the error containment and repair capabilities of systems for a wide range of conditions.

Torres-Pomales, Wilfredo↗

NASA NTRS2013

A Statistical Theory of Bidirectionality

Original concepts related to the quantification and assessment of bidirectionality in strain-gage balances were introduced by Ulbrich in 2012. These concepts are extended here in three ways: 1) the metric originally proposed by Ulbrich is normalized, 2) a categorical variable is introduced in the regression analysis to account for load polarity, and 3) the uncertainty in both normalized and non-normalized bidirectionality metrics is quantified. These extensions are applied to four representative balances to assess the bidirectionality characteristics of each. The paper is tutorial in nature, featuring reviews of certain elements of regression and formal inference. Principal findings are that bidirectionality appears to be a common characteristic of most balance outputs and that unless it is taken into account, it is likely to consume the entire error budget of a typical balance calibration experiment. Data volume and correlation among calibration loads are shown to have a significant impact on the precision with which bidirectionality metrics can be assessed.

DeLoach, Richard↗