Results for “Tolerance Bounds”

NASA NTRS1983

Consistent Tolerance Bounds for Statistical Distributions

Assumption that sample comes from population with particular distribution is made with confidence C if data lie between certain bounds. These "confidence bounds" depend on C and assumption about distribution of sampling errors around regression line. Graphical test criteria using tolerance bounds are applied in industry where statistical analysis influences product development and use. Applied to evaluate equipment life.

Mezzacappa, M. A.↗

DOE OSTI2021

Characterizing Electrical Device Behavior with Functional Tolerance Bounds.

Abstract not provided.

Adams, Jason↗

NASA NTRS1983

Determining Normal-Distribution Tolerance Bounds Graphically

Graphical method requires calculations and table lookup. Distribution established from only three points: mean upper and lower confidence bounds and lower confidence bound of standard deviation. Method requires only few calculations with simple equations. Graphical procedure establishes best-fit line for measured data and bounds for selected confidence level and any distribution percentile.

Mezzacappa, M. A.↗

NASA NTRS1985

Tolerance bounds for log gamma regression models

The present procedure for finding lower confidence bounds for the quantiles of Weibull populations, on the basis of the solution of a quadratic equation, is more accurate than current Monte Carlo tables and extends to any location-scale family. It is shown that this method is accurate for all members of the log gamma(K) family, where K = 1/2 to infinity, and works well for censored data, while also extending to regression data. An even more accurate procedure involving an approximation to the Lawless (1982) conditional procedure, with numerical integrations whose tables are independent of the data, is also presented. These methods are applied to the case of failure strengths of ceramic specimens from each of three billets of Si3N4, which have undergone flexural strength testing.

Jones, R. A.↗

NASA NTRS2017

Flight Deck Surface Trajectory-Based Operations (STBO): A Four-Dimensional Trajectory (4DT) Simulation

In four-dimensional trajectory (4DT) Surface Trajectory-Based Operations (STBO), aircraft are assigned a conflict-free 4DT which defines an expected location (x,y coordinates) at all times, t, along the taxi route (with altitude, being fixed). These 4DTs afford the highest temporal certainty at all points along the taxi route, and at the departure runway. In the present study, a 4DT flight deck display was presented on the Airport Moving Map (AMM) to support pilot conformance to a 4DT clearance while taxiing under manual control. This pilot-in-the-loop simulation compared the effect of 4DT flight deck display formats on distance from the expected 4DT location, conformance to the displayed tolerance band, eyes-out time, and pilot ratings of safety and workload. In the defined-tolerance display format, a graphical representation of the expected 4DT location, with a distance-based allowable-tolerance band, was depicted on the AMM. Two defined-tolerance band sizes were tested: plus or minus 164 feet and plus or minus 405 feet. In the undefined-tolerance display format, the expected 4DT location was displayed graphically on the AMM, with no indicated allowable-tolerance bounds. Each taxi trial included 4DT speed changes (two or five, per trial) and a range of 4DT taxi speeds. Results showed that the larger (plus or minus 405 feet) defined-tolerance band yielded higher conformance levels than the smaller (plus or minus 164 feet) band, with pilots staying within the specified and displayed conformance bounds more in the larger (99.71%) than the smaller defined-tolerance band (93.37 percent). However, in terms of being able to predict the location of the aircraft compared to the expected 4DT location, the smaller defined-tolerance band resulted in pilots keeping their aircraft closer to the 4DT location, for both average distance and for a given confidence interval (e.g., 95 percent), than either the larger defined-tolerance band or the undefined-tolerance display format. The larger tolerance band yielded more “eyes-out-the-window” time than the smaller tolerance band. Pilots also rated taxing with the larger tolerance band as safer than the smaller tolerance band.

STBO↗

NASA NTRS1985

Load-deflection tests and computer analyses of a high-precision adhesive-bonded antenna reflector panel

New adhesive-bonded panels are being investigated as a part of an effort to extend and upgrade the 64-m to a 70-m antenna network. Load-deflection tests were conducted on a sample high-precision adhesive-bonded panel for comparison with design criteria. Two computerized structural models were developed in order to predict the deformation patterns under different types of distributed and concentrated loadings. The main purpose was to obtain empirical stiffness factors for the slit beams and girders in the panel structure. With determination and use of the empirical stiffness factors, there is a good agreement between the theoretically predicted deflections and the test measurements. It was also found that the new bonded panels satisfy the stringent design specifications and surface tolerance bounds.

Chian, C. T.↗

NASA NTRS1990

Wood Products Analysis

Structural Reliability Consultants' computer program creates graphic plots showing the statistical parameters of glue laminated timbers, or 'glulam.' The company president, Dr. Joseph Murphy, read in NASA Tech Briefs about work related to analysis of Space Shuttle surface tile strength performed for Johnson Space Center by Rockwell International Corporation. Analysis led to a theory of 'consistent tolerance bounds' for statistical distributions, applicable in industrial testing where statistical analysis can influence product development and use. Dr. Murphy then obtained the Tech Support Package that covers the subject in greater detail. The TSP became the basis for Dr. Murphy's computer program PC-DATA, which he is marketing commercially.

Source record↗

NASA NTRS1985

Reliability bounds for fault-tolerant systems with competing responses to component failures

Bounds are established on the probability of system failure for fault-tolerant systems of the type used, for example, in aviation control. Event series leading to system failure are assumed to follow a semi-Markov model in which the potential sojourn times associated with component failures have exponential distributions and those associated with system responses have distributions with unspecified form. A product form of the bounds is derived by using a model that provides for multiple competing system responses to component failures.

Lee, L. D.↗

NASA NTRS1986

Reliability bounds for fault-tolerant systems with competing responses to component failures

Bounds are established on the probability of system failure for fault-tolerant systems of the type used, for example, in aviation control. Event series leading to system failure are assumed to follow a semi-Markov model in which the potential sojourn times associated with component failures have exponential distributions and those associated with system responses have distributions with unspecified form. A product form of the bounds is derived by using a model that provides for multiple competing system responses to component failures.

Lee, L. D.↗

NASA NTRS1990

Bounded-time fault-tolerant rule-based systems

Two systems concepts are introduced: bounded response-time and self-stabilization in the context of rule-based programs. These concepts are essential for the design of rule-based programs which must be highly fault tolerant and perform in a real time environment. The mechanical analysis of programs for these two properties is discussed. The techniques are used to analyze a NASA application.

Browne, James C.↗

NASA NTRS2020

Demonstration of Deployment Accuracy of the Starshade Inner Disk Subsystem

We present experimental results that demonstrate the required in-plane deployment accuracy of the starshade Inner Disk Subsystem (IDS). This effort was to address Milestone 7C of the Starshade Technology Activity S5, which requires that the in-plane deployment accuracy of the petal interfaces on the IDS be within +/-300um. A full-scale 10m-diameter IDS prototype was constructed. This prototype comprised a medium-fidelity perimeter truss, medium-fidelity spokes, and a low-fidelity optical shield (OS). The testbed also included gravity compensation systems and a laser tracker metrology system. The post-processed measurement uncertainties of the laser tracker were less than 30um at the 3 sigma level. Design, engineering and fabrication of these components was done by JPL, Tendeg, and Roccor. Testing was performed at the Tendeg facility in Louisville, Colorado. The IDS prototype was deployed 22 times and the locations of petal interfaces on the IDS were measured after each deployment. Based on this data, tolerance intervals were calculated that would contain 99.73% of future deployment accuracy errors with 90% confidence. These tolerance intervals are conservative estimates for 3 sigma bounds. The tolerance intervals for the three pertinent error components were found to be within the required allocations, with at least 19% margin.

Turse, Dana↗

NASA NTRS1996

Adjustment of Sensor Locations During Thermal Property Parameter Estimation

The temperature dependent thermal properties of a material may be evaluated from transient temperature histories using nonlinear parameter estimation techniques. The usual approach is to minimize the sum of the squared errors between measured and calculated temperatures at specific locations in the body. Temperature measurements are usually made with thermocouples and it is customary to take thermocouple locations as known and fixed during parameter estimation computations. In fact, thermocouple locations are never known exactly. Location errors on the order of the thermocouple wire diameter are intrinsic to most common instrumentation procedures (e.g., inserting a thermocouple into a drilled hole) and additional errors can be expected for delicate materials, difficult installations, large thermocouple beads, etc.. Thermocouple location errors are especially significant when estimating thermal properties of low diffusively materials which can sustain large temperature gradients during testing. In the present work, a parameter estimation formulation is presented which allows for the direct inclusion of thermocouple positions into the primary parameter estimation procedure. It is straightforward to set bounds on thermocouple locations which exclude non-physical locations and are consistent with installation tolerances. Furthermore, bounds may be tightened to an extent consistent with any independent verification of thermocouple location, such as x-raying, and so the procedure is entirely consonant with experimental information. A mathematical outline of the procedure is given and its implementation is illustrated through numerical examples characteristic of light-weight, high-temperature ceramic insulation during transient heating. The efficacy and the errors associated with the procedure are discussed.

Milos, Frank S.↗

DOE OSTI2021

Bounding uncertainty in functional data: A case study

Functional data are fast becoming a preeminent source of information across a wide range of industries. A particularly challenging aspect of functional data is bounding uncertainty. In this unique case study, we present our attempts at creating bounding functions for selected applications at Sandia National Laboratories (SNL). The first attempt involved a simple extension of functional principal component analysis (fPCA) to incorporate covariates. Though this method was straightforward, the extension was plagued by poor coverage accuracy for the bounding curve. This led to a second attempt utilizing elastic methodology which yielded more accurate coverage at the cost of more complexity.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2016

Application of Design of Experiments and Surrogate Modeling within the NASA Advanced Concepts Office, Earth-to-Orbit Design Process

Decisions made during early conceptual design have a large impact upon the expected life-cycle cost (LCC) of a new program. It is widely accepted that up to 80% of such cost is committed during these early design phases.1 Therefore, to help minimize LCC, decisions made during conceptual design must be based upon as much information as possible. To aid in the decision making for new launch vehicle programs, the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) provides rapid turnaround pre-phase A and phase A concept definition studies. The ACO team utilizes a proven set of tools to provide customers with a full vehicle mass breakdown to tertiary subsystems, preliminary structural sizing based upon worst-case flight loads, and trajectory optimization to quantify integrated vehicle performance for a given mission.2 Although the team provides rapid turnaround for single vehicle concepts, the scope of the trade space can be limited due to analyst availability and the manpower requirements for manual execution of the analysis tools. In order to enable exploration of a broader design space, the ACO team has implemented an Advanced Design Methods (ADM) based approach. This approach applies the concepts of Design of Experiments (DOE) and surrogate modeling to more exhaustively explore the trade space and provide the customer with additional design information to inform decision making. This paper will first discuss the automation of the ACO tool set, which represents a majority of the development e ort. In order to t a surrogate model within tolerable error bounds a number of DOE cases are needed. This number will scale with the number of variable parameters desired and the complexity of the system's response to those variables. For all but the smallest design spaces, the number of cases required cannot be produced within an acceptable timeframe using a manual process. Therefore, automation of the tools was a key enabler for the successful application of an ADM approach to an ACO design study. Following the overview of the tool set automation, an example problem will be given to illustrate the implementation of the ADM approach. The example problem will first cover the inclusion of Ground Rules and Assumptions (GR&A) for a study. The GR&A are very important to the study as they determine the constraints within which a trade study can be conducted. These trades must ultimately reconcile with the customer's desired output and any anticipated \what if" questions. The example problem will then illustrate the setup and execution of a DOE through the automated ACO tools. This process is accomplished more efficiently in this work by splitting the tools into two separate environments. The first environment encompasses the structural optimization and mass estimation tools, while the second is focused on trajectory optimization. Surrogate models are t to the outputs of each environment and are integrated via connection of the surrogate equations. Throughout this process, checks are implemented to compare the output of the surrogates to the output of manually run cases to ensure that the error of the final surrogates is at an acceptable level. The conclusion of the example problem demonstrates the utility of the ADM based approach. Using surrogate models gives the ACO team the ability to visualize vehicle sensitivities to various design parameters and identify regions of interest within the design space. The ADM approach can thus be used to inform concept down selection and isolate promising vehicle configurations to be explored in more detail through the manual design process. In addition it provides the customer with an almost instantaneous turnaround on any \what if" questions that may arise within the bounds of the surrogate model. This approach ultimately expands the ability of the ACO team to provide its customer with broad and rapid turnaround trade studies for launch vehicle conceptual design. The ability to identify a selection of designs which can meet the customer requirements will have the potential to lower LCC of launch vehicle designs originating from ACO.

Zwack, Mathew R.↗

NASA NTRS2016

Application of Design of Experiments and Surrogate Modeling within the NASA Advanced Concepts Office, Earth-to-Orbit Design Process

Decisions made during early conceptual design have a large impact upon the expected life-cycle cost (LCC) of a new program. It is widely accepted that up to 80% of such cost is committed during these early design phases [1]. Therefore, to help minimize LCC, decisions made during conceptual design must be based upon as much information as possible. To aid in the decision making for new launch vehicle programs, the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) provides rapid turnaround pre-phase A and phase A concept definition studies. The ACO team utilizes a proven set of tools to provide customers with a full vehicle mass breakdown to tertiary subsystems, preliminary structural sizing based upon worst-case flight loads, and trajectory optimization to quantify integrated vehicle performance for a given mission [2]. Although the team provides rapid turnaround for single vehicle concepts, the scope of the trade space can be limited due to analyst availability and the manpower requirements for manual execution of the analysis tools. In order to enable exploration of a broader design space, the ACO team has implemented an advanced design methods (ADM) based approach. This approach applies the concepts of design of experiments (DOE) and surrogate modeling to more exhaustively explore the trade space and provide the customer with additional design information to inform decision making. This paper will first discuss the automation of the ACO tool set, which represents a majority of the development effort. In order to fit a surrogate model within tolerable error bounds a number of DOE cases are needed. This number will scale with the number of variable parameters desired and the complexity of the system's response to those variables. For all but the smallest design spaces, the number of cases required cannot be produced within an acceptable timeframe using a manual process. Therefore, automation of the tools was a key enabler for the successful application of an ADM approach to an ACO design study. Following the overview of the tool set automation, an example problem will be given to illustrate the implementation of the ADM approach. The example problem will first cover the inclusion of ground rules and assumptions (GR&A) for a study. The GR&A are very important to the study as they determine the constraints within which a trade study can be conducted. These trades must ultimately reconcile with the customer's desired output and any anticipated "what if" questions.

Zwack, Mathew R.↗

NASA NTRS2016

Application of Design of Experiments and Surrogate Modeling within the NASA Advanced Concepts Office, Earth-to-Orbit Design Process

Decisions made during early conceptual design have a large impact upon the expected life-cycle cost (LCC) of a new program. It is widely accepted that up to 80% of such cost is committed during these early design phases. Therefore, to help minimize LCC, decisions made during conceptual design must be based upon as much information as possible. To aid in the decision making for new launch vehicle programs, the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) provides rapid turnaround pre-phase A and phase A concept definition studies. The ACO team utilizes a proven set of tools to provide customers with a full vehicle mass breakdown to tertiary subsystems, preliminary structural sizing based upon worst-case flight loads, and trajectory optimization to quantify integrated vehicle performance for a given mission. Although the team provides rapid turnaround for single vehicle concepts, the scope of the trade space can be limited due to analyst availability and the manpower requirements for manual execution of the analysis tools. In order to enable exploration of a broader design space, the ACO team has implemented an advanced design methods (ADM) based approach. This approach applies the concepts of design of experiments (DOE) and surrogate modeling to more exhaustively explore the trade space and provide the customer with additional design information to inform decision making. This paper will first discuss the automation of the ACO tool set, which represents a majority of the development effort. In order to fit a surrogate model within tolerable error bounds a number of DOE cases are needed. This number will scale with the number of variable parameters desired and the complexity of the system's response to those variables. For all but the smallest design spaces, the number of cases required cannot be produced within an acceptable timeframe using a manual process. Therefore, automation of the tools was a key enabler for the successful application of an ADM approach to an ACO design study. Following the overview of the tool set automation, an example problem will be given to illustrate the implementation of the ADM approach. The example problem will first cover the inclusion of ground rules and assumptions (GR&A) for a study. The GR&A are very important to the study as they determine the constraints within which a trade study can be conducted. These trades must ultimately reconcile with the customer's desired output and any anticipated "what if" questions. The example problem will then illustrate the setup and execution of a DOE through the automated ACO tools. This process is accomplished more efficiently in this work by splitting the tools into two separate environments. The first environment encompasses the structural optimization and mass estimation tools, while the second is focused on trajectory optimization. Surrogate models are fit to the outputs of each environment and are "integrated" via connection of the surrogate equations. Throughout this process, checks are implemented to compare the output of the surrogates to the output of manually run cases to ensure that the error of the final surrogates is at an acceptable level. The conclusion of the example problem demonstrates the utility of the ADM based approach. Using surrogate models gives the ACO team the ability to visualize vehicle sensitivities to various design parameters and identify regions of interest within the design space. The ADM approach can thus be used to inform concept down selection and isolate promising vehicle configurations to be explored in more detail through the manual design process. In addition it provides the customer with an almost instantaneous turnaround on any ''what if" questions that may arise within the bounds of the surrogate model. This approach ultimately expands the ability of the ACO team to provide its customer with broad and rapid turnaround trade studies for launch vehicle conceptual design. The ability to identify a selection of designs which can meet the customer requirements will help ensure lower LCC of launch vehicle designs originating from ACO.

Zwack, Mathew R.↗

NASA NTRS2023

A Common Trajectory Language for New Airspace Domains

Revolutionary new aviation services are currently in development, including small package delivery and short-range urban passenger transportation. These new services need a language to represent and deconflict trajectories, and a common language will simplify coordination between the new airspace domains as well as traditional airspace. A Trajectory Specification Language (TSL) was previously proposed for traditional air traffic, and it can also serve as a common language for the new aviation domains and services. The TSL specifies a reference trajectory in 4D space along with spatial tolerances that determine a bounding volume at any given time in flight. The tolerances are defined in terms of the route-oriented cross-track, along-track, and vertical axes, and they are allowed to vary with distance along the route. This bounding model can guarantee safe separation between flights as long as they are in conformance with their assigned trajectories. The advantages of this model over the previously proposed Operational Intent Volumes (OIVs) in terms of airspace usage efficiency are explained.

air traffic control, aircraft trajectory, language↗

DOE OSTI2023

Quantum error correction in the black hole interior

We study the quantum error correction properties of the black hole interior in a toy model for an evaporating black hole: Jackiw-Teitelboim gravity entangled with a non-gravitational bath. After the Page time, the black hole interior degrees of freedom in this system are encoded in the bath Hilbert space. We use the gravitational path integral to show that the interior density matrix is correctable against the action of quantum operations on the bath which (i) do not have prior access to details of the black hole microstates, and (ii) do not have a large, negative coherent information with respect to the maximally mixed state on the bath, with the lower bound controlled by the black hole entropy and code subspace dimension. Thus, the encoding of the black hole interior in the radiation is robust against generic, low-rank quantum operations. For erasure errors, gravity comes within an O (1) distance of saturating the Singleton bound on the tolerance of error correcting codes. For typical errors in the bath to corrupt the interior, they must have a rank that is a large multiple of the bath Hilbert space dimension, with the precise coefficient set by the black hole entropy and code subspace dimension.

2D gravity↗