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NASA NTRS1992

An improved approach for flight readiness certification: Methodology for failure risk assessment and application examples. Volume 3: Structure and listing of programs

An improved methodology for quantitatively evaluating failure risk of spaceflight systems to assess flight readiness and identify risk control measures is presented. This methodology, called Probabilistic Failure Assessment (PFA), combines operating experience from tests and flights with engineering analysis to estimate failure risk. The PFA methodology is of particular value when information on which to base an assessment of failure risk, including test experience and knowledge of parameters used in engineering analyses of failure phenomena, is expensive or difficult to acquire. The PFA methodology is a prescribed statistical structure in which engineering analysis models that characterize failure phenomena are used conjointly with uncertainties about analysis parameters and/or modeling accuracy to estimate failure probability distributions for specific failure modes. These distributions can then be modified, by means of statistical procedures of the PFA methodology, to reflect any test or flight experience. Conventional engineering analysis models currently employed for design of failure prediction are used in this methodology. The PFA methodology is described and examples of its application are presented. Conventional approaches to failure risk evaluation for spaceflight systems are discussed, and the rationale for the approach taken in the PFA methodology is presented. The statistical methods, engineering models, and computer software used in fatigue failure mode applications are thoroughly documented.

Moore, N. R.↗

NASA NTRS2014

Quantitative Risk Modeling of Fire on the International Space Station

The International Space Station (ISS) Program has worked to prevent fire events and to mitigate their impacts should they occur. Hardware is designed to reduce sources of ignition, oxygen systems are designed to control leaking, flammable materials are prevented from flying to ISS whenever possible, the crew is trained in fire response, and fire response equipment improvements are sought out and funded. Fire prevention and mitigation are a top ISS Program priority - however, programmatic resources are limited; thus, risk trades are made to ensure an adequate level of safety is maintained onboard the ISS. In support of these risk trades, the ISS Probabilistic Risk Assessment (PRA) team has modeled the likelihood of fire occurring in the ISS pressurized cabin, a phenomenological event that has never before been probabilistically modeled in a microgravity environment. This paper will discuss the genesis of the ISS PRA fire model, its enhancement in collaboration with fire experts, and the results which have informed ISS programmatic decisions and will continue to be used throughout the life of the program.

Castillo, Theresa↗

DOE OSTI2020

Wattile: Probabilistic Deep Learning-based Forecasting of Building Energy Consumption [SWR-20-94]

Accurate energy forecasting is becoming critical due to many reasons: i ) optimal distributed energy resources operations and dispatch, ii) fault detection and diagnostics, and iii) meeting operational energy efficiency targets. Wattile uses deep learning (DL) for the building's short-term load forecasting application. Two specific types of neural networks called, Long Short Term Memory (LSTM) and Sequence-to-Sequence (S2S) models are used to make predictions. Forecasting models are trained using online historical weather and occupancy indicator data streams from the Intelligent Campus Program's data acquisition systems at the National Renewable Energy Laboratory (NREL) for main meters and sub-meters of multiple building types. These models use probabilistic methods to provide quantile-based forecasts in addition to nominal conditional median predictions of electricity consumption.

Frank, Stephen↗

NASA NTRSDate not supplied

Development of A Crew Health and Performance System Probabilistic Risk Assessment Tool: Proof-of-Concept Approach

The crew health and performance (CHP) system represents the span of technological interventions and tested processes and procedures that in combination address the human risk to space flight. The Human Research Program (HRP) mental model of the CHP system breaks the capabilities needed to meet NASA human flight systems standards into specific categories (i.e., countermeasures, behavioral health, medical intervention). These categories are further broken down into specific sub-groups generally associated with the human system risks that these capabilities seek to mitigate. Like the approach used to develop the Integrated Medical Model (IMM) and the Medical Extensible Dynamic Probabilistic Risk Analysis Tool (MEDPRAT), HRP tasked NASA GRC’s Cross-Cutting Computational Modeling Project with developing a CHP probabilistic risk assessment tool, the CHP-PRA. The CHP-PRA model seeks to quantify and relatively assess the human risk state within the crew health and performance domain, using a combination of knowledge about human system risks and technology and practices likely to be applied during space flight missions. This modeling system will incorporate customer and stakeholder feedback and be flexible enough to address multiple different questions about important low-level mission-specific parameters. This presentation will introduce the initial concept and development timeline for this tool and demonstrate proof-of-concept through an application addressing a specific human risk question posed within the Artemis program.

Risk analysis↗

DOE OSTI2019

Mass calibration of the CODEX cluster sample using SPIDERS spectroscopy – I. The richness–mass relation

Abstract We use galaxy dynamical information to calibrate the richness–mass scaling relation of a sample of 428 galaxy clusters that are members of the CODEX sample with redshifts up to z ∼ 0.7. These clusters were X-ray selected using the ROSAT All-Sky Survey (RASS) and then cross-matched to associated systems in the redMaPPer (the red sequence Matched-filter Probabilistic Percolation) catalogue from the Sloan Digital Sky Survey. The spectroscopic sample we analyse was obtained in the SPIDERS program and contains ∼7800 red member galaxies. Adopting NFW mass and galaxy density profiles and a broad range of orbital anisotropy profiles, we use the Jeans equation to calculate halo masses. Modelling the scaling relation as $\lambda \propto \text{A}_{\lambda } {M_{\text{200c}}}^{\text{B}_{\lambda }} ({1+z})^{\gamma _{\lambda }}$, we find the parameter constraints $\text{A}_{\lambda }=38.6^{+3.1}_{-4.1}\pm 3.9$, $\text{B}_{\lambda }=0.99^{+0.06}_{-0.07}\pm 0.04$, and $\gamma _{\lambda }=-1.13^{+0.32}_{-0.34}\pm 0.49$, where we present systematic uncertainties as a second component. We find good agreement with previously published mass trends with the exception of those from stacked weak lensing analyses. We note that although the lensing analyses failed to account for the Eddington bias, this is not enough to explain the differences. We suggest that differences in the levels of contamination between pure redMaPPer and RASS + redMaPPer samples could well contribute to these differences. The redshift trend we measure is more negative than but statistically consistent with previous results. We suggest that our measured redshift trend reflects a change in the cluster galaxy red sequence (RS) fraction with redshift, noting that the trend we measure is consistent with but somewhat stronger than an independently measured redshift trend in the RS fraction. We also examine the impact of a plausible model of correlated scatter in X-ray luminosity and optical richness, showing it has negligible impact on our results.

Capasso, R.↗

DOE OSTI2020

Uncertainty Analysis of Consequence Management Data Products

An interlaboratory effort has developed a probabilistic framework to characterize uncertainty in data products that are developed by the US Department of Energy Consequence Management Program in support of the Federal Radiological Monitoring and Assessment Center. The purpose of this paper is to provide an overview of the probability distributions of input variables and the statistical methods used to propagate and quantify the overall uncertainty of the derived response levels that are used as contours on data products due to the uncertainty in input parameters. Uncertainty analysis results are also presented for several study scenarios. This paper includes an example data product to illustrate the potential real-world implications of incorporating uncertainty analysis results into data products that inform protective action decisions. Data product contours that indicate areas where public protection actions may be warranted can be customized to an acceptable level of uncertainty. Finally, the investigators seek feedback from decision makers and the radiological emergency response community to determine how uncertainty information can be used to support the protective action decision-making process and how it can be presented on data products.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2017

RAVEN User Manual

RAVEN is a generic software framework to perform parametric and probabilistic analy- sis based on the response of complex system codes. The initial development was aimed to provide dynamic risk analysis capabilities to the Thermo-Hydraulic code RELAP-7, currently under development at the Idaho National Laboratory (INL). Although the initial goal has been fully accomplished, RAVEN is now a multi-purpose probabilistic and uncer- tainty quantification platform, capable to agnostically communicate with any system code. This agnosticism includes providing Application Programming Interfaces (APIs). These APIs are used to allow RAVEN to interact with any code as long as all the parameters that need to be perturbed are accessible by inputs files or via python interfaces. RAVEN is capable of investigating the system response, and investigating the input space using Monte Carlo, Grid, or Latin Hyper Cube sampling schemes, but its strength is focused to- ward system feature discovery, such as limit surfaces, separating regions of the input space leading to system failure, using dynamic supervised learning techniques. The development of RAVEN has started in 2012, when, within the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the need to provide a modern risk evaluation framework became stronger. RAVEN principal assignment is to provide the necessary software and algorithms in order to employ the concept developed by the Risk Informed Safety Margin Characterization (RISMC) program. RISMC is one of the pathways defined within the Light Water Reactor Sustainability (LWRS) program. In the RISMC approach, the goal is not just the individuation of the frequency of an event potentially leading to a system failure, but the closeness (or not) to key safety-related events. Hence, the approach is in- terested in identifying and increasing the safety margins related to those events. A safety margin is a numerical value quantifying the probability that a safety metric (e.g. for an important process such as peak pressure in a pipe) is exceeded under certain conditions. The initial development of RAVEN has been focused on providing dynamic risk assess- ment capability to RELAP-7, currently under develop-ment at the INL and, likely, future replacement of the RELAP5-3D code. Most the capabilities that have been implemented having RELAP-7 as principal focus are easily deployable for other system codes. For this reason, several side activates are currently ongoing for coupling RAVEN with soft- ware such as RELAP5-3D, etc. The aim of this document is the explaination of the input requirements, focalizing on the input structure.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

RAVEN User Manual

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

Probability approach for strength calculations

The use of probabilistic structural analysis methods (PSAM) to predict structural reliability is the subject of an on-going NASA research program. The elements of the new technology developed to date is reported. Applications of the developed software to structural problems are demonstrated for simple validation problems and for large scale application problems. On-going research to support component and system reliability predictions suitable for analytical certification of aerospace structures is briefly reviewed.

Chamis, Christos C.↗

NASA NTRS2008

Stochastic Analysis of Orbital Lifetimes of Spacecraft

A document discusses (1) a Monte-Carlo-based methodology for probabilistic prediction and analysis of orbital lifetimes of spacecraft and (2) Orbital Lifetime Monte Carlo (OLMC)--a Fortran computer program, consisting of a previously developed long-term orbit-propagator integrated with a Monte Carlo engine. OLMC enables modeling of variances of key physical parameters that affect orbital lifetimes through the use of probability distributions. These parameters include altitude, speed, and flight-path angle at insertion into orbit; solar flux; and launch delays. The products of OLMC are predicted lifetimes (durations above specified minimum altitudes) for the number of user-specified cases. Histograms generated from such predictions can be used to determine the probabilities that spacecraft will satisfy lifetime requirements. The document discusses uncertainties that affect modeling of orbital lifetimes. Issues of repeatability, smoothness of distributions, and code run time are considered for the purpose of establishing values of code-specific parameters and number of Monte Carlo runs. Results from test cases are interpreted as demonstrating that solar-flux predictions are primary sources of variations in predicted lifetimes. Therefore, it is concluded, multiple sets of predictions should be utilized to fully characterize the lifetime range of a spacecraft.

Sasamoto, Washito↗

DOE OSTI2023

PipeSight: A High-Performance Computing Platform for Pipeline Integrity Management

The Phase I feasibility study completed as part of this project has led to a number of innovative technologies being developed and has laid the foundation for a successful Phase II effort to commercialize a platform for managing the integrity of pipelines for the damage mechanisms of the new, hybrid-energy based economy. To ground the development efforts and direction of the project, an extensive market research and customer discovery effort was undertaken early in Phase I. Through this effort, a number of pipeline owners and operators were interviewed, and the following key findings were discovered about the pipeline industry: • Small pipeline operators do not have the central engineering groups necessary to perform their own independent analysis of inspection data, but instead rely on summarized tally sheets provided to them by inspection service providers. • The time it takes to go from an inspection to a completed engineering assessment, even for small segments of pipeline, can take anywhere from 30-120 days. During this delay, critical threats can (and have been known to) cause failures. • Uncertainty is often not accounted for in the assessment of pipeline integrity. The tally sheets provided by third-party service providers are almost always deterministic in nature, identifying threats that present a concern only to the current (not the future) integrity of the pipeline. • It is uncommon to apply the latest technologies to perform advanced assessments of damaged pipelines. There is a desire to use more advanced analysis capabilities to assess threats. Many pipeline operators indicated that they would often excavate a pipeline to perform an inspection and find that the damage was not as bad as they anticipated, thus using limited resources unnecessarily. Companies are not consistent in their use of inspection data to determine corrosion rates, and those that do only calculate deterministic corrosion rates. • The industry has prominently relied on time-based inspections but has recently started to transition to risk-based inspections. However, there appears to be no uniform guidance on how to do so while properly accounting for all sources of uncertainty. • Companies are not storing inspection data in a manner that allows for the ready determination of temporal trends. • Predictive maintenance principles and practices are beginning to be used by early adopters • Some pipelines are being re-purposed to transport different process fluids than they were designed for, e.g., H 2 and CO 2 rich process streams to serve the new hybrid-energy based economy, which are presenting new integrity concerns for the existing pipeline network that crisscrosses the United States. As a result of these discoveries, we were able to target the development efforts in Phase I to best serve the needs of the industry. In Phase I, we developed a way to correlate multiple large-scale scans of the pipeline to determine a probabilistic corrosion rate that accounts for all sources of error and uncertainty in the inspection process. This probabilistic corrosion rate can be used to predict the future thickness distribution of the pipe wall. We demonstrate how this analysis may be performed in an analytical fashion and has been implemented in such a manner that it can be readily distributed using GPU computing through integration of the Kokkos programming model. We also make a very novel extension of the analytical corrosion rate model to Bayesian Networks (an explainable AI technique) that can account for non-parametric distributions of corrosion rates. With the predictions made above for the probabilistic corrosion rate and corresponding future distribution of the pipe wall thickness, we can assess the integrity of the pipeline through the use of a probabilistic engineering assessment. We developed a novel screening data analysis approach that can rapidly identify ‘hotspots’ (local thin areas) where the integrity of the pipeline is a concern. Once more, we implemented this screening approach in C++ to leverage GPU computing via the Kokkos programming model. After the critical hotspots are identified, we developed a program that can automatically generate an advanced finite element model of the damaged regions. Since the number of damaged regions that require advanced analysis can number in the thousands, we integrated an open-source container-native workflow engine for orchestrating parallel jobs on the cloud. Initially, these advanced numerical models were only designed to account for loading due to internal pressure. However, in a slight pivot from the initial Phase I proposal, we developed a complete pipe stress analysis program (called Simflex) which can simulate the complete pipeline and its response to thermal expansion, pressure, thermal bowing, weight, wind, earthquake, support displacement, support friction and external forces. This pipe stress analysis program was written generically, to handle any piping system, but contains the features needed to model long pipelines (i.e., it incorporates a model for soil mechanics and can account for the nonlinear boundary conditions necessary to simulate long underground pipelines). This pipe stress analysis program can simulate any segment of the pipeline (simple or complex) under any set of conditions and loads, to determine the supplemental loads (axial forces and bending moments) at the location of damage. This enables the most accurate state of stress to be accounted for in the pipeline, which can prove critical when evaluating the integrity of a damaged region. In the process of developing the technologies to perform the integrity assessment of the pipeline, we also extended one of the industry standard approaches for performing the assessment of local thin areas that extend more in the circumferential direction than the longitudinal direction of the pipeline. This approach was presented to the API 579-1/AS ME FFS-1 steering committee in November 2021 for consideration in the next edition of the industry standard for Fitness-For-Service (expected to be released in 2023). To help pipeline operators make decisions with the results on any integrity assessment, we developed a new approach to the life-cycle management of pipelines which uses a Bayesian Decision Network. The network is designed to help pipeline operators plan and prioritize inspection activities and ultimately make smarter, more cost-effective decisions. The Bayesian approach accounts for all sources of uncertainty and carries them through to the final optimal decisions, providing a probabilistic framework for optimizing inspection intervals. The proof-of-concept networks developed in the feasibility study are complete, verified, and are focused on a subset of the pipeline. To expand this novel approach to the scale necessary for an entire network of pipelines in Phase II, we will leverage the DOE-funded Bengi solver for industrial-scale decision making with Bayesian Networks [22]. Once implemented, we will be able to provide the pipeline industry with a much-needed tool for optimal inspection planning using truly explainable artificial intelligence (XAI). To handle all of these advanced capabilities into a cloud-based platform, the architecture of the Equity Engineering Cloud (EEC) was extended to include Argo Workflows, a framework capable of distributing and managing a massive number of jobs that consume their own resources, such that thousands of serial finite element simulations can be run in parallel. As part of this substantial undertaking, we also integrated Argo Continuous Delivery (CD) into the EEC, to aid with the rapid prototyping and iterations that will be imperative to the success of the PipeSight platform’s Agile development process in Phase II. As part of the pipe stress analysis program, we also developed a custom visualizer that leverages the DOE-funded VTK visualization library. We added custom contouring capabilities and a means for interacting visually with both the inputs and outputs of the pipe stress analysis program. We also developed routines for automating the post-processing of the finite element simulations to determine if any failure criteria are met and to visualize the deformations, stresses and strains in ParaView using the exodus II file format (a subset of netCDF).

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2002

Risk-Based Probabilistic Approach to Aeropropulsion System Assessment

In an era of shrinking development budgets and resources, where there is also an emphasis on reducing the product development cycle, the role of system assessment, performed in the early stages of an engine development program, becomes very critical to the successful development of new aeropropulsion systems. A reliable system assessment not only helps to identify the best propulsion system concept among several candidates, it can also identify which technologies are worth pursuing. This is particularly important for advanced aeropropulsion technology development programs, which require an enormous amount of resources. In the current practice of deterministic, or point-design, approaches, the uncertainties of design variables are either unaccounted for or accounted for by safety factors. This could often result in an assessment with unknown and unquantifiable reliability. Consequently, it would fail to provide additional insight into the risks associated with the new technologies, which are often needed by decision makers to determine the feasibility and return-on-investment of a new aircraft engine. In this work, an alternative approach based on the probabilistic method was described for a comprehensive assessment of an aeropropulsion system. The statistical approach quantifies the design uncertainties inherent in a new aeropropulsion system and their influences on engine performance. Because of this, it enhances the reliability of a system assessment. A technical assessment of a wave-rotor-enhanced gas turbine engine was performed to demonstrate the methodology. The assessment used probability distributions to account for the uncertainties that occur in component efficiencies and flows and in mechanical design variables. The approach taken in this effort was to integrate the thermodynamic cycle analysis embedded in the computer code NEPP (NASA Engine Performance Program) and the engine weight analysis embedded in the computer code WATE (Weight Analysis of Turbine Engines) with the fast probability integration technique (FPI). FPI was developed by Southwest Research Institute under contract with the NASA Glenn Research Center. The results were plotted in the form of cumulative distribution functions and sensitivity analyses and were compared with results from the traditional deterministic approach. The comparison showed that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system. The current work addressed the application of the probabilistic approach to assess specific fuel consumption, engine thrust, and weight. Similarly, the approach can be used to assess other aspects of aeropropulsion system performance, such as cost, acoustic noise, and emissions. Additional information is included in the original extended abstract.

Tong, Michael T.↗

DOE OSTI2019

Assessment of verification and validation status - RELAP5-3D and RAVEN

The United States nuclear industry is facing a strong challenge to ensure maximum safety while enhancing economic benefit. Safety is a key parameter to all aspects related to light water reactor (LWR) nuclear power plants (NPPs), especially cost savings. Since the goal is to extend the lifetimes of these NPPs, the traditional deterministic safety concept may not guarantee a current economic asset. The Light Water Reactor Sustainability (LWRS) Program has been promoting a wide range of research and development (R&D) in this field to maximize the safety, economics, and performance of these NPPs through improved scientific understanding. One of the best practices to achieve this goal is to identify and optimize safety margins, which can lead to cost reduction. To do this, under the LWRS framework, the Risk-Informed Systems Analysis (RISA) Pathway will focus on the optimization of safety margin and minimization of uncertainties to ensure both safety and economics at the highest level. The RISA Pathway will provide enhanced capabilities for analyzing and characterizing LWR systems performance by developing and demonstrating methods, tools, and data to enable risk-informed margins management (RIMM). The goals of the RISA Pathway are twofold: (1) deploy the risk-informed tools and methods that enable better representation of safety margins and factors that contribute to cost and safety; and (2) conduct advanced risk assessment applications with industry to support margin management strategies that enable more cost-effective plant operation. The tools and methods provided by the RISA Pathway will support effective margin management for both active and passive safety systems, structures, and components (SSC) of an NPP. The tools and methods used in the RISA Pathway should have high confidence and highest technical maturity for and implementation to industry at its current setting. They should also have a capability to support risk-informed decision making for both probabilistic and deterministic elements of safety. The RISA Pathway will, therefore, perform a comprehensive assessment of verification and validation (V&V) status of RISA Toolkit to enhance credibility RISA Toolkit which be used by industry. This report summarizes assessment technical maturity of RISA thermal-hydraulics accident analysis code RELAP5-3D and multi-purpose probabilistic risk analysis tool RAVEN V&V status including specific information of the tool such as capability and features, quality assurance program, developer/independent V&V record, separation/integral tests history, user documents, and feedback.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2004

The Application of Probabilistic Methods to the Mistuning Problem

FMM is a reduced order model for efficiently calculating the forced response of a mistuned bladed disk. FMM ID is a companion program which determines the mistuning in a particular rotor. Together, these methods provide a way to acquire data on the mistuning in a population of bladed disks, and then simulate the forced response of the fleet. This process is tested experimentally, and the simulated results are compared with laboratory measurements of a fleet of test rotors. The method is shown to work quite well. It is found that accuracy of the results depends on two factors: the quality of the statistical model used to characterize mistuning, and how sensitive the system is to errors in the statistical modeling.

Griffin, J. H.↗

NASA NTRS1986

Automatic discovery of optimal classes

A criterion, based on Bayes' theorem, is described that defines the optimal set of classes (a classification) for a given set of examples. This criterion is transformed into an equivalent minimum message length criterion with an intuitive information interpretation. This criterion does not require that the number of classes be specified in advance, this is determined by the data. The minimum message length criterion includes the message length required to describe the classes, so there is a built in bias against adding new classes unless they lead to a reduction in the message length required to describe the data. Unfortunately, the search space of possible classifications is too large to search exhaustively, so heuristic search methods, such as simulated annealing, are applied. Tutored learning and probabilistic prediction in particular cases are an important indirect result of optimal class discovery. Extensions to the basic class induction program include the ability to combine category and real value data, hierarchical classes, independent classifications and deciding for each class which attributes are relevant.

Cheeseman, Peter↗

NASA NTRS1999

Reliability/Risk Methods and Design Tools for Application in Space Programs

Since 1984 NASA has funded several major programs to develop Reliability/Risk Methods and tools for engineers to apply in the design and assessment of aerospace hardware. Two probabilistic software tools that show great promise for practical application are the finite element code NESSUS and the system risk analysis code QRAS. This paper examines NASA's past, present, and future directions in reliability and risk engineering applications, Both the NESSUS and QRAS software tools are detailed.

Townsend, John S.↗

NASA NTRS2010

Risk Informed Design as Part of the Systems Engineering Process

This slide presentation reviews the importance of Risk Informed Design (RID) as an important feature of the systems engineering process. RID is based on the principle that risk is a design commodity such as mass, volume, cost or power. It also reviews Probabilistic Risk Assessment (PRA) as it is used in the product life cycle in the development of NASA's Constellation Program.

Deckert, George↗

NASA NTRS2002

Reliability Analysis of Brittle Material Structures - Including MEMS(?) - With the CARES/Life Program

Brittle materials are being used, or considered, for a wide variety of high tech applications that operate in harsh environments, including static and rotating turbine parts. thermal protection systems, dental prosthetics, fuel cells, oxygen transport membranes, radomes, and MEMS. Designing components to sustain repeated load without fracturing while using the minimum amount of material requires the use of a probabilistic design methodology. The CARES/Life code provides a general-purpose analysis tool that predicts the probability of failure of a ceramic component as a function of its time in service. For this presentation an interview of the CARES/Life program will be provided. Emphasis will be placed on describing the latest enhancements to the code for reliability analysis with time varying loads and temperatures (fully transient reliability analysis). Also, early efforts in investigating the validity of using Weibull statistics, the basis of the CARES/Life program, to characterize the strength of MEMS structures will be described as as well as the version of CARES/Life for MEMS (CARES/MEMS) being prepared which incorporates single crystal and edge flaw reliability analysis capability. It is hoped this talk will open a dialog for potential collaboration in the area of MEMS testing and life prediction.

Nemeth, Noel N.↗