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Acceptance sampling using judgmental and randomly selected samples

We present a Bayesian model for acceptance sampling where the population consists of two groups, each with different levels of risk of containing unacceptable items. Expert opinion, or judgment, may be required to distinguish between the high and low-risk groups. Hence, high-risk items are likely to be identifed (and sampled) using expert judgment, while the remaining low-risk items are sampled randomly. We focus on the situation where all observed samples must be acceptable. Consequently, the objective of the statistical inference is to quantify the probability that a large percentage of the unsampled items in the population are also acceptable. We demonstrate that traditional (frequentist) acceptance sampling and simpler Bayesian formulations of the problem are essentially special cases of the proposed model. We explore the properties of the model in detail, and discuss the conditions necessary to ensure that required samples sizes are non-decreasing function of the population size. The method is applicable to a variety of acceptance sampling problems, and, in particular, to environmental sampling where the objective is to demonstrate the safety of reoccupying a remediated facility that has been contaminated with a lethal agent.

54 ENVIRONMENTAL SCIENCES↗

INFRARED AND ULTRAVIOLET STAR FORMATION IN BRIGHTEST CLUSTER GALAXIES IN THE ACCEPT SAMPLE

We present infrared (IR) and ultraviolet (UV) photometry for a sample of brightest cluster galaxies (BCGs). The BCGs are from a heterogeneous but uniformly characterized sample, the Archive of Chandra Cluster Entropy Profile Tables (ACCEPT), of X-ray galaxy clusters from the Chandra X-ray telescope archive with published gas temperature, density, and entropy profiles. We use archival Galaxy Evolution Explorer (GALEX), Spitzer Space Telescope, and Two Micron All Sky Survey (2MASS) observations to assemble spectral energy distributions (SEDs) and colors for BCGs. We find that while the SEDs of some BCGs follow the expectation of red, dust-free old stellar populations, many exhibit signatures of recent star formation in the form of excess UV or mid-IR emission, or both. We establish a mean near-UV (NUV) to 2MASS K color of 6.59 {+-} 0.34 for quiescent BCGs. We use this mean color to quantify the UV excess associated with star formation in the active BCGs. We use both fits to a template of an evolved stellar population and library of starburst models and mid-IR star formation relations to estimate the obscured star formation rates (SFRs). We show that many of the BCGs in X-ray clusters with low central gas entropy exhibit enhanced UV (38%) and mid-IR emission (43%) from 8 to 160 {mu}m, above that expected from an old stellar population. These excesses are consistent with ongoing star formation activity in the BCG, star formation that appears to be enabled by the presence of high-density, X-ray-emitting intergalactic gas in the core of the cluster of galaxies. This hot, X-ray-emitting gas may provide the enhanced ambient pressure and some of the fuel to trigger star formation. This result is consistent with previous works that showed that BCGs in clusters with low central gas entropies host H{alpha} emission-line nebulae and radio sources, while clusters with high central gas entropy exhibit none of these features. GALEX UV and Spitzer mid-IR measurements combined provide a complete picture of unobscured and obscured star formation occurring in these systems. We present IR and UV photometry and estimated equivalent continuous SFRs for a sample of BCGs.

79 ASTRONOMY AND ASTROPHYSICS↗

Results from the Interim Salt Disposition Program Macrobatch 11 Tank 21H Acceptance Samples

Savannah River National Laboratory (SRNL) analyzed samples from Tank 21H in support of verification of Macrobatch (Salt Batch) 11 for the Interim Salt Disposition Program (ISDP) for processing. This document reports characterization data on the samples of Tank 21H and fulfills the requirements of Deliverable 3 of the Technical Task Request (TTR).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Results from the Interim Salt Disposition Program Macrobatch 11 Tank 21H Acceptance Samples

Savannah River National Laboratory (SRNL) analyzed samples from Tank 21H in support of verification of Macrobatch (Salt Batch) 11 for the Interim Salt Disposition Program (ISDP) for processing. This document reports characterization data on the samples of Tank 21H and fulfills the requirements of Deliverable 3 of the Technical Task Request (TTR).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Sample Size Effects on Petrophysical Characterization and Fluid-to-Pore Accessibility of Natural Rocks

Laboratory-scale analysis of natural rocks provides petrophysical properties such as density, porosity, pore diameter/pore-throat diameter distribution, and fluid accessibility, in addition to the size and shape of framework grains and their contact relationship with the rock matrix. Different types of laboratory approaches for petrophysical characterization involve the use of a range of sample sizes. While the sample sizes selected should aim to be representative of the rock body, there are inherent limitations imposed by the analytical principles and holding capacities of the different experimental apparatuses, with many instruments only able to accept samples at the μm–mm scale. Therefore, a total of nine (three limestones, three shales, two sandstones, and one dolomite) samples were collected from Texas to fill the knowledge gap of the sample size effect on the resultant petrophysical characteristics. The sample sizes ranged from 3 cm cubes to <75 μm particles. Using a combination of petrographic microscopy, helium expansion pycnometry, water immersion porosimetry, mercury intrusion porosimetry, and (ultra-) small-angle X-ray scattering, the impact of sample size on the petrophysical properties of these samples was systematically investigated here. The results suggest that the sample size effect is influenced by both pore structure changes during crushing and sample size-dependent fluid-to-pore connectivity.

36 MATERIALS SCIENCE↗

An Overview of Manufacturing Controls for Production of High-Consequence, Single-Use Systems

Extended Testing (Crowder, et al. (2025) ) is a reliability demonstration technique that can be used to dramatically reduce sample size requirements. Manufacturing controls are needed to supplement extended testing by identifying production issues that a reduced sample sizes might overlook, especially built-in, or latent, manufacturing defects. This report focuses on some of the most commonly used, yet most impactful, manufacturing control tools that are used to limit production-related defects and efficiently screen any remaining defects at final inspection. These tools include statistical process control (SPC), acceptance sampling, environmental stress screening (HASS and ESS), and mistake proofing. The goal is to minimize the probability that built-in defects ever reach the customer. In terms of nuclear weapons (NW), the goal is to prevent defective units from ever entering the nation’s NW stockpile. Examples of each of the techniques are illustrated with case studies.

42 ENGINEERING↗

Impact on quality activities of measurement systems meeting an L:1 rule

This study considers the impact of a measurement system that meets an L:1 rule on various quality activities. These activities include inspection, acceptance sampling, and control charting. A measurement system that meets a 10:1 rule performs much better than one that meets a 4:1 rule. R code is provided so that the practitioner is able to evaluate these activities to his or her particular situation.

97 MATHEMATICS AND COMPUTING↗

Synthesis, Structural Characterization, and Growth Mechanism of Li 1+ x V 3 O 8 Submicron Fibers for Lithium-Ion Batteries

Here, we report on the synthesis of submicron Li 1+x V 3 O 8 fibers through a facile mixed ethanol/water solution-mediated solvothermal route in the absence of surfactants. All the raw materials used are commercially available, relatively inexpensive, and low-toxic, and these can be handled in an ambient atmosphere, rendering this synthetic route as reasonably facile and efficient. To ensure a desirable and acceptable sample crystallinity and purity, we introduced a postannealing treatment at 500°C. The monoclinic phase formation of the fiber sample was probed in detail using a series of X-ray diffraction, scanning electron microscopy, transmission electron microscopy, infrared spectroscopy, X-ray photoelectron spectroscopy, high resolution transmission electron microscopy, and selected area electron diffraction measurements. Both morphology and chemical composition could be carefully and systematically tuned in terms of generating a class of novel, pure, and well-defined motifs of Li 1+x V 3 O 8 . A plausible mechanism for the formation of submicron-diameter fibers has been discussed in addition to the expected phase transformation within our Li-V-O materials. Our comprehensive study should provide for needed fundamental insights into putting forth a viable synthesis strategy for the generation of well-defined morphological variants of layered oxide materials for battery applications.

25 ENERGY STORAGE↗

Completion of Level 2 Milestone – M2AT 19IN030401044, Complete construction of the gas and moisture supply systems and receive the custom-designed tube furnace from the vendor

The Advanced Gas Reactor (AGR) program has designed and is now constructing the Air/Moisture Ingress Experiment (AMIX) facility to test irradiated tristructural isotropic (TRISO) fuels under air or moisture-ingress accidents postulated for high-temperature gas-cooled reactors. AMIX will ultimately be installed in the Fuel Conditioning Facility at the Materials and Fuels Complex (MFC) at Idaho National Laboratory. AMIX consists of a gas supply (capable of supplying mixtures of air/helium and steam/helium), a tube furnace capable of accepting samples up to 6 cm in diameter and heating them to 1650°C, gamma detectors for measuring the release of condensable, gamma-emitting fission products, and cold traps with gamma detectors for measuring the release of fission gases. Data obtained from AMIX experiments will be used to qualify this new generation of TRISO fuels with the U.S. Nuclear Regulatory Commission, and inform models and simulations of TRISO fuel accident performance and source term.

42 ENGINEERING↗

Chemical Characterization Results for Tank 40 Sludge Batch 10 Waste Acceptance Product Specifications (WAPS) Sample

A 3-L sample (HTF-40-23-24) obtained from Tank 40 following transfer of Tank 51 to achieve the final Sludge Batch 10 processing composition was received by Savannah River National Laboratory (SRNL). SRNL was tasked with characterization of the sample in accordance with requirements for reporting the Waste Acceptance Product Specifications. A representative subsample, approximately 500 mL, was prepared by continuously agitating the 3-L sample via a mixing blade inserted into the bottle. This subsample was then used for the chemical and physical characterization reported here. This characterization includes the following: (1) Supernate and slurry density; (2) Weight percent solids; (3) Mercury Analysis (supernate and slurry); (4) Anions; (5) Total Organic/Inorganic Carbon; (6) Free Hydroxide; (7) Other Base; (8) Elementals; (9) Volatile Organic Analysis and Semi-volatile Organic Analysis; and (10) Fissile Radionuclides and Uranium Enrichment. The results of this physical and chemical characterization of the sample are documented in this report.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Accelerating multilevel Markov Chain Monte Carlo using machine learning models

Here, this work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to accelerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive the expression for cost reduction due to machine learning model to facilitate cost analysis of the hierarchical sampling algorithm. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.

97 MATHEMATICS AND COMPUTING↗

ISOLOK VALVE ACCEPTANCE TESTING FOR DWPF SME SAMPLING PROCESS

Evaluation of the Defense Waste Processing Facility (DWPF) Chemical Process Cell (CPC) cycle time identified several opportunities to improve the CPC processing time. Of the opportunities, a focus area related to optimizing the equipment and efficiency of the sample turnaround time for DWPF Analytical Laboratory was identified. The Mechanical Systems & Custom Equipment Development (MS&CED) Section of the Savannah River National Laboratory (SRNL) evaluated the possibility of using an Isolok{reg_sign} sampling valve as an alternative to the Hydragard{reg_sign} valve for taking process samples. Previous viability testing was conducted with favorable results using the Isolok sampler and reported in SRNL-STI-2010-00749 (1). This task has the potential to improve operability, reduce maintenance time and decrease CPC cycle time. This report summarizes the results from acceptance testing which was requested in Task Technical Request (TTR) HLW-DWPF-TTR-2010-0036 (2) and which was conducted as outlined in Task Technical and Quality Assurance Plan (TTQAP) SRNL-RP-2011-00145 (3). The Isolok to be tested is the same model which was tested, qualified, and installed in the Sludge Receipt Adjustment Tank (SRAT) sample system. RW-0333P QA requirements apply to this task. This task was to qualify the Isolok sampler for use in the DWPF Slurry Mix Evaporator (SME) sampling process. The Hydragard, which is the current baseline sampling method, was used for comparison to the Isolok sampling data. The Isolok sampler is an air powered grab sampler used to 'pull' a sample volume from a process line. The operation of the sampler is shown in Figure 1. The image on the left shows the Isolok's spool extended into the process line and the image on the right shows the sampler retracted and then dispensing the liquid into the sampling container. To determine tank homogeneity, a Coliwasa sampler was used to grab samples at a high and low location within the mixing tank. Data from the two locations were compared to determine if the contents of the tank were well mixed. The Coliwasa sampler is a tube with a stopper at the bottom and is designed to obtain grab samples from specific locations within the drum contents. A position paper (4) was issued to address the prototypic flow loop issues and simulant selections. A statistically designed plan (5) was issued to address the total number of samples each sampler needed to pull, to provide the random order in which samples were pulled and to group samples for elemental analysis. The TTR required that the Isolok sampler perform as well as the Hydragard sampler during these tests to ensure the acceptability of the Isolok sampler for use in the DWPF sampling cells. Procedure No.L9.4-5015 was used to document the sample parameters and process steps. Completed procedures are located in R&D Engineering job folder 23269.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Thermally stable and self-healable lignin-based polyester

The increased use of plastics and the associated environmental impact has catalyzed research on the development of bio-derived polymers. Bio-based polyesters have gained increased attention due to the abundance of their starting materials and ease of processing. Lignin is naturally occurring in biomass with rich carbon content, whose functionality and rigidity make it an ideal bio-derived candidate for bio-based polyesters. Herein, a lignin-based polyester with good thermal stability and self-repairability was synthesized from carboxylated lignin and epoxidized soybean oil. The synthesized lignin/epoxidized soybean oil (ESO) vitrimer was brittle such that its mechanical performance could not be recorded. However, when polyethylene glycol (PEG) was incorporated as a plasticizer, polymer samples exhibited acceptable ductility. From thermomechanical analysis of the synthesized polyesters, the plasticizer did not impair thermal stability of polymers, but greatly enhanced mechanical properties. Notably, all samples exhibited stability at high temperatures, and good glass transition temperatures (51.0 ± 0.9–78.0 ± 1.2 °C). The highest tensile strength (3.983 ± 0.1 MPa) and storage modulus (1463.67 ± 12.6 MPa) were recorded for the polyester containing 6 % w/w PEG. Moreover, the polymer samples exhibited self-healing capability at 180 °C. This work expands on valorization of lignin through the synthesis of bio-derived materials.

36 MATERIALS SCIENCE↗

Statistical Sampling Plan for AGR-5/6/7 Fuel Materials

Kernels, coated particles, and compacts will be manufactured to predefined specifications for irradiation in the AGR 5/6/7 experiments. Many tests will be performed for quality assurance and most of these tests correspond to criteria that have to be met with 95% confidence, based on random samples. This report describes the statistical acceptance testing methods and gives minimum sample sizes for kernels to achieve 95% confidence. Coated particles and compacts will be addressed in revisions to this report. The methods used for sample size determination are described in detail in INL/EXT 05 00349, Statistical Methods Handbook for Advanced Gas Reactor Fuel Materials (Einerson 2005). The statistical approach is to collect a representative sample, apply an acceptance test to the sample, and accept or reject the product based on this test for each criterion. The criteria or “product specifications” are contained in SPC-1352, “AGR 5/6/7 Fuel Specification,” Revision 1 and are duplicated in this plan.

Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients

This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-ρAMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the coarse basis used to define the new two-level method of our interest. We illustrate the performance of this adaptive two-level procedure with a large set of numerical experiments that demonstrate its efficiency over building the solvers from scratch.

97 MATHEMATICS AND COMPUTING↗

Glycolate Analysis in Tank 22: Developing and Testing Analytical Methods for the Savannah River Site Liquid Waste System

Researchers developed and tested a range of techniques to support a low mg/L Limit of Quantitation (LOQ) of glycolate in radioactive Tank 22 waste solution by Ion Chromatography (IC) and by proton NMR. For the IC method, Dionex OnGuard II cartridges were tested as a means of removing alkali earth and transition metals that can interfere during ion chromatography applications especially when analyzing for low-concentration, chelating analytes. Additionally, concentrations of nitrate in the raw Tank 22 sample (5,000 to 10,000 mg/L) were managed by using reasonable levels of sample dilution. The resulting IC performance quality was enhanced by improving the baseline, increasing sensitivity [Limit of Quantitation (LOQ) of 12 mg/L and Limit of Detection (LOD) of 4.0 mg/L], and resolving analytes into well-defined Gaussian peaks when using the Dionex OnGuard II H⁺ cartridges to remove matrix interferences. High concentrations of nitrate limited the performance of the IC method. To achieve an acceptable baseline, samples with high nitrate content require more dilution, resulting in higher detection limits. Tests on samples with higher concentrations of nitrate (Tank 30 and 32 supernate with approximately 150000 mg/L nitrate) suggested that IC detection limits for glycolate in these samples would be > 500 mg/L. Thus, an LOQ of 12 mg/L is not feasible by this IC method on evaporator feed samples. An alternative method of glycolate analysis, using proton nuclear magnetic resonance (H NMR), was developed by the research team. In initial tests, the H NMR technique provided reasonable quantitation of glycolate in Tank 22 conditions by direct observation of the liquid. The H NMR method may provide improved detection limits for solutions with higher nitrate concentrations. We recommend further development of this analysis for high nitrate LWS samples such as evaporator feed and evaporator drop tank content. A method for pretreatment of samples using crystalline silicotitanate (CST) was developed and tested. The objective of the pretreatment was to facilitate analysis of samples with higher levels of radioactivity. The pretreatment did not influence the glycolate concentration in solution, and the pretreatment is projected to reduce Cs 137 activity in a sample by a factor of 16,200. The double strike CST pretreatment was demonstrated and would allow milliliters of higher activity samples to be transferred from the Shielded Cells and handled in a containment unit for glycolate analysis. The various studies validated IC and H NMR methods for glycolate analysis, defined the range of applicability, and demonstrated key supporting analytical protocols. Based on the results, high quality glycolate analysis of Tank 22 is feasible down to approximately 12 mg/L, with the potential for broader applicability of the methods to other conditions in the Savannah River Site Liquid Waste System (LWS).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Recent Bremsstrahlung-based Assays of 210Pb in Lead and Comments on Current Availability of Low-Background Lead in North America

Abstract Low-background lead for radiation measurement shielding is often assayed for 210Pb to ensure acceptable backgrounds. Samples of lead assayed with a germanium spectrometer calibrated for bremsstrahlung-based assay of 210Pb provide a view into the 210Pb content of commercial lead in the U.S. (other than stockpiled Doe Run lead). Results suggest that the loss of lead smelting in the U.S. has eliminated the traditional supply of “low background” lead (~30 Bq·kg-1), and indicate current commercial supplies contain roughly an order of magnitude higher 210Pb levels.

Low background, gamma spectroscopy, lead, bremsstr↗

The effect of ultraviolet irradiation on the ultra-thin HfO{sub 2} based CO gas sensor

In this work, an effort has been made to fabricate ultrathin HfO{sub 2}/Al{sub 2}O{sub 3} sample by atomic layer deposition method for the fast detection of CO gas at room temperature. The effect of the operating temperature and the UV light on the gas sensing characteristics has been studied. We investigated the optimum operating temperature for the sample by sensing 25 ppm CO and CO{sub 2} gases from room temperature to 150 °C for 10 °C steps. The maximum response was obtained at 150 °C for both gases in the measurement temperature range. Also, the photoresponse measurements clearly show the effect of UV light on the sample. At room temperature, sensor showed superior response (14%) for 5 ppm CO gas. The response time of sensor is 6 s to 5 ppm CO gas concentration. The ultrathin HfO{sub 2} based sample shows acceptable gas sensitivity for 5 ppm CO gas at room temperature under UV light irradiation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗