Adam L. Pintar

Bayesian Estimation of Reliability for Batches of High Reliability Single-Use Parts

ABSTRACT When batches of critical, very high-reliability single-use parts are being produced, rigorous testing is often required to qualify the parts and allow them to be used by the customer. Frequentist and Bayesian approaches are described for predicting the reliability of the remaining subset of the batch, conditional on all of the other tested parts working correctly. Answers from different methods are compared, their strengths and weaknesses are considered, and their robustness to initial assumptions are examined. Some related questions are explored to consider the impact on reliability from different choices of the relative number of the tested and sale units, and the condition for passing the batch from both the manufacturers and customers’ points of view. We describe the approach in the context of automotive air bag inflation devices on most vehicles, but the approach is relevant to batches of single-use parts that have a very high requirement for reliability and must be destructively tested.

Experimental and statistical methods to evaluate antibacterial activity of a quaternary pyridinium salt on planktonic, biofilm-forming, and biofilm states

Abstract Robust evaluation and comparison of antimicrobial technologies are critical to improving biofilm prevention and treatment. Herein, a multi-pronged experimental framework and statistical models were applied to determine the effects of quaternary pyridinium salt, 4-acetyl-1-hexadecylpyridin-1-ium iodide (QPS-1), on Streptococcus mutans in the planktonic, biofilm-forming and biofilm cell states. Minimum inhibitory and bactericidal concentrations (MIC and MBC, respectively) were determined via common methods with novel application of statistical approaches combining random effects models and interval censored data to estimate uncertainties. The MICs and MBCs for planktonic and biofilm-forming states ranged from 3.12 to 12.5 μg ml−1, with biofilm values only ≈ 8 times higher. Potent anti-biofilm activity and reactive structural features make QPS-1 a promising antibacterial additive for dental and potentially other biomedical devices. Together, the experimental framework and statistical models provide estimates and uncertainties for effective antimicrobial concentrations in multiple cell states, enabling statistical comparisons and improved characterization of antibacterial agents.

Mapping Return Values of Extreme Wind Speeds

Structures subjected to wind loads must be designed to perform adequately from the points of view of stress and serviceability. Wind loading specified for design is based in part on the wind speeds affecting the site of interest. A particular quantity of interest in design is the N-year extreme wind speed, regardless of its direction, at a location of interest, defined by its longitude and latitude. Wind maps consisting of isotachs for N-year extreme wind speeds defined in building codes and standards are therefore required for structural design purposes. Alternatively, numerical versions of maps can be developed wherein automatic interpolations are performed that yield the N-year speeds at points defined by longitude and latitude. The raw data to be analyzed to develop the map are irregular time series of wind speeds above a specified threshold at multiple wind reporting stations. This work presents a two-stage approach to creating the map. The first stage involves the estimation of the parameters of an extreme value distribution at each station. In the second stage an interpolant based on the estimated parameters is created so that the N-year extreme wind speeds may be estimated at the geographical coordinates of interest. Standard errors and confidence bounds for the estimates are calculated using a non-parametric bootstrap algorithm. Results are presented for a region within Kansas, and those results are compared to the ASCE 7-10 Standard over the same region.

A Bayesian Approach to the Analysis of Split-Plot Combined and Product Arrays and Optimization in Robust Parameter Design

Many robust parameter design (RPD) studies involve a split-plot randomization structure and it is essential to account for the induced correlation structure to obtain valid inferences in the analysis. Bayesian methods are appealing for these studies because they naturally accommodate a general class of models, can account for parameter uncertainty in process optimization, and offer the necessary flexibility when one is interested in nonstandard performance criteria, e.g., the probability that a new response exceeds some threshold value. In this paper, we present a Bayesian approach to process optimization for a general class of RPD models, including both normal and non-normal responses, in the split-plot context using an empirical approximation of the posterior distribution for an objective function of interest. Two examples from the literature, one involving a crossed array and the other a combined array, are used for illustration.

Algorithm for rapid determination of optical scattering parameters

Preliminary experiments at the NIST Spectral Tri-function Automated Reference Reflectometer (STARR) facility have been conducted with the goal of providing the diffuse optical properties of a solid reference standard with optical properties similar to human skin. Here, we describe an algorithm for determining the best-fit parameters and the statistical uncertainty associated with the measurement. The objective function is determined from the profile log likelihood, including both experimental and Monte Carlo uncertainties. Initially, the log likelihood is determined over a large parameter search box using a relatively small number of Monte Carlo samples such as 2·104. The search area is iteratively reduced to include the 99.9999% confidence region, while doubling the number of samples at each iteration until the experimental uncertainty dominates over the Monte Carlo uncertainty. Typically this occurs by 1.28·106 samples. The log likelihood is then fit to determine a 95% confidence ellipse. The inverse problem requires the values of the log likelihood on many points. Our implementation uses importance sampling to calculate these points on a grid in an efficient manner. Ultimately, the time-to-solution is approximately six times the cost of a Monte Carlo simulation of the radiation transport problem for a single set of parameters with the largest number of photons required. The results are found to be 64 times faster than our implementation of Particle Swarm Optimization.

Wind Load Factors for Use in the Wind Tunnel Procedure

AbstractPublished standards may be incomplete because they provide no guidance on wind load factors appropriate for use with the wind tunnel procedure. The purpose of this paper is to contribute to...

Monitoring Process Variability for Stationary Process Data

Processes that arise naturally, for example, from manufacturing or the environment, often exhibit complicated autocorrelation structures. When monitoring such a process for changes in variance, accounting for that structure is critical. While charts for monitoring the variance of processes of independent observations and some specific autocorrelated processes have been proposed in the past, the chart presented in this article can handle a general stationary process. The performance of the proposed chart was examined through simulations for the first-order autoregressive and first-order autoregressive-moving average processes and demonstrated with examples. Copyright

Standard Reference Materials for Medical CT

NIST Standard Reference Materials 2087 and 2088 for medical computed tomography (CT) have become available. The materials allow CT reconstructions to be tied to the International System of Units in length, density, and mass attenuation coefficient.

Model Selection for Good Estimation and Prediction over a User-Specified Covariate Distribution for Linear Models under the Frequentist Paradigm

Model selection is an important part of estimation and prediction for linear models with multiple explanatory variables (covariates). A variety of approaches exist that focus on the estimation of model parameters or the fit of the model where data have been observed. This article proposes an alternative strategy that selects models based on the mean squared error of the estimated expected response for a user-specified distribution of interest on the covariate space. We discuss numerical and graphical tools for detailed comparisons among different models. These tools help select a best model based on its ability to estimate the mean response over covariate locations likely to arise from a distribution of interest and can be combined with cost for deciding whether to include specific covariates. The proposed method is illustrated with three examples. We also present simulation results demonstrating situations where the proposed method shows improvement over some standard alternatives. Copyright

Uncertainties in RECIST as a measure of volume for lung nodules and liver tumors.

PURPOSE The authors wish to determine the extent to which the Response Evaluation Criteria in Solid Tumors (RECIST) and the criteria of the World Health Organization (WHO) can predict tumor volumes and changes in volume using clinical data. METHODS The data presented are a reanalysis of data acquired in other studies, including the public database from the Lung Image Database Consortium (LIDC) and from a study of liver tumors. RESULTS The principal result is that a given RECIST diameter predicts volume to a factor of 16 or 10 for the two data sets, respectively, by examining 95% prediction bounds and that changes in volume are predicted only little better: to within a factor of 7 for the liver data. The WHO criteria reduce the prediction bounds by a factor of 1.3 in all cases. Also, the RECIST threshold of 10 mm to measure a nodule corresponds to a transition zone width of a factor of more than 2 in volume for the nodules in the LIDC database. CONCLUSIONS While the RECIST diameter is certainly correlated with the volume, and similarly for changes in these quantities, the use of the diameter introduces additional variation assuming volume is the quantity of interest. Exactly how much this reduces the statistical power of clinical drug trials is a key open question for future research.