Incorporating Component and System Test Data into the Same Assessment: A Bayesian Approach

This focus issue of Physiological Measurement follows the 38th Annual International Computing in Cardiology (CinC) Conference, hosted in Hangzhou, China in September 2011 by Zhejiang University. Each year, the NIH-sponsored PhysioNet resource (http://physionet.org/) runs an open competition lasting several months, aimed at encouraging the development of solutions to an unsolved or poorly solved problem in biomedicine, in most cases making use of relevant clinical and experimental data provided freely by PhysioNet. Participants in these annual challenges discuss their diverse approaches to the Challenge problems during dedicated scientific sessions at CinC. The topics of these PhysioNet/CinC Challenges range from physiologic signal processing and analysis to forecasting and modelling clinically important events and processes.

On the meaning of probability and frequency

A crucial decision in designing a spatial sample for soil survey is the number of sampling locations required to answer, with sufficient accuracy and precision, the questions posed by decision makers at different levels of geographic aggregation. In the Indian Soil Health Card (SHC) scheme, many thousands of locations are sampled per district. In this paper the SHC data are used to estimate the mean of a soil property within a defined study area, e.g., a district, or the areal fraction of the study area where some condition is satisfied, e.g., exceedence of a critical level. The central question is whether this large sample size is needed for this aim. The sample size required for a given maximum length of a confidence interval can be computed with formulas from classical sampling theory, using a prior estimate of the variance of the property of interest within the study area. Similarly, for the areal fraction a prior estimate of this fraction is required. In practice we are uncertain about these prior estimates, and our uncertainty is not accounted for in classical sample size determination (SSD). This deficiency can be overcome with a Bayesian approach, in which the prior estimate of the variance or areal fraction is replaced by a prior distribution. Once new data from the sample are available, this prior distribution is updated to a posterior distribution using Bayes’ rule. The apparent problem with a Bayesian approach prior to a sampling campaign is that the data are not yet available. This dilemma can be solved by computing, for a given sample size, the predictive distribution of the data, given a prior distribution on the population and design parameter. Thus we do not have a single vector with data values, but a finite or infinite set of possible data vectors. As a consequence, we have as many posterior distribution functions as we have data vectors. This leads to a probability distribution of lengths or coverages of Bayesian credible intervals, from which various criteria for SSD can be derived. Besides the fully Bayesian approach, a mixed Bayesian-likelihood approach for SSD is available. This is of interest when, after the data have been collected, we prefer to estimate the mean from these data only, using the frequentist approach, ignoring the prior distribution. The fully Bayesian and mixed Bayesian-likelihood approach are illustrated for estimating the mean of log-transformed Zn and the areal fraction with Zn-deficiency, defined as Zn concentration <0.9 mg kg −1, in the thirteen districts of Andhra Pradesh state. The SHC data from 2015–2017 are used to derive prior distributions. For all districts the Bayesian and mixed Bayesian-likelihood sample sizes are much smaller than the current sample sizes. The hyperparameters of the prior distributions have a strong effect on the sample sizes. We discuss methods to deal with this. Even at the mandal (sub-district) level the sample size can almost always be reduced substantially. Clearly SHC over-sampled, and here we show how to reduce the effort while still providing information required for decision-making. R scripts for SSD are provided as supplementary material.

We conduct an exploratory data analysis of a specific system test data set that includes concomitant variables measuring aspects of test effort as well as the failure count and time variables considered in standard software reliability analyses. We consider a family of Poisson process models for which failure rates may depend on time as well as on the test effort variables. We analyze failure rates computed from this test data using least squares parameter estimation and model selection via the predicted residual sum of squares (PRESS). >

This paper deals with the problem of determining statistical tolerance limits for the time-to-failure of a k -out-of-n :F system from component life data. The lifetimes of the components are assumed to be s -independently and identically distributed exponential variates. On the basis of a random sample of components, exact β-content, and β-expectation s-tolerance limits for the system lifetime are provided, which are valid even when certain percentages of the smallest, and the largest component failure times are missing. The proportion of conforming systems in a large batch is assessed by constructing an appropriate s-tolerance limit. The results presented are extended to several distributions, including the Weibull case with an unknown scale parameter. An example concerning a system of water pumps for cooling a reactor is used for illustration. The proposed method of obtaining s -tolerance limits can be readily applied, and requires only minimal computational effort. Our perspective is particularly attractive when system test data are not available, or are very scarce. In many circumstances, component testing is also advantageous in terms of time and cost savings.

Missile rocket-engine noise- and vibration-measurement system components are subjected to severe environments which may introduce spurious signals in the data. Thus, all components and systems must be subjected to environmental tests prior to their use to assure good data quality. Such a program is described in this paper. Several types of commercial microphones. accelerometers, preamplifiers, and cables were subjected to environmental tests, and their outputs analyzed to determine effect upon data. In addition, an entire data-acquisition system (to recorder input), including mounting brackets, was subjected to vibration tests. The results are discussed in the following manner: (a) Test data are graphically presented. (b) Test results are analyzed to predict their effect on the data. (c) The results of the prediction are compared to measured missile data. (d) Individual components and system test data are compared to show differences in results. Both good and poor data taken from missile firings are also presented to show environmental effects.

At the start of new operation, a production process is commonly unstable. Then, a process condition is into being stable gradually over time. For the purpose of shifting to mass production, the stability in a process should be evaluated. This paper proposes a method of evaluating the process stability based on Bayesian statistics and information theory. In Bayesian statistics, the knowledge for a process is renewed by deriving posterior distribution based on current prior distribution and observations. Here, equivalency between prior and posterior distributions could be considered to be a criterion for the stability in a process. It is needed to define difference between prior and posterior distributions in order to evaluate the equivalency between prior and posterior distributions. We first formulate the relation between the prior distribution and the posterior distribution for process mean using Bayesian statistics. Secondly, we evaluate the difference between the both distributions based on Kullback‐Leibler (K‐L) divergence in information theory. Finally, some numerical examples in the method of evaluating the stability in process mean are illustrated. Also, we discuss about a decision rule for the stability in process mean through the numerical investigation.

SummaryAccurate prediction of the solubility of chemical substances in solvents remains a challenge. The sparsity of high-quality solubility data is recognized as the biggest hurdle in the development of robust data-driven methods for practical use. Nonetheless, the effects of the quality and quantity of data on aqueous solubility predictions have not yet been scrutinized. In this study, the roles of the size and the quality of data sets on the performances of the solubility prediction models are unraveled, and the concepts of actual and observed performances are introduced. In an effort to curtail the gap between actual and observed performances, a quality-oriented data selection method, which evaluates the quality of data and extracts the most accurate part of it through statistical validation, is designed. Applying this method on the largest publicly available solubility database and using a consensus machine learning approach, a top-performing solubility prediction model is achieved.

The traditional method for gaining knowledge on the state of a motor is to take test data in time increments and plot the progression of the machine parameters, looking for trending data. This leads to a reactive reliability mode, where one performs maintenance or takes corrective action once data have been collected that indicates cause for concern. Standard test methods are generally employed and over time one may become a knowledgeable expert on the condition of the motor and when to repair it prior to failure.Emulation and Uncertainty Quantification (UQ) can be used as a machine learning powered approach to improve upon traditional predictive maintenance practices, allowing for corrective action to be taken prior to the real-time data itself indicating concern. Machine Learning strategies also take the potentially unreliable human guess work out of the intuition-based approach to predicting failure based on prior experience and knowledge.Emulators (aka predictive models) are statistical models trained using advanced analytics and machine learning algorithms to learn the input-output relationships of an underlying data set, often called the training data. Once trained, the key strength of the emulator is the ability to rapidly make predictions of the output of a system for input combinations not contained in the training data, eliminating the need for further direct data collection to perform any desired analyses.Data collected from a motor can be used to train an emulator capable of predicting the future performance of that motor. If these predictions indicate a need for corrective action, the predictive speed of the emulator can be used to check the outcomes of different "what-if" scenarios to determine the best course of action. UQ tools can be used along with the statistical prediction process to place error bounds on the various outcomes.This paper will present the above concepts in more detail. This will include the steps of emulator training, beginning with a design of experiments to select appropriate training data to be collected from the motor, validation of the emulator’s predictive accuracy, and its use for predictive maintenance and UQ, including sensitivity analyses of inputs on the output(s) of interest, uncertainty propagation, and optimization.

Model occurrence and model selection in panel data sets

We investigated the propagation of population pharmacokinetic information across clinical studies by applying Bayesian techniques. The aim was to summarize the population pharmacokinetic estimates of a study in appropriate statistical distributions in order to use them as Bayesian priors in consequent population pharmacokinetic analyses. Various data sets of simulated and real clinical data were fitted with WinBUGS, with and without informative priors. The posterior estimates of fittings with non-informative priors were used to build parametric informative priors and the whole procedure was carried on in a consecutive manner. The posterior distributions of the fittings with informative priors where compared to those of the meta-analysis fittings of the respective combinations of data sets. Good agreement was found, for the simulated and experimental datasets when the populations were exchangeable, with the posterior distribution from the fittings with the prior to be nearly identical to the ones estimated with meta-analysis. However, when populations were not exchangeble an alternative parametric form for the prior, the natural conjugate prior, had to be used in order to have consistent results. In conclusion, the results of a population pharmacokinetic analysis may be summarized in Bayesian prior distributions that can be used consecutively with other analyses. The procedure is an alternative to meta-analysis and gives comparable results. It has the advantage that it is faster than the meta-analysis, due to the large datasets used with the latter and can be performed when the data included in the prior are not actually available.

Characterizing the low cycle fatigue (LCF) properties of each alloy used in a gas turbine is expensive and time consuming. As such, each material is typically characterized over only the necessary cyclic range to insure safe, reliable component design. If it is desired to understand properties outside of that range, the accepted procedure is to acquire additional LCF test data. The objective of this project is to test the validity of several extrapolation methods versus acquiring additional test data for a particular alloy. Several models are developed by the following techniques: a monotonic test data anchor point, a strain-compatibility derived anchor point, and temperature independence of the Coffin-Manson relation. Predictions are made using a base data set of Ni-base superalloy IN738 LC at several test temperatures. High stress amplitude data points are acquired, and incorporated into the base data set to form an augmented data set. The extrapolation methods are compared to the results from the augmented data set to test validity. The results show that the strain compatibility anchor point model has marginal improvement over extrapolation using the base data set, and the other two models had reduced accuracy relative to extrapolation using the base data set. Anomalies were found in the base test data set due to serrated yielding and oxidation. Two models offer improved fit to test data when used with data sets that contain anomalies. If this is a general trend, it offers potential that the models could be used to indicate anomalous behavior. It is not known whether the results of this study can be applied to other materials.

A typical end-release safety belt buckle has been analyzed to determine its failure modes. These failure modes were evaluated based on crash test, sled test and component test data. A verification of the hypothesized failure modes was found in the patent literature. The component tests that were conducted confirmed the hypothetical failure modes and verified that the failures could and would occur in real world collisions as well as testing.

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;There is a demonstrated need for effective design verification testing to support certification strategies for nascent electric motors and electric propulsion systems. Design efforts pursue efficiency pushing electrified propulsion rotors to be lighter and incorporate greater power density; however, there is no clear path established for supporting structural integrity and durability test requirements as required by global certification agencies.&lt;/div&gt;&lt;div class="htmlview paragraph"&gt;Application of new materials, unique rotor design characteristics, and modified certification requirements drive unusual requirements for rotor modeling substantiated by component test data that addresses complex stress distribution characteristics.&lt;/div&gt;&lt;div class="htmlview paragraph"&gt;Our paper addresses testing electrified propulsion rotors using spin test protocols adapted to support integrity and durability test goals. We further incorporate key concerns for planning and executing component spin tests of rotating structures necessary to support global engine certification efforts. Results from component tests are effective for mitigating risks associated with the preservation of certification test schedules and potential end product safety issues.&lt;/div&gt;&lt;div class="htmlview paragraph"&gt;This paper presents data measurement techniques that are incorporated with specific spin tests to enhance the value of acquired data. Adapted test protocols include Overspeed and Low cycle fatigue (LCF) tests, which are more relevant types of spin tests for certification purposes.&lt;/div&gt;&lt;div class="htmlview paragraph"&gt;Innovative measurement techniques for capturing the rotor growth behavior for both mappings the speed-dependent growth trends and the circumferential profile of deforming rotor under centrifugal load generate useful data to evaluate materials and structural behavior affecting performance up to failure.&lt;/div&gt;&lt;/div&gt;

This work presents a survey of five theories to assess the uncertainty of projectile impact induced damage on multi-layered carbon-epoxy composite plates. Because the types of uncertainty dealt with in this application are multiple (variability, ambiguity, and conflict) and because the data sets collected are sparse, characterizing the amount of delamination damage with probability theory alone is possible but incomplete. This motivates the exploration of methods contained within a broad Generalized Information Theory (GIT) that rely on less restrictive assumptions than probability theory. Probability, fuzzy sets, possibility, and imprecise probability (probability boxes (p-boxes) and Dempster-Shafer) are used to assess the uncertainty in composite plate damage. Furthermore, this work highlights the usefulness of each theory. The purpose of the study is not to compare directly the different GIT methods but to show that they can be deployed on a practical application and to compare the assumptions upon which these theories are based. The data sets consist of experimental measurements and finite element predictions of the amount of delamination and fiber splitting damage as multilayered composite plates are impacted by a projectile at various velocities. The physical experiments consist of using a gas gun to impact suspended plates with a projectile accelerated to prescribed velocities, then, taking ultrasound images of the resulting delamination. The nonlinear, multiple length-scale numerical simulations couple local crack propagation implemented through cohesive zone modeling to global stress-displacement finite element analysis. The assessment of damage uncertainty is performed in three steps by, first, considering the test data only; then, considering the simulation data only; finally, performing an assessment of total uncertainty where test and simulation data sets are combined. This study leads to practical recommendations for reducing the uncertainty and improving the prediction accuracy of the damage modeling and finite element simulation.