Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.
Accuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements are to their true value, while precision is how close the measurements are to each other.
Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science.
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.
There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. "Calibration" can mean
Prognostics is an engineering discipline focused on predicting the time at which a system or a component will no longer perform its intended function. This lack of performance is most often a failure beyond which the system can no longer be used to meet desired performance. The predicted time then becomes the remaining useful life (RUL), which is an important concept in decision making for contingency mitigation. Prognostics predicts the future performance of a component by assessing the extent of deviation or degradation of a system from its expected normal operating conditions. The science of prognostics is based on the analysis of failure modes, detection of early signs of wear and aging, and fault conditions. An effective prognostics solution is implemented when there is sound knowledge of the failure mechanisms that are likely to cause the degradations leading to eventual failures in the system. It is therefore necessary to have initial information on the possible failures in a product. Such knowledge is important to identify the system parameters that are to be monitored. Potential uses for prognostics is in condition-based maintenance. The discipline that links studies of failure mechanisms to system lifecycle management is often referred to as prognostics and health management (PHM), sometimes also system health management (SHM) or—in transportation applications—vehicle health management (VHM) or engine health management (EHM). Technical approaches to building models in prognostics can be categorized broadly into data-driven approaches, model-based approaches, and hybrid approaches.
Ensemble forecasting is a method used in or within numerical weather prediction. Instead of making a single forecast of the most likely weather, a set of forecasts is produced. This set of forecasts aims to give an indication of the range of possible future states of the atmosphere. Ensemble forecasting is a form of Monte Carlo analysis. The multiple simulations are conducted to account for the two usual sources of uncertainty in forecast models: (1) the errors introduced by the use of imperfect initial conditions, amplified by the chaotic nature of the evolution equations of the atmosphere, which is often referred to as sensitive dependence on initial conditions; and (2) errors introduced because of imperfections in the model formulation, such as the approximate mathematical methods to solve the equations. Ideally, the verified future atmospheric state should fall within the predicted ensemble spread, and the amount of spread should be related to the uncertainty (error) of the forecast. In general, this approach can be used to make probabilistic forecasts of any dynamical system, and not just for weather prediction.
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation. By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value. It is a non-negative parameter.
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject.
A measurement systems analysis (MSA) is a thorough assessment of a measurement process, and typically includes a specially designed experiment that seeks to identify the components of variation in that measurement process. Just as processes that produce a product may vary, the process of obtaining measurements and data may also have variation and produce incorrect results. A measurement systems analysis evaluates the test method, measuring instruments, and the entire process of obtaining measurements to ensure the integrity of data used for analysis and to understand the implications of measurement error for decisions made about a product or process. Proper measurement system analysis is critical for producing a consistent product in manufacturing and when left uncontrolled can result in a drift of key parameters and unusable final products. MSA is also an important element of Six Sigma methodology and of other quality management systems. MSA analyzes the collection of equipment, operations, procedures, software and personnel that affects the assignment of a number to a measurement characteristic.
Uncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example would be to predict the acceleration of a human body in a head-on crash with another car: even if the speed was exactly known, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc., will lead to different results that can only be predicted in a statistical sense.
A wind power forecast corresponds to an estimate of the expected production of one or more wind turbines in the near future, up to a year. Forecast are usually expressed in terms of the available power of the wind farm, occasionally in units of energy, indicating the power production potential over a time interval.
Quantification of Margins and Uncertainty (QMU) is a decision support methodology for complex technical decisions. QMU focuses on the identification, characterization, and analysis of performance thresholds and their associated margins for engineering systems that are evaluated under conditions of uncertainty, particularly when portions of those results are generated using computational modeling and simulation. QMU has traditionally been applied to complex systems where comprehensive experimental test data is not readily available and cannot be easily generated for either end-to-end system execution or for specific subsystems of interest. Examples of systems where QMU has been applied include nuclear weapons performance, qualification, and stockpile assessment. QMU focuses on characterizing in detail the various sources of uncertainty that exist in a model, thus allowing the uncertainty in the system response output variables to be well quantified. These sources are frequently described in terms of probability distributions to account for the stochastic nature of complex engineering systems. The characterization of uncertainty supports comparisons of design margins for key system performance metrics to the uncertainty associated with their calculation by the model. QMU supports risk-informed decision-making processes where computational simulation results provide one of several inputs to the decision-making authority. There is currently no standardized methodology across the simulation community for conducting QMU; the term is applied to a variety of different modeling and simulation techniques that focus on rigorously quantifying model uncertainty in order to support comparison to design margins.
Human Cognitive Reliability Correlation (HCR) is a technique used in the field of Human reliability Assessment (HRA), for the purposes of evaluating the probability of a human error occurring throughout the completion of a specific task. From such analyses measures can then be taken to reduce the likelihood of errors occurring within a system and therefore lead to an improvement in the overall levels of safety. There exist three primary reasons for conducting an HRA; error identification, error quantification and error reduction. As there exist a number of techniques used for such purposes, they can be split into one of two classifications; first generation techniques and second generation techniques. First generation techniques work on the basis of the simple dichotomy of ‘fits/doesn’t fit’ in the matching of the error situation in context with related error identification and quantification and second generation techniques are more theory based in their assessment and quantification of errors. HRA techniques have been utilised in a range of industries including healthcare, engineering, nuclear, transportation and business sector; each technique has varying uses within different disciplines.
The technique for human error-rate prediction (THERP) is a technique used in the field of human reliability assessment (HRA), for the purposes of evaluating the probability of a human error occurring throughout the completion of a specific task. From such analyses measures can then be taken to reduce the likelihood of errors occurring within a system and therefore lead to an improvement in the overall levels of safety. There exist three primary reasons for conducting an HRA: error identification, error quantification and error reduction. As there exist a number of techniques used for such purposes, they can be split into one of two classifications: first-generation techniques and second-generation techniques. First-generation techniques work on the basis of the simple dichotomy of ‘fits/doesn’t fit’ in matching an error situation in context with related error identification and quantification. Second generation techniques are more theory-based in their assessment and quantification of errors. ‘HRA techniques have been utilised for various applications in a range of disciplines and industries including healthcare, engineering, nuclear, transportation and business.
Causal inference is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed. The science of why things occur is called etiology. Causal inference is said to provide the evidence of causality theorized by causal reasoning.
Willem Egbert (Wim) Saris is a Dutch sociologist and Emeritus Professor of Statistics and Methodology, especially known for his work on "Causal modelling in non-experimental research" and measurement errors.
optiSLang is a software platform for CAE-based sensitivity analysis, multi-disciplinary optimization (MDO) and robustness evaluation. It is developed by Dynardo GmbH and provides a framework for numerical Robust Design Optimization (RDO) and stochastic analysis by identifying variables which contribute most to a predefined optimization goal. This includes also the evaluation of robustness, i.e. the sensitivity towards scatter of design variables or random fluctuations of parameters. In 2019, Dynardo GmbH was acquired by Ansys.
