Quality quandaries: A gentle introduction to Bayesian statistics

We provide a gentle introduction to this powerful analysis method that can handle complex data and modeling situations.     

Quality quandaries: Uses of simulation

Key Point

This article provides a number of examples that show how useful simulation is in addressing many problems encountered in applied statistics.     

Quality quandaries: Predicting a population of curves

A random effects spline regression model based on splines provides an integrated approach for analyzing functional data, i.e., curves, when the shape of the curves is not parametrically specified. An analysis using this model is presented that makes inferences about a population of curves as well as features of the curves.     

Quality quandaries: Impact of only below limit of detection data

Treating below limit of detection data as left-censored data rather than as passes can lead to large reductions in the number of tests needed to demonstrate a design requirement.     

Quality quandaries: Understanding aspects influencing different types of multiple response optimization

Optimizing with several responses can benefit from an objective approach of eliminating non-contenders, understanding trade-offs between competing responses, and then identifying a final choice that matches optimization priorities. To offer insights that can help guide thoughtful decisions, we explore and summarize different patterns of solution sets and their trade-offs for different types of optimization with responses that are to be maximized and/or to achieve a target.     

Quality quandaries: Statistical detective work to understand the isotopic ratios in Drum 68660 and the radioactive release at WIPP

An incident at the Department of Energy's Waste Isolation Pilot Plant (WIPP) in 2014 resulted in the release of radioactive material into the environment. Initially, it was known that at least one drum in WIPP, identified as drum 68660, was involved. However, questions remained. Could the air-monitor isotopic ratios measured in WIPP at the time of the release be explained by materials in drum 68660 or were other drums involved? Could internal conditions in drum 68660 have caused the breach? What were the implications for 68660's sister drum? These questions needed to be answered as quickly as possible. This analysis, which was completed in three weeks, combined combinatorics and uncertainty analysis to provide scientists with the timely evidence they needed to either answer these important questions or to design experiments to answer them.     

Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics

The authors generalise the concept of the geometric phase in stochastic kinetics to a non-cyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the non-periodic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. The authors apply these ideas to a model of chemical reactions in a bacterial culture of a growing size, where the geometric correction qualitatively changes the outcome of the reaction kinetics.     

A method to assess the effects of engineering change propagation

This paper presents a modelling method that seeks to support the prediction and management of undesired engineering change (EC) propagation during the design and development of complex products. The method builds on the house of quality and the change prediction method to model the effects of potential change propagation brought about by different change options. The objective is to better reflect how well each change option can address the product requirements. The method was applied to the design of a jet engine fan during a case study with an aerospace company. The findings suggest that this modelling approach is suitable for assessing the effects of potential EC propagation and can support companies in effective exploration of the design space.     

The use of probability in engineering design—an historical survey

The development of the use of probabilistic and statistical concepts in engineering design is traced from nineteenth-century beginnings through the period in the 1950s and 1960s when reliability engineering became established as an important component of engineering practice and onward to the present day when safety as well as reliability goals can form part of the design specification.     

Nonlinear estimators of probability of an event in a bernoulli scheme accounting for prior information

A general approach to estimation of probability of an event in a Bernoulli scheme is proposed. It is shown that the available estimators are particular cases of those obtained using this more general estimation approach. Basic expressions for the general estimators obtained by means of the maximum likelihood method and the minimum S-criterion are derived. Translated from Izmeritel'naya Tekhnika, No. 7, pp. 13–14, July, 1995.     

Comparison of probability density functions for analyzing irradiance statistics due to atmospheric turbulence

A large number of model probability density functions (PDFs) are used to analyze atmospheric scintillation statistics. We have analyzed scintillation data from two different experimental setups covering a range of scintillation strengths to determine which candidate model PDFs best describe the experimental data. The PDFs were fitted to the experimental data using the method of least squares. The root-mean-squared fitting error was used to monitor the goodness of fit. The results of the fitting were found to depend strongly on the scintillation strength. We find that the log normally modulated Rician and the log normal PDFs are the best fit to the experimental data over the range of scintillation strengths encountered.     

Mass imagineering: Combining human imagination and automated engineering from early education to digital afterlife

Imagineering is a portmanteau combining the words imagination and engineering. The term, imagineering, was coined during the early 1940s. Since the new Millennium, imagineering has grown to the scale of a mass paradigm, because of the increasing scope and availability of automated engineering. Automated engineering is enabled by sophisticated software and artificial intelligence (AI) across the virtual-social-physical convergence (VSP) of consumer devices, desktop machines, and Web platforms. The combining of human imagination with automated engineering is enabling millions of vloggers, self-publishers and makers to imagineer at high speed and low cost. This mass imagineering can range from early education to digital afterlife. It involves makerspaces, fab labs, hackerspaces, as well as use of disparate devices, machines, and platforms “in the wild”. In this paper, three principal contributions to the literature are provided. First, mass imagineering is described from early education to digital afterlife. Second, analysis of structure and agency in mass imagineering is provided. This reveals that individual agency varies in different settings for mass imagineering, but is always more than in mass production and mass customization settings. Third, division of labour analysis of mass imagineering is provided. This reveals that mass imagineering extends labour outside of paid employment, such as in the home, towards greater self-expression and increased entrepreneurship. This is possible because of increasing automated engineering across VSP enabled by devices, machines, and platforms.     

Representing imprecision in engineering design: Comparing fuzzy and probability calculus

A technique to perform design calculations on imprecise representations of parameters using the calculus of fuzzy sets has been previously developed [25]. An analogous approach to representing and manipulatinguncertainty in choosing among alternatives (design imprecision) using probability calculus is presented and compared with the fuzzy calculus technique. Examples using both approaches are presented, where the examples represent a progression from simple operations to more complex design equations. Results of the fuzzy sets and probability methods for the examples are shown graphically. We find that the fuzzy calculus is well suited to representing and manipulating the imprecision aspect of uncertainty in design, and that probability is best used to represent stochastic uncertainty.     

Adaptive directional stratification for controlled estimation of the probability of a rare event

Within the structural reliability context, the aim of this paper is to present a new accelerated Monte-Carlo simulation method, named ADS, Adaptive Directional Stratification, and designed to overcome the following industrial constraints: robustness of the estimation of a low structural failure probability (less than 10⁻³), limited computational resources and complex (albeit often monotonic) physical model. This new stochastic technique is an original variant of adaptive accelerated simulation method, combining stratified sampling and directional simulation and including two steps in the adaptation stage (ADS-2). First, we theoretically study the properties of two possible failure probability estimators and get the asymptotic and non-asymptotic expressions of their variances. Then, we propose some improvements for our new method. To begin with, we focus on the root-finding algorithm required for the directional approach: we present a stop criterion for the dichotomic method and a strategy to reduce the required number of calls to the costly physical model under monotonic hypothesis. Lastly, to overcome the limit involved by the increase of the input dimension, we introduce the ADS-2⁺ method which has the same ground as the ADS-2 method, but additionally uses a statistical test to detect the most significant inputs and carries out the stratification only along them. To conclude, we test the ADS-2 and ADS-2⁺ methods on academic examples in order to compare them with the classical structural reliability methods and to make a numerical sensitivity analysis over some parameters. We also apply the methods to a flood model and a nuclear reactor pressurized vessel model, to practically demonstrate their interest on real industrial examples.     

危岩破坏激振信号概率统计特征研究

具有复杂成生关系的危岩块聚集体是孕发大型及特大型崩塌灾害的基本条件,聚集体内任何一个危岩块的突发性破坏均会释放能量,并向周围传播,产生激振效应,可用激振加速度表征危岩破坏激振信号。针对坠落式危岩,通过室内模型试验,分析了实验条件下危岩破坏激振信号的概率统计特征。分析结果表明,危岩破坏所释放的能量具有点荷载特征,激振信号具有一定的自相关性;激振信号的概率密度呈现单峰型近似正态分布,概率密度水平方向的峰值强度大于竖直方向的峰值强度;危岩破坏瞬间,距离激振源越近,激振信号的均值、有效值和标准差数值越大,且竖直方向的量值大于水平方向的量值;危岩块之间界面的完整性影响着激振信号的传递效果,完整性越好,激振信号的统计特征值及概率密度峰值越大,激振信号衰减用时越长。研究成果对于实施考虑相似条件下危岩破坏激振效应实验研究有积极意义。     

Evaluation of an electronic nose to assess fruit ripeness

The main goal of our study was to see whether an artificial olfactory system can be used as a nondestructive instrument to measure fruit maturity. In order to make an objective comparison, samples measured with our electronic nose prototype were later characterized using fruit quality techniques. The cultivars chosen for the study were peaches, nectarines, apples, and pears. With peaches and nectarines, a PCA analysis on the electronic nose measurements helped to guess optimal harvest dates that were in good agreement with the ones obtained with fruit quality techniques. A good correlation between sensor signals and some fruit quality indicators was also found. With pears, the study addressed the possibility of classifying samples regarding their ripeness state after different cold storage and shelf-life periods. A PCA analysis showed good separation between samples measured after a shelf-life period of seven days and samples with four or less days. Finally, the electronic nose monitored the shelf-life ripening of apples. A good correlation between electronic nose signals and firmness, starch index, and acidity parameters was found. These results prove that electronic noses have the potential of becoming a reliable instrument to assess fruit ripeness.