bluuebunny/crossref_metadata_2025 huggingface dataset:
Categorical Data, Marginal Models for
Authors: Molenberghs Geert
Published: September 2014

We briefly review two building blocks (generalized linear models and linear mixed models) for models for repeated categorical data. Three families of models for repeated categorical data are introduced: marginal models, conditional models, and random‐effects models. A number of marginal models are presented for binary and for ordinal data in turn. Major differences between marginal models and conditional models (such as loglinear models) are discussed.
Folded Transformations
Authors: Hoaglin David C.
Published: September 2014

Introduced in John W. Tukey's book
Exploratory Data Analysis
,
folded transformation
refers to a transformation
T
of a proportion
u
for which
T
(1 −
u
) = −
T
(
u
). Examples include the folded fraction or plurality,
T
(
u
) = 2
u
− 1, and the folded logarithm or logit, logit(
u
) = log

e

(
u
) − log

e

(1 −
u
).
Functional Data Analysis ‐ Theory
Authors: Ramsay J. O.
Published: September 2014

When either data or the models for them involve functions, and when only weak assumptions about these functions such as smoothness are permitted, familiar statistical methods must be modified and new approaches developed in order to take advantage of this smoothness. The first part of the article considers some general issues such as characteristics of functional data, uses of derivatives in functional modelling, estimation of phase variation by the alignment or registration of curve features, the nature of error, and so forth. The second section describes functional versions of traditional methods such principal components analysis and linear modelling, and also mentions purely functional approaches that involve working with and estimating differential equations in the functional data analysis process.
Box‐Cox Transformations for Linear Models
Authors: Loh Wei‐Yin
Published: September 2014

The Box–Cox transformation is a potentially powerful technique for extending the applicability of the classical linear model. The procedure is described, and three examples are given to illustrate its power as well as its limitations. Philosophical issues regarding the interpretation of the results have led to some controversy and debate.
Monte Carlo Studies, Empirical Response Surfaces in
Authors: Power Simon
Published: September 2014

This article discusses the role of empirical response surfaces in succinctly summarizing the results of Monte Carlo studies and providing a simple means of predicting the outcome of Monte Carlo experiments that were not explicitly included in a particular study. It includes a simple illustrative example and provides a bridge to the literature.
Editing Statistical Data
Authors: Naus Joseph
Published: September 2014

There are several statistical and data‐processing techniques that exist in the literature to mnitor data and also to detect and correct errors in them. This area of Statistics has developed its own extensive terminology. In this entry, the terminology and the important techniques used in data editing and imputation are described.
Sequential Order Statistics
Authors: Cramer Erhard
Published: September 2014

Sequential order statistics have been introduced in order to model effects of component failures on the reliability ofk‐out‐of‐nsystems. Aside from this interpretation, they are related to several other models of ordered random variables such as Pfeifer's record values and generalized order statistics.
C
opula Process,
A
rchimedean
Authors: Malov S. V.
Published: September 2014

Archimedean copulas have a wide field of applications in probability theory and in mathematical statistics. The copula arose first in the work of Sklar [14]. It is the function which characterizes principal connection of components in a random vector independently of marginal distributions. Archimedean copula process was introduced as a generalization of the scheme of independent random variables. The most of interesting applications of this object was in the order statistics theory and in the extreme values theory. The extreme type theorems and some characterizations of classes of sequences via properties of order statistics and record values can be improved from the class of independent random variables to the class of Archimedean copula processes. In this way the proportional Archimedean copula process appeared as the generalization of the
F
α
‐scheme for independent random variables. Some representations of the Archimedean copula process via independent random variables will be also given.
Charlier (Series) Distributions, Discrete
Authors: Nadarajah Saraless , Kotz Samuel
Published: September 2014

The Charlier series distribution (both univariate and bivariate) and some its properties are discussed.
Elliptically Contoured Distributions
Authors: Fang Kai‐Tai
Published: September 2014

The elliptically contoured distribution (ECD for short) is a class of multivariate distributions that are considered as an extension of the multivariate normal distributions. In this entry, we introduce a historical perspective, basic properties, and subclasses of the ECD. The estimation of parameters of an ECD implies the study of elliptical matrix distributions. A brief review on elliptical matrix distributions is given. Some applications of ECD are discussed.
Kotz‐Type Distribution
Authors: Kotz Samuel , Nadarajah Saraless
Published: September 2014

The Kotz‐type distribution and some of its properties are discussed.
Pearson Type
VII
Distribution on the Unit Sphere
Authors: Nadarajah Saralees
Published: September 2014

A new distribution referred to as the Pearson type VII distribution is introduced and some of its properties discussed.
Discrete Multivariate Distributions
Authors: Balakrishnan N.
Published: September 2014

In this article, we present a concise review of developments on discrete multivariate distributions. We first present some basic definitions and notations. Then, we present several important discrete multivariate distributions and list their significant properties and characteristics.
Income Distribution Models
Authors: Dagum Camilo
Published: September 2014

Since Pareto specified his Type I model in 1895, scores of income distribution (ID) models have been proposed. Many of them follow Edgeworth's approach, starting with a probability function and a transformation of its random variable, to derive a positive asymmetric distribution as an ID model. Some of them are supported by a realistic scientific foundation, others are the outcome of a formal analogy, and the remainder are only ad hoc specifications. Almost all of these models are organized here in three generating systems, and their respective foundations are outlined. We introduce a set of seven basic properties to be fulfilled by a probability distribution for consideration as an ID model. Their main purpose is to guide researchers in the evaluation and choice of an appropriate and robust model to describe observed IDs in different epochs and countries in different states of socioeconomic development, and according to several socioeconomic attributes of the observed populations of economic units.
Stirling Family of Distributions
Authors: Sibuya Masaaki
Published: September 2014

A family of pmf's that have Stirling numbers as a factor, including record number distributions and classical occupancy distributions, is treated. An extended family and related distributions are mentioned.
Dependence, Tests for
Authors: Hollander Myles
Published: September 2014

This paper is designed to provide a sound introduction for a reasonably well informed reader who is, however, not a specialist in tests for dependence. The paper contains references to many tests but emphasizes the parametric test of independence based on Pearson's sample correlation coefficient*rand certain nonparametric tests based on ranks. The ranks tests are generally preferable to the test based onrin that they have wider applicability, are much less sensitive to outlying observations, are exact under mild assumptions that do not require an underlying bivariate normal* population, and have good efficiency (power) properties.
Gamma‐Minimax Inference
Authors: Ruggeri Fabrizio
Published: September 2014

Γ‐minimax theory deals with the problem of selecting decision rules under partial prior information on the distribution of the unknown parameter. The selected rule is the one minimizing the supremum of the payoff (Bayes and regret risk in a frequentist approach, and posterior expected loss and regret in a Bayesian one) over the priors in Γ.
Mean, Searls' Estimators of
Authors: Kotz Samuel , Nadarajah Saraless
Published: September 2014

Some extensions of Searls' estimator of population mean are discussed.
Counting Process: Basic
Authors: Keiding Neils
Published: September 2014

Since the pioneering work of O.O. Aalen (1975, 1978), the statistical theory of continuous‐time survival analysis and event history analysis has been based on the probabilistic theory of counting processes, martingales, and stochastic integrals. The important features are a full mathematical theory of censoring, the most important feature of these areas of applied statistics, and a master central limit theorem for martingales that allows a general asymptotic theory of many functionals used for parametric and nonparametric estimation and hypothesis testing. In this way, the tool of counting processes has provided a uniform background for what used to be scattered results.

While survival analysis is the basic example of these techniques, more detailed statistical models are also covered, including competing risk models and multistate processes including illness‐death models.
Step‐Stress Testing
Authors: Gouno Evans
Published: September 2014

Step‐stress accelerated life test have been studied at least since the 1950s. The strategy consists in testing items successively under different levels of stresses. The main advantage of this strategy is to overcome the issue of selecting the proper level of stress that generates enough failures to make inference in classical accelerated life test where the stress is constant. It reduces test time and the variability of the failure times. Various types of data are obtained from step‐stress tests. According the nature of the basic assumptions, different statistical techniques can be used. The following work gives an overview of various approaches to handle step‐stress accelerated life test data.
Hazard Change Point Estimation
Authors: Gürler Ülkü
Published: September 2014

In survival and reliability studies, hazard‐rate function plays an important role. Sudden changes in the hazard function may occur due to treatment effects or maintenance activities. A problem of statistical interest is the estimation of the times of the changes, as well as their sizes. In this note, we review the basic estimation methods for hazard change‐point models for complete data. Some related literature is also provided for estimation with incomplete data and hypothesis testing.
Principal Differential Analysis
Authors: Ramsay James O.
Published: September 2014

Differential equation systems are often a natural way of describing sets of variables changing over time or space. For example, in controlling industrial systems, engineers consider the time course of a set of inputs and outputs for a system such as a chemical reactor with a view to developing useful feedback processes. Principal differential analysis uses functional data to estimate a system of linear differential equations that fit the data. The estimate minimizes an integrated squared error criterion. The coefficient functions that define the linear differential equation are estimated by expansions in terms of basis functions such as Fourier series orB‐splines, and the estimates are calculated rapidly and without iteration.
Functional Networks
Authors: Castillo Enrique , Hadi Ali S.
Published: September 2014

Functional networks (FNs) are a general framework useful for solving a wide range of problems in various fields. In FNs, the network structure is not necessarily a black box; it is derived from the reality being modeled, that is, it is design‐driven. Unlike in neural networks (NNs), the neural functions in FNs are true multiargument, and different for all neurons. In FNs, neural functions are learned instead of weights as in NNs. In addition, neural functions can be forced to output the same values, thus leading to a system of functional equations that impose strong conditions on the neuron functions and allow simplification of the topology. FNs are illustrated by an example of application.
Antieigenvalues and Antieigenvectors
Authors: Khattree Ravindra
Published: September 2014

In this entry, the concepts of antieigenvalues and antieigenvectors are first introduced. Then, various statistical situations wherein these entities arise naturally are explained.
Correlation, Weighted
Authors: Shieh Grace S.
Published: September 2014

Testing the equality of two population correlation coefficients when the data are bivariate normal and Pearson correlation coefficients are used as estimates of the population parameters is a straightforward procedure covered in many introductory statistics courses. The coefficients are converted using Fisher's z‐transformation with standard errors (N‐3)‐1/2. The two transformed values are then compared using a standard normal procedure. When data are not bivariate normal, Spearman's correlation coefficient rho is often used as the index of correlation. Comparison of two Spearman rhos is not as well documented. Three approaches were investigated using Monte Carlo simulations. Treating the Spearman coefficients as though they were Pearson coefficients and using the standard Fisher's z‐transformation and subsequent comparison was more robust with respect to Type I error than either ignoring the nonnormality and computing Pearson coefficients or converting the Spearman coefficients to Pearson equivalents prior to transformation.
Fisher Information: Nonstandard Situations
Authors: Zheng Gang , Balakrishnan N.
Published: September 2014

Fisher's measure of information is a fundamental concept in statistical science. It plays an important role in statistical theory of inference. The definition and applications of Fisher information in standard inference based on random samples have been discussed extensively in the literature. The Fisher information in nonstandard situations involving ordered data has recently attracted considerable attention with discussions focusing on Fisher information in order statistics, percentiles, randomly censored data, concomitants, progressively censored data, and record values, with numerous applications including optimal linear estimates, characterizations, ranked set sampling, and genetic studies. Direct calculation of Fisher information in these nonstandard situations is tedious and computationally difficult. Main techniques to simplify the calculation are discussed here with many examples. Finally, some applications of Fisher information in ordered data are also highlighted.
Statistical Methods in Risk Management by Futures Clearinghouses
Authors: Shanker Latha
Published: September 2014

Futures clearinghouses guarantee the open futures positions of their clearing members. The risk that clearinghouses face as a consequence is managed by the following five tools‐margin requirements, daily settlement, capital requirements, daily price limits and position limits. Clearing members deposit margin with the clearinghouse to support their open futures positions. Under the system of daily settlement of profits and losses, the clearinghouse transfers funds from the margin accounts of clearing members who have incurred losses to the accounts of members who have incurred profits. The margin requirement is usually set to cover the loss expected in a normal trading day. Losses of clearing members in excess of their margin are supported by requiring each member to contribute to the capital requirements of the clearinghouse. The daily price limit specifies the daily trading range for the futures price. A properly chosen price limit can reduce the margin and capital requirement below the levels required in its absence. The position limit constrains the net speculative futures position of one individual to reduce the possibility of clearinghouse failure due to default by one speculator. The optimal values for the tools of risk management depend on the statistical distribution of futures price changes. Moreover, the tools have to be carefully chosen so as to protect the clearinghouse without driving traders away from the market. Evaluation of the different systems for setting the optimal values of these tools and their effects upon the volatility and trading activity in futures markets also depends on the application of statistical tests. This article therefore reviews the statistical methodology used by previous research on risk management by futures clearinghouses.
The Black–Scholes Formula and Its Applications in Finance
Authors: Kijima Masaaki , Muromachi Yukio
Published: September 2014

This chapter overviews a continuous‐time model for securities market and its applications in finance. Self‐financing and replicating portfolios play key roles for the pricing of derivative securities. The Black–Scholes model is explained in detail, and valuation of exotic options, interest‐rate derivatives, corporate bonds and real options is also discussed as applications of the Black–Scholes model.
Spearman Correlation Coefficients, Differences between
Authors: Myers Leann , Sirois Maria J.
Published: September 2014

Testing the equality of two population correlation coefficients when the data are bivariate normal and Pearson correlation coefficients are used as estimates of the population parameters is a straightforward procedure covered in many introductory statistics courses. The coefficients are converted using Fisher's
z
‐transformation with standard errors (
N
 − 3)
−1/2
. The two transformed values are then compared using a standard normal procedure. When data are not bivariate normal, Spearman's correlation coefficient rho is often used as the index of correlation. Comparison of two Spearman rhos is not as well documented. Three approaches were investigated using Monte Carlo simulations. Treating the Spearman coefficients as though they were Pearson coefficients and using the standard Fisher's
z
‐transformation and subsequent comparison was more robust with respect to Type I error than either ignoring the nonnormality and computing Pearson coefficients or converting the Spearman coefficients to Pearson equivalents prior to transformation.
Chernoff‐Savage Theorem
Authors: Sen Pranab K.
Published: September 2014

The Chernoff‐Savage Theorem, in the setting of two independent samples, exploits the basic asymptotic properties of the two sample (empirical) distributions in a novel approach to the study of asymptotic normality of a general class of two‐sample linear rank statistics. Prior to the evolution of weak convergence of probability measures and contiguity of probability measures, both taking place in the 1960’s, this Theorem provided a completely new avenue of research in asymptotics in rank tests in a far more general set‐up comprising general linear models, time‐series, and multivariate as well as sequential models
Coincidences and Patterns in Sequences
Authors: Dasgupta Anirban
Published: September 2014

This entry provides a contemporary exposition at a moderately quantitative level of the distribution theory associated with sequences and patterns in iid multinomial trials, the birthday problem, and the matching problem. The section on patterns includes the classic distribution theory for waiting time for runs and more general patterns, and their means and moments. It also includes the central limit theorem and a.s. properties of the longest run, and modern applications to DNA sequence alignment. The section on birthdays reviews the Poisson approximation in the classical birthday problem, with new bounds on the total variation distance. It also includes a number of variants of the classic birthday problem, including the case of unequal probabilities, similar triplets, and the Bayesian version with Dirichlet priors on birthday probabilities. A new problem called the strong birthday problem with application to criminology is introduced. The section on matching covers the Poisson asymptotics, errors of Poisson approximations, and some variants such as near matches. It also briefly reviews the recent extraordinary developments in the area of longest increasing subsequences in random permutations. The entry provides a large number of examples, many not well known, to help a reader have a feeling for these questions at an intuitive level
Crop Area Estimation, Landsat Data Analysis in
Authors: Day Charles , Hanuschak George
Published: September 2014

Since the early 1970s, the National Agricultural Statistics Service (NASS) has developed and applied statistical procedures that use Landsat satellite data to significantly improve the precision of estimates from ground‐gathered data from a stratified area frame sample. These procedures fall into two major categories:(1)Gaussian multivariate clustering and classification, and(2)direct expansion and regression estimation. This article describes these procedures in detail.
Forestry, Statistics and Biometry in
Authors: Gregoire Timothy , Lappi Juha
Published: September 2014

Statistical methods are used in surveys of forest resources, and in the development of predictive models of individual‐tree size and growth, as well as the growth and yield of aggregations of trees in forest stands. Statistically designed experiments are conducted in order to understand better the responses to(i)management interventions, such as fertilization, genetic improvement, site preparation, harvesting; and to(ii)natural events like insect infestations, ice storms, hurricanes, temperature change.
Income Inequality Measures
Authors: Dagum Camilo
Published: September 2014

This study purports to present, analyze, and evaluate the following:

The income inequality measures (IIMs) proposed since Pareto and Gini and to derive their corresponding utility and disutility functions from the specification of a fundamental equation of income. Furthermore, a dual relationship between utility and disutility functions and between IIMs and social welfare functions are established.

The decomposition approach of the generalized entropy measure (GEM) and the Gini ratio showing the extreme limitations of GEM to meaningful account for the contribution of the between‐group inequalities.

The directional distance ratio (DDR) between binary combinations of income distributions showing that it is a better alternative to the decomposition approach, and unlike the latter, DDR offers sound policy implications.

The distance function between income distributions.
Fair Value of Insurance Liabilities
Authors: Biffis Enrico , Millossovich Pietro
Published: September 2014

We outline the basic principles underlying accounting standards aimed at marking to market insurers' balance sheets. Some issues specific to insurance liabilities are examined.
Large Insurance Losses Distributions
Authors: Fasen Vicky , Klüppelberg Claudia
Published: September 2014

Large insurance losses happen infrequently, but they happen. In this paper we present the standard distribution models used in fire, wind–storm, or flood insurance. We also present the Cramér–Lundberg model for the total claim amount and some more recent extensions. The classical insurance risk measure is the ruin probability, and we give a full account of the ruin event in such models. Finally, we present some results for an integrated insurance risk model, where investment risk is also taken into account.
Multistate Models for Life Insurance Mathematics
Authors: Norberg Ragnar
Published: September 2014

The subject matter and methodology of modern life insurance mathematics are surveyed in the framework of a multistate model for life‐history analysis. Standard insurance products with payments depending only on life‐ history events are described and analyzed in the commonly used Markov chain model under the assumption of deterministic interest rates. The actuarial equivalence principle for determining premiums and reserves is motivated by risk diversification in large portfolios. Differential equations for reserves and other conditional expected values are obtained and proclaimed basic, constructive, and computational tools. The traditional method for managing nondiversifiable risk arising from changes in e.g., mortality rates and interest rates is outlined; premiums are calculated under prudent assumptions, and systematic surpluses thus created are repaid as bonus. An alternative way of managing nondiversifiable risk is to link the contractual payments to the development of mortality, interest, and possibly other demographic or economic indexes. Examples of so‐called index‐linked products are given, and premiums and reserves are determined by combined use of classical actuarial principles and principles of pricing and hedging from financial mathematics. Transfer of nondiversifiable risk to the financial markets through creation of tradeable insurance derivatives is outlined as an idea. The present article is a revised and shortened version of an entry in the Encyclopedia of Actuarial Science published by Wiley in 2004.
Optimal Risk‐Sharing and Deductibles in Insurance
Authors: Aase Knut K.
Published: September 2014

Risk sharing in insurance is analyzed, with a view toward explaining the prevalence of deductibles.

First we introduce, in a modern setting, the main concepts of the theory of risk sharing in a group of agents. We apply this theory to the risk‐sharing problem between an insurer and an insurance customer. We develop the concept further through simple examples, illustrating some of the subtle points of this theory.

To deduce deductibles endogenously, not explained in the neoclassical model, we separately introduce (a) the insurable asset as a decision variable, (b) administrative costs, and (c) moral hazard, and illustrate these with the help of examples.
Premium Calculation and Insurance Pricing
Authors: Laeven Roger J.A. , Goovaerts Marc J.
Published: September 2014

This survey of premium calculation and insurance pricing explains classical theories and their recent generalizations, summarizes main issues and results, and describes current developments in the area.
Ruin Probabilities: Computational Aspects
Authors: Lefèvre Claude
Published: September 2014

This paper is concerned with the numerical evaluation of the probability of ruin or nonruin in insurance mathematics. Our attention is primarily focused on the classical model in collective risk theory, named the compound Poisson model. We present a review of the different methods that are usually proposed to calculate or approximate the (non)ruin probabilities, over an infinite horizon and in finite time.
Ruin Theory
Authors: Lin X. Sheldon , Willmot Gordon E.
Published: September 2014

This article gives an overview of ruin theory. It briefly discusses the probability models for the surplus process of an insurance portfolio and the mathematical tools used for the investigation of these models. An extensive list of references is provided.
Stochastic Control for Insurance Companies
Authors: Schmidli Hanspeter
Published: September 2014

We consider some (simple) optimization problems in insurance. In particular, we want to minimize the ruin probability by dynamic decisions, maximize the value of future dividends, and keep the contribution rate and the size of a pension fund close to some predefined values. The method is stochastic control theory. We illustrate how a Hamilton–Jacobi–Bellman equation can be obtained. We also show how to solve the equation and how the optimal strategies can be obtained.
Estimation of Mortality Rates From Insurance Data
Authors: Melnick Edward L. , Tenenbein Aaron
Published: September 2014

The problem of using insurance intercompany data to determine mortality rates has had a long history of development. The development of these mortality rates involves two steps, namely, the estimation of the rates from the data and the interpolation and smoothing of these rates to conform to known trends in the mortality rates by age, and time since first insured. This paper will discuss the different methods used to determine these rates and discuss the advantages and disadvantages of each approach.
Behavioral Decision Studies
Authors: Brandstätter Eduard , Riedl René
Published: September 2014

Probability judgments are pivotal in guiding human decision making. The prevailing assumption in psychology is that human probability judgments are often biased. We challenge this view and present evidence of humans' remarkable capacities in judging probabilities. In particular, we discuss regression to the mean, probability judgments of conjunctive and disjunctive events, the consideration of base‐rate information, probability judgments based on small samples, judgments of personal risks, and external influences on probability judgments. We conclude that in real‐life contexts, in which the correct normative solutions are usually unknown, heuristics are useful tools for making fast and frugal judgments and decisions.
Decision Conferencing/Facilitated Workshops
Authors: Phillips Lawrence D.
Published: September 2014

Decision conferencing provides a structured group approach for assessing the risks associated with several options, with expert judgment providing some or all of the inputs and models based on decision theory used to combine the inputs into an overall assessment. A facilitated workshop brings together experts about a specific risk criterion, with an impartial facilitator taking the group through the process of discussing the meaning of each criterion, establishing measurement scales, and appraising options on the scales. At a subsequent decision conference attended by the key players, the facilitator guides participants through the process of making the final judgments about inputs and trade‐offs between criteria that allow the decision theory model to bring together all the inputs to provide an overall ordering of the options. This approach allows the collective experience of specialists and key players to be brought to bear on issues of risk assessment, and creates committed alignment backed by the authority of the entire group.
Expert Judgment
Authors: Hora Stephen C.
Published: September 2014

Experts are often used to provide uncertainty distributions in risk analyses. They play an important role when insufficient data exist for quantification, or when the available data or models are conflicting. Multiple steps are required in constructing a successful expert judgment process. These steps include selecting and framing the issues, identifying the experts, deciding upon an organization structure, and possibly combining the distributions from multiple experts.

Expert judgments are normally given as probabilities or probability distributions that express the uncertainty about future events or unmeasured quantities. The goodness of probabilistic judgments is measured through calibration and information, which, in turn, can be measured through a scoring rule.

Various behavioral and mathematical methods have been proposed for combining the judgments of experts. There is, however, no single method that has emerged as the best.
Interpretations of Probability
Authors: Lenk Peter
Published: September 2014

Probability plays a central role in quantifying risk and uncertainty. In contrast to the laws of probability, which are well established, there are several different interpretations of probability. This article traces the major positions of the frequency, subjective, and logical schools, and summarizes the implications of these approaches for risk professionals. The article concludes that despite profoundly different interpretations and consequences, current industry demands require professionals to be facile in using different approaches to probability.
Multiattribute Value Functions
Authors: Stewart Theodor J.
Published: September 2014

The multiattribute value function is a means of systematically analyzing preferences in the context of multiattribute or multicriteria decision making. We discuss in some detail the axiomatic foundations of the additive form of the multiattribute value function as an ordinal measure of preference, and the implications of these axioms for eliciting the parameters of the function. Extensions of the basic model to cardinal preference measures (generally implying nonadditive forms of the value function), and to application in mathematical programming problems (multiobjective optimization) are then discussed. We conclude with a brief discussion on the treatment of risk and of time values within the context of multiattribute value functions.
Subjective Expected Utility
Authors: Munier Bertrand R.
Published: September 2014

Origins of expected utility are sketched. Uncertainty is distinguished from simple risk. The axiomatic foundation of subjective expected utility is then developed. Two main currents of thought are presented and discussed.
Subjective Probabilities: Overview
Authors: Curley Shawn P.
Published: September 2014

The need for subjective probabilities arises from the variability that is pervasive in our world. A subjective probability is intended to meaningfully communicate the degree of uncertainty in the face of variability. Surrounding this common theme are several different approaches to defining and using subjective probabilities. The mathematical theory of probability is summarized as a basis for understanding these approaches. This article then describes the alternative perspectives on subjective probability relative to the mathematical theory: subjective probability as one of several interpretations for mathematical probability theory, as a behavioral assessment, as an inherent aspect of all uses of probability theory, and as an uncertainty measure that can be detached from the mathematical theory. The issue of assessing the quality of subjective probabilities is also discussed as it relates to these approaches.
Supra Decision Maker
Authors: Morton Alec
Published: September 2014

Decisions about the regulation of risks typically impact on a number of different sectors of society, and so have to take cognizance of the views of a variety of stakeholders. One way to conceptualize such decisions is to think of the regulatory or governmental decision maker as a “supra decision maker” (supra DM). The notion of a supra DM represents a distinctively decision‐theoretic take on the aggregation of individual preferences, whereby stakeholders' value functions are arguments in the supra DM's utility function. A normative theory of the supra DM exists, which provides conditions for an additive representation of the supra DM's value function, but this theory avoids key questions about securing honest statements of stakeholders' values, and about the comparability of these statements. Despite this drawback, the idea of a supra DM is a useful frame for thinking about, and for private analysis of, decisions that impact multiple stakeholders.
Utility Function
Authors: Sarin Rakesh K.
Published: September 2014

Expected utility is used as a criterion to rank order lotteries. Axioms for expected utility are given. Assessment and behavioral properties of utility functions are discussed. Allais paradox, which challenges expected utility, is illustrated.
Value Function
Authors: Sarin Rakesh K.
Published: September 2014

Value functions rank order a set of objects. A measurable value function orders the differences in strength of preference between pairs of objects.
Odds and Odds Ratio
Authors: Landau Sabine
Published: September 2014

This article introduces odds and motivates their use. It then proceeds to define the odds ratio.
Monte Carlo Methods
Authors: O'Neill Terence J. , Barry Simon C. , Puza Borek
Published: September 2014

Monte Carlo techniques are used in situations in which the analytic solution of the problem is either intractable or time consuming. Instead of calculating exact quantities, simulation is used to produce stochastic approximations to the solution.
Computer Security: A Historical Perspective
Authors: Schell Roger R. , Reed Edwards E.
Published: September 2014

The pervasive dependence on computers today gives us no choice but to use them in the face of professional attackers. That threat, for which software subversion is often the tool of choice, is serious and growing, so computers are increasingly a major source of risk. Responsible risk assessment and risk management requires that we not only create computers that are secure but also verify that we have succeeded. A productive history of more than 30 years of research and practical experience has produced a theory of computer security rich with solutions and tools. The greatest achievement is the demonstrated ability to build and operationally deploy truly bulletproof systems having verifiable protection. This remains the most powerful solution available for many of today's hard computer and network security problems.
Truncation
Authors: Rai Shesh N. , Sun Jianguo
Published: September 2014

In collection and analysis of real‐life data, we always encounter incomplete data. Censoring and truncation are types of incomplete data that arise owing to a type of sampling scheme. We describe the differences and similarities between censoring and truncation. We also describe types of truncation and the role of truncation in the analysis of real‐life data.
Imprecise Reliability
Authors: Coolen Frank P.A. , Utkin Lev V.
Published: September 2014

We present a concise overview of imprecise reliability, particularly focusing on reliability theory with uncertainty quantifiedvialower and upper probabilities. We discuss the main approaches and opportunities of the theory, include references to guide further study, and briefly discuss some research challenges.
Markov Modeling in Reliability
Authors: Trivedi Kishor S. , Selvamuthu Dharmaraja
Published: September 2014

We present an overview of evaluating the reliability of the complex systems with Markov modeling. In this article, the definition of reliability and the description of basic reliability models are given. Markov models are discussed in detail and illustrations are provided to explain the technique of Markov modeling.
Warranty Analysis
Authors: Murthy D.N. Prabhakar , Blischke Wallace R.
Published: September 2014

For products sold with warranty, an important element of risk for the manufacturer is the potential cost resulting from the servicing of failures occurring under warranty. These costs depend on several factors, the most important being the reliability of the product. For planning purposes, the manufacturer must estimate (a) the expected cost of warranty per unit sold and (b) the expected cost per unit time over the product life cycle. This must be done in the product development stage. This article deals with models that may be used to obtain these cost estimates for products sold with free‐replacement and pro rata warranties.
Ultrahigh Reliability
Authors: Resnick Marc L.
Published: September 2014

Ultrareliability is a system of systems approach to modeling and achieving reliability. It seeks to increase reliability metrics and mission success by an order of magnitude or more by going beyond traditional approaches to reliability. It involves a rigorous examination of the interacting relationships among system components, people, and the external context at all stages of the system life cycle from determining requirements to system disposal. Interactions are evaluated to quantify their effects on system reliability and mission success and to discover ways to mitigate sources of error and component failure. Interactions include communication, training, operating processes and procedures, and human factors. The external context includes customers, supply chains, and culture.

There are many benefits when organizations achieve ultrareliability in their systems. Maintenance costs can often be reduced significantly because breakdowns become rare. Systems fail rarely and last longer. There are also indirect benefits such as streamlined development, increased customer satisfaction, and a better understanding of how systems operate. For many organizations, even the process of attempting ultrareliability yields several of these benefits, increasingly so as the organization develops its ultrareliability capability.
Common Cause Failure Modeling
Authors: Vaurio Jussi K.
Published: September 2014

Modeling and quantification of simultaneous failures of multiple components due to common causes is a frequent and often crucial task in safety system reliability and risk assessments. Several models of common cause failures (CCF) are introduced. Their mutual relationships, limitations, and advantages, as well as sources of parametric values, are described. The models are presented in terms of basic multiple‐failure rates and probabilities that are independent of system testing schemes and intervals, and have direct connection to the basic event probabilities needed in system logic models.

The early CCF models such as the β factor, binomial failure rate, common load, and distributed failure probability models are all special cases of stochastic reliability analysis. Even if mathematically attractive, these models are inherently constrained by certain mutual couplings between the CCF rates or CCF probabilities.

More general α factor and multiple Greek letter models are based on the ratios of multiple‐failure rates or probabilities. In applications, both models need some additional failure rate from outside of the model to yield CCF rates and basic event probabilities.

Extensive national and international common cause failure data collection efforts are making it feasible to estimate plant‐specific multiple‐failure rates and probabilities by combining data from many similar systems with empirically oriented Bayesian methods without assuming common generic parametric values. This methodology is briefly described. It takes into account both statistical and assessment uncertainties due to limited observations, interpretations, and documentation of CCF events.
Probabilistic Design
Authors: Gelder Petrus H.A.J.M. , Vrijling Johannes K.
Published: September 2014

In this article, the probabilistic approach to design and risk analysis in civil engineering is outlined. The application of probabilistic design methods offers the designer a way to unify the design of engineering structures, processes, and management systems. For this reason, there is a growing interest in the use of these methods. This article begins with an introduction to probabilistic analysis, a discussion on uncertainties, and a reflection on the deterministic approach versus the probabilistic approach. The article then addresses the tools, design, and calculation methods for a probabilistic systems analysis. Failure probability calculation for an element is reviewed and the article concludes with a description of the evaluation methods of a calculated risk level.
Condition Monitoring
Authors: Banjevic Dragan , Jardine Andrew K.S.
Published: September 2014

Condition monitoring (CM) is a set of various techniques and procedures used in industry to measure the “parameters” of the state/health of equipment, or to observe conditions under which the equipment is operating. People apply CM for early detection of signs of malfunctioning and faults, and then for fault diagnosis and timely corrective or predictive maintenance. The whole combination of CM data acquisition, processing, interpretation, fault detection, and maintenance strategy is called the
CM system
/
program
(alternatively, condition‐based maintenance (CBM)). The most common CM techniques are vibration analysis, tribology (oil/debris analysis), visual inspections, current monitoring, conductivity testing, performance (process parameters) monitoring, thermal monitoring, corrosion monitoring, and acoustic (sound/noise) monitoring. The three major steps in a CM system are data acquisition, data processing, and data assessment for decisions (maintenance decision making and fault diagnostics and prediction). This article describes the key points of all three major steps, including CBM; gives a short history of CM; discusses the implementation, advantages and disadvantages of CM; comments on the future development of CM; and recommends further reading. An example of CM implementation is also included.
Maintenance Modeling and Management
Authors: Scarf Philip A.
Published: September 2014

The specification of a maintenance design is at the heart of maintenance modeling and management. This design is essentially a structured description of the system of interest in terms of its parts (components, sockets, and their interrelationships), and prescribed maintenance rules for the components in the system. The maintenance rules are determined by the following: the risk that component failure poses to system performance, the economic priorities of the system owner and the maintainer, the availability of data relating to components, and the interrelationships beteen components within the system. This article describes how one might determine a structured description of a system of interest, how maintenance actions for the resultant components might be chosen, and then how these maintenance actions may be optimized using maintenance models to provide the system owner with a set of efficient and effective maintenance rules for the system.
Reliability Optimization (Multistate and Multiobjective)
Authors: Coit David W.
Published: September 2014

Reliability optimization involves the simultaneous evaluation and selection of components and a system‐level design configuration that collectively meets all design constraints, and at the same time, optimizes some objective function, often system reliability or availability. Often these problems are very constrained because of physical or budgetary limitations. There are several variations of reliability optimization and there have been many attempts to determine optimal design configurations for different problem formulations. Applicable optimization methods include dynamic programming, integer programming, mixed integer and nonlinear programming, and metaheuristics, e.g., genetic algorithms (GA). Notable extensions to this problem include multistate reliability optimization and multiple‐objective system reliability optimization.
Quantitative Reliability Assessment of Electricity Supply
Authors: Billinton Roy
Published: September 2014

This paper illustrates the hierarchical relationship of the basic functional zones of generation, transmission, and distribution in an electric power system. The techniques used to quantitatively assess the reliability of the overall system and the hierarchical levels are briefly discussed. The importance in reliability assessment of consistent and comprehensive data on relevant equipment, load characteristics, and system constraints is illustrated.
NoFaultFound
Authors: Jones Jeffrey A.
Published: September 2014

This article describes the No Fault Found (NFF) phenomenon that occurs when a system is tested after a failure is reported but no failure is found during the test. This basic phenomenon is known by a large number of terms, which are often abbreviated to three letter acronyms, and are described in this article. The level of occurrence of such false positive faults in various technical fields is described and a number of possible reasons for the incidence are discussed. Finally a discussion of the management of such faults within the context of quantitative risk assessment is included.