bluuebunny/crossref_metadata_2025 huggingface dataset:
Mixture Experiments
Authors: Piepel Greg F.
Published: September 2014

Amixture experimentinvolves combining two or more components in various proportions or amounts and then measuring one or more responses for the resulting end products. Other factors that affect the response(s), such as process variables and/or the total amount of the mixture, may also be studied in the experiment. Amixture experiment designspecifies the combinations of mixture components and other experimental factors (if any) to be studied and the response variable(s) to be measured.Mixture experiment data analysesare then used to achieve the desired goals, which may include (a) understanding the effects of components and other factors on the response(s), (b) identifying components and other factors with significant and nonsignificant effects on the response(s), (c) developing models for predicting the response(s) as functions of the mixture components and any other factors, and (d) developing end products with desired values and uncertainties of the response(s).

Given a mixture experiment problem, a practitioner must consider the possible approaches for designing the experiment and analyzing the data, and then select the approach best suited to the problem. Eight possible approaches are (a) component proportions, (b) mathematically independent variables, (c) slack variable, (d) mixture amount, (e) component amounts, (f) mixture‐process variable, (g) mixture of mixtures, and (h) multifactor mixture. The article provides an overview of the mixture experiment designs, models, and data analyses for these approaches.
Dispersion Effects
Authors: Tort‐Martorell Xavier , Marco Lluis
Published: September 2014

Reduction of variation is a crucial ingredient for quality and productivity improvement. An economical and effective approach is to conduct statistically designed experiments, not only to identify controllable factors that affect the mean level (location) of the response, but also to identify and learn about the ones that affect the dispersion. This article explains how control factors can affect the response variability, how they can be identified and estimated, and gives two well‐documented examples that show how this knowledge can be used to improve products and processes.
Product Array Designs
Authors: Zhu Yu
Published: September 2014

This article is a review of product arrays proposed by Taguchi for robust design experiments. The motivation and advantage of using product arrays in robust design are discussed. Furthermore, alternative modeling approaches such as the location‐dispersion modeling approach and the response modeling approach are introduced. As an extension of product arrays, compound orthogonal arrays are defined. This article also discusses the optimal selection of product arrays.
Signal‐Response Systems
Authors: Miller Arden
Published: September 2014

The defining characteristic of a signal–response system is that the function of the system requires a response variable to take different values when the value of a signal factor changes. The performance of the system depends on the relationship between the signal and the response. Improving signal–response systems using designed experiments is usually approached as a special case of parameter design. This article describes several types of signal–response systems, discusses how their performance depends on the signal–response relationship and presents methodology for analyzing experiments aimed at improving their performance.
Tolerance Design
Authors: Joseph V. Roshan
Published: September 2014

The output variations can be reduced by tightening the tolerances of the input parameters, thus improving the quality. However, a product with a tighter tolerance is more difficult to manufacture and thus it increases the manufacturing cost. Therefore the tolerances should be decided carefully by balancing cost with quality. This chapter explains how to do this.
Box‐Meyer Method for Dispersion Effects
Authors: Meyer R. Daniel
Published: September 2014

One aspect of product quality is variability in finished product. Taguchi showed the world that variability is a consequence of product design and not just manufacturing performance. He also showed us that variability can be studied in engineering optimization experiments. Product variables that affect variability are said to have dispersion effects (
see
Dispersion Effects
). Using the Box‐Meyer method, dispersion effects can be estimated simply from the same unreplicated two‐level designs used to study effects on the mean performance.
Harvey's Method for Dispersion Effects
Authors: Brenneman William A.
Published: September 2014

There has been considerable interest in the use of unreplicated designed experiments to identify both location and dispersion effects. This article takes a look at the two‐step approach which incorporates a noniterative identification step followed by an iterative final estimation step. This two‐step approach eliminates some of the bias present in the noniterative methods.
Process Yield
Authors: Lin Pi‐Chuan , Pearn Wen Lea
Published: September 2014

Process capability indices (PCIs), establishing the relationship between the actual process performance and the manufacturing specifications, have been the focus of recent research in quality assurance and capability analysis. In this article, PCIs dedicated to the measurement of the yield of normally distributed processes with two‐sided specification limits and one‐sided specification limit are discussed. The yield measure formulas based on
C

pk

,
C

pm

,
C

pmk

,
S

pk

,
C

PU

, and
C

PL

are all displayed. The corresponding upper bounds of nonconforming parts per million (NCPPM) for various values of
C

pk

,
C

pm

, and
C

pmk

and the corresponding NCPPM for various
S

pk

values are tabulated.
Gauge Repeatability and Reproducibility (
R
&
R
) Studies, Misclassification Rates
Authors: Burdick Richard K.
Published: September 2014

To properly monitor and improve a manufacturing process, it is necessary to measure attributes of the process output. Measurements of these attributes are taken by a gauge that has associated measurement variability. Gauge R&R studies are used to determine if the measurement system variability is harmfully large. The approach for evaluating the goodness of the measurement system based on a gauge R&R study is to determine the probability that a part is misclassified. The better a measurement system, the less likely it is to classify a “good” part as “bad”, and a “bad” part as “good”. References are provided for computing bounds on the probabilities of these misclassifications.
Gauge Repeatability and Reproducibility (
R
&
R
) Studies, Confidence Intervals for
Authors: Leong Chiang Andy Kok
Published: September 2014

Gauge repeatability and reproducibility (R&R) studies are often conducted to determine the capability of a gauge for monitoring a manufacturing process. In this paper, we discuss common measures of gauge capability as well as established confidence intervals for them, based on the modified large sample and generalized confidence interval methods.
Warranty Claims and Costs: Statistical Analysis of
Authors: Robinson Jeffrey A.
Published: September 2014

This article summarizes approaches to the modeling and analysis of warranty data with an emphasis on the special characteristics of the data that distinguish it from reliability data in general. The special characteristics include the existence of costs and data limitations caused by warranty coverage limits. Practical considerations are emphasized as opposed to theory.
Nonparametric Methods for Analysis of Repair Data
Authors: Hollander Myles , Samaniego Francisco J. , Sethuraman Jayaram
Published: September 2014

Repair models specify the joint distribution of the failure times of a system subject to repair. Prominent models include the minimal repair model, the Brown–Proschan model, the Block–Borges–Savits model, the Kijima models, and the general Dorado–Hollander–Sethuraman model. For such models, failure‐time data and data on the types of repairs performed allow inference for the distribution
F
of the time to first failure of the system and other features of the system that can be defined in terms of
F
. This article surveys some nonparametric inference procedures for repair data, including frequentist and Bayesian estimation of
F
, simultaneous confidence bands for
F
, two‐sample tests, tests of the minimal repair assumption, and goodness‐of‐fit tests.
Analysis of Recurrent Events from Repairable Systems
Authors: N. Agustin Ma. Zenia , Agustin Marcus A. , Peña Edsel A.
Published: September 2014

This article provides a review of recently developed dynamic stochastic models for recurrent events, in particular, recurrent events arising from monitoring of repairable systems. Inference methods such as the estimation of model parameters and goodness‐of‐fit testing are also discussed. The procedures described are demonstrated using a reliability data from load–haul–dump machines.
Reliability Growth Modeling
Authors: Sen Ananda
Published: September 2014

At the initial developmental phase of any production involving complex systems, a test‐analyze‐and‐fix (TAAF) process is often undertaken to promote the detection of system faults and incorporate appropriate redesigns or other corrective actions, and the modified system is retested. As this test–redesign–retest sequence contributes to an improvement in the system performance, failure data become increasingly sparse at the later stages of testing, making it more difficult to assess the current reliability. A reliability growth model provides a structure through which failure data from the current as well as previous stages of testing could be analyzed in an integrated way in order to make efficient inference on reliability, and other process parameters. Reliability growth models have been applied extensively in analyzing failure data arising from hardware as well as a piece of software. Further, for systems with single‐shot missions that undergo a developmental program, reliability growth models arise quite naturally while studying the effectiveness of design fixes. In this article, we describe some popular reliability growth models that have been developed in the context of observing either time to failure or sequence of polytomous outcomes.
Warranty Cost Prediction Based on Warranty Data
Authors: Karim M. Rezaul , Suzuki Kazuyuki
Published: September 2014

This article discusses methods for predicting warranty cost to the manufacturer during a given future value(s) of the variable(s) defining the warranty terms. It models the predicted cost as a function of the lifetime distribution of the product and the average cost per claim based on observed costs of previous claims or costs from previous model years.
Warranty Servicing
Authors: Murthy D.N. Prabhakar , Nat Jack
Published: September 2014

Warranty costs are the additional expenses that a manufacturer incurs to service all the claims made by customers. These costs can be reduced by performing effective waranty servicing. In this article, a framework is given to link all the issues involved in warranty servicing and models that a manufacturer can use to make optimal servicing decisions are received.
Accelerated Life Tests: Classical Methods for Design and Analysis
Authors: Giorgio Massimiliano
Published: September 2014

Accelerated life tests are used to quickly obtain information about the failure time distribution of very reliable technological products. Tests are conducted in conditions more severe than the normal operating ones to accelerate the mechanism of failure and compress the life of components and materials of interest.

An estimate of the lifetime distribution at normal use conditions is extrapolated from data, obtained at higher stresses, through the use of appropriate statistical models that incorporate a special relationship accounting for the effect of stress conditions on specific lifetime characteristics of the products under study.

After a brief introduction that describes motivations and objectives of accelerated testing, the following topics are addressed:

methods for accelerating reliability tests;

models for classical accelerated tests;

procedures for point estimation, interval estimation, and checking model assumptions; and

basic criteria for planning accelerated life tests.

In this article only the classical approach to design and analysis of accelerated constant‐stress tests will be discussed. Moreover only fully parametric acceleration models are considered.
Masked Failure Data
Authors: Yashchin Emmanuel
Published: September 2014

We discuss life‐testing situations in which some of the failures are not identified as being due to a single cause, but are rather explained by one of the causes in a group. Failures of this type are called
masked
. Within this framework, we discuss the problems of modeling, estimation, and diagnostics. Such problems involve, for example, identification of survival curves for individual causes, or estimation of parameters related to conditions under which masking occurs. Another class of problems is related to the impact of masking on root‐cause analysis of individual failures. We also discuss the impact of masking on quality and reliability management issues.
Accelerated Life Tests:Bayesian Models
Authors: Soyer Refik , Erkanli Alaattin , Merrick Jason R.
Published: September 2014

In this article we consider accelerated life test models where the effect of accelerated environments on failure behavior is described by time transformation functions. We present extensions of basic models by introducing hierarchical and dynamic strategies to allow for changes in the time transformation function with the accelerated environment. We develop Markov chain Monte Carlo methods to make Bayesian inferences from these models where no analytical forms are available for the posterior and predictive distributions of interest. We illustrate our approach with two examples and discuss what type of insights can be obtained from Bayesian analysis.
Single Sampling by Attributes and by Variables
Authors: von Collani Elart , Göb Rainer , Suresh Kodakanallur Krishnaswamy
Published: September 2014

Single sampling plans excel among statistical product inspection procedures. They are simple in structure, intuitive, and easy for implementation. The study of single sampling plans is illustrative for the understanding of acceptance sampling since single sampling plans exemplify all basic features of acceptance sampling in a particularly simple and transparent instance. Single sampling plans are sometimes theoretically inferior to more refined sampling algorithms like double, multiple, and sequential sampling plans. However, simplicity and ease in implementation have made single sampling the most widely used statistical product inspection procedure.
Variables Sampling Schemes in International Standards
Authors: Balamurali Saminathan , Göb Rainer , Jun Chi‐Hyuck
Published: September 2014

Variables sampling schemes are based on the specification range quality model: a specification range
R
is prescribed for a continuous measurement characteristic like weight, length, volume, and an item is considered as conforming, if the associated measurement
X
is in
R
. Issued in 1957, MIL‐STD‐414 was the first industrial standard on variables sampling. On the international level, the International Standards Organization (ISO) introduced in 1989, the first variables sampling standard ISO 3951, compatible with the attributes sampling standard ISO 2859, which is a civilian counterpart of MIL‐STD‐105E. ISO 3951 has been adopted as a national standard in many countries. The article analyzes the purpose, structure, and operation of the latest version of ISO 3951 which was issued in three parts in 2005 and 2006.
Continuous Sampling
Authors: Suresh Kodakanallur Krishnaswamy , von Collani Elart
Published: September 2014

This article considers the control of item‐by‐item production in contrast to the control of lot‐by‐lot production. The methods covered are the continuous sampling plan, CSP‐1, some of its extensions and the corresponding MIL‐STD‐1253C, each of them referring to attribute sampling. The situation, in which these methods can be applied, are for example conveyor and moving assembly lines. The mode of operation and the statistical and operational properties of continuous sampling plans are stated.
Economic Sampling Schemes
Authors: von Collani Elart
Published: September 2014

The process of globalization has resulted in a situation where an increasing number of companies operate production locations all over the world and especially in the so‐called low‐cost countries. This trend has significantly increased the importance of outgoing and incoming quality inspection, normally by sampling inspection, because in many cases the inspection costs represent a considerable part of the total costs. Despite this situation, there is almost no research done on the application of economic sampling plans. The aim of this chapter is to give a short introduction into the state of the art with respect to economic sampling schemes to initiate further research in this important area of statistical quality control.
Sampling Inspection of Products and Statistical Process Control
Authors: Hryniewicz Olgierd
Published: September 2014

Acceptance control charts, originally proposed by Freund, are the tools of statistical process control (SPC) that combine features of classical control charts and sampling plans used in acceptance sampling of products and services. In contrast with classical Shewhart control charts, their design is based on the requirements typical for acceptance sampling plans by variables. In the article, we present the design principles of the acceptance control charts. The similarity between acceptance control charts and acceptance sampling systems shows that the latter might be used for the purpose of SPC.
Sampling in Software Development
Authors: Runeson Per
Published: September 2014

In software development, sampling inspection is applied during the development process, as the production process for software is trivial. Insoftware inspection, which is a manual scrutiny of software code or specifications, sampling is applied to estimate the number of remaining faults and to guide which parts of the artifact to inspect. Capture–recapture techniques are used in the fault content estimation. Insoftware testing, which is the dynamic execution of code, sampling is implicitly or explicitly applied to select test cases. Since the number of states is extremely high in software products, a complete coverage of all cases is practically impossible. In addition to scoping the tests to a reasonable magnitude of size, sampling is used to estimate the number of remaining faults and to predict the operational failure behavior of the software, e.g. through software reliability growth models. The theory is quite well established in the field, while the industrial practice is underdeveloped.
Sampling in Data Mining
Authors: Weiß Christian H.
Published: September 2014

After a brief review of basic terms and concepts of knowledge discovery in databases (KDD) and data mining, this article investigates aspects of sampling in data mining. A general scheme of sampling, and particular techniques used in data mining are discussed. The main objective of this article is to provide an overview on areas of KDD and data mining, where sampling approaches are applied.
Sampling in Implementation of Statistical Process Control
Authors: Nishina Ken
Published: September 2014

In this article, we explain how to obtain data by sampling and implement statistical process control (SPC) over its life cycle. The SPC life cycle consists of three steps: mass production preparation, early‐stage mass production, and routine mass production. In mass production preparation, machine performance is ensured by sampling according to an experimental design. In mass production stage, by sampling in control charts, process variation is reduced and process capability is ensured. Sampling to prevent the escape of a nonconforming product in routine mass production is also explained. In addition, considering semiconductor wafer process, the inherent process variation related to sampling is introduced.
Internal and External Quality Measures
Authors: Ograjenšek Irena
Published: September 2014

There are two distinct general approaches to the use of statistical methods in quality improvement. These are theproduction approachand themarketing approach. The production approach focuses on quality improvement from the management (internal) point of view using the statistical quality control (SQC) tools and producing predominantly internal quality measures. The marketing approach builds on the customer (external) assessment of quality using tools of survey research, producing predominantly external quality measures. One of the biggest challenges that companies face is a meaningful integration of these two groups of measures with the goal of facilitating continuous quality improvement.
Sampling Designs in Surveys
Authors: Gabler Siegfried
Published: September 2014

Survey sampling basically consists of the selection of a part of a population and the subsequent inference from this selected sample. To derive statistical conclusions from the actually collected data, a stochastic background based on a random selection procedure is necessary. Depending on the availability of frames, surveys will use simple or complex samples.
Data Management in Survey Sampling
Authors: Heerwegh Dirk
Published: September 2014

An overview of new technology applications in data collection and data management is given. Attention is paid to advantages and disadvantages, both in methodological and statistical terms.
k

‐out‐of‐

n

Systems
Authors: Shepherd Deborah K.
Published: September 2014

A
k
‐out‐of‐
n
system is a system with
n
components which functions or works if at least
k
out of the
n
components work. Parallel and series systems are special cases of a
k
‐out‐of‐
n
system. There are many different arrangements of the components in a
k
‐out‐of‐
n
system and many assumptions that can be made about the lifetimes of the components. In this chapter, the lifetimes of the components in the system are assumed to be independent and identically distributed. The reliability function of the system is found by calculating the probability that at least
k
components out of the
n
components work. The mean time to failure of the system is also found for the case of components with exponential distributions of lifetimes. In addition, the reliability function for a linear and circular consecutive
k‐out‐of‐n
system is given.
Modules and Modular Decomposition
Authors: Zuo Ming J.
Published: September 2014

Modules are system structures that have well‐established reliability evaluation algorithms. The technique of modular decomposition identifies such modules in complex systems and uses their efficient reliability evaluation algorithms for reliability evaluation of the whole system. In this article, we provide the formal definitions of modules and modular decomposition for system reliability analysis, illustrate the technique of modular decomposition, and outline reliability evaluation algorithms for several well‐studied modules. References for further reading in this area will also be provided.
Reliability Databases
Authors: Bedford Tim , Hardman Gavin , Walls Lesley , Quigley John
Published: September 2014

We present an overview of the development of reliability databases and their use in the analysis of failure data. We consider through examples the construction of a reliability database and the implementation of standard methods of analysis. We also discuss common criticisms of the use of reliability databases.
Asymptotic Reliability Analysis of Very Large Structural Systems
Authors: Adhikari Sondipon
Published: September 2014

In the reliability analysis of safety‐critical complex engineering structures, a very large number of the system parameters can be considered to be random variables. The difficulty in computing the failure probability using the classical first and second‐order reliability methods (FORM and SORM) increases rapidly with the number of variables or “dimension”. On the basis of the asymptotic distribution of quadratic form in Gaussian random variables, two formulations, for the case when the number of random variables
n
 → ∞, are provided. The first is called
strict asymptotic formulation
and the second is called
weak asymptotic formulation
. Both approximations result in simple closed‐form expressions for the probability of failure of an engineering structure. The proposed asymptotic approximations are compared with existing approximations and Monte Carlo simulations using numerical examples.
Inflation Impact on Aggregate Claims
Authors: Garrido José , Léveillé Ghislain
Published: September 2014

Inflation can have a significant impact on insured losses. Insurance companies recognize this effect on their aggregate claims when setting premiums and reserves.

Interest earned by insurance companies on their reserves can, to some extent, offset the effect of inflation on claims. This article looks at the combined effect of these economical variables, inflation and interest, on the distribution of aggregate claims.
S
undt's Classes of Distributions
Authors: Vernic Raluca
Published: September 2014

Computing the aggregate claims distribution is generally not an easy task. Among various methods used for such computations, recursive methods have the advantage of giving accurate values with considerable savings in the computing time. The purpose of this article is to give an overview of the classes of counting distributions introduced by Sundt 8, these classes leading to recursive evaluation of the corresponding aggregate claims distributions.
Coverage ‐ Non‐Life Insurance
Authors: Taylor Greg
Published: September 2014

This article discusses the circumstances under which a claim will be paid by an insurance policy and some basic matters affecting the amount of claim payable. Various pieces of terminology are defined.
Dividends
Authors: Dickson David C.M.
Published: September 2014

In this article, we discuss risk processes modified by the inclusion of a constant dividend barrier. We give expressions for moments of the present value of dividend payments until ruin occurs, and describe strategies for setting the level of a dividend barrier. We also describe the distribution of the amount of dividends payable prior to ruin.
Decrement Analysis
Authors: Pollard John
Published: September 2014

Decrement analysis intends to provide approximate values for some actuarial quantities that are not fully observable. The most common and single‐mode decrement is death and mortality rates are not fully known due to censoring of the observed lives. By using graduation methods, workable alternatives are provided. More complicated situations arise in a multiple‐decrement situation where the dependence between different causes needs to be taken into account.
Stochastic Simulation
Authors: Bølviken Erik
Published: September 2014

Stochastic simulation is reviewed with its main areas of application in insurance, finance and economics and its principal techniques of implementation. An extensive list of references into many fields is provided.
Gamma Function
Authors: Drekic Steve
Published: September 2014

This article summarizes some of the key mathematical/computational properties associated with the gamma function and incomplete gamma function that find use in applications to probability theory and parametric claims modeling.
Compound Distributions
Authors: Lin X. Sheldon
Published: September 2014

In this article, compound distributions and their basic properties are discussed in an actuarial context. A brief survey of the evaluation of compound distributions is given.
Compound Poisson Frequency Models
Authors: Panjer Harry H.
Published: September 2014

This article describes the role of the compound Poisson distribution in the modeling of the number of insurance losses or claims. Some examples and related results are given.
Discrete Parametric Distributions
Authors: Panjer Harry H.
Published: September 2014

This article describes some counting distributions that are frequently used in modeling the number of insurance claims, the number of losses, the number of payments, or the number of insurance events such as accidents or fires.
Phase‐Type Distributions
Authors: Drekic Steve
Published: September 2014

This article summarizes some of the key distributional properties associated with phase‐type distributions, which are used extensively in many areas of applied probability, namely, queueing theory and insurance ruin theory (
see
).
Continuous Parametric Distributions
Authors: Klugman Stuart A.
Published: September 2014

Actuaries model a variety of uncertain phenomena, foremost among them, the amount of a claim and the time until a claim. Parametric probability distributions provide simple models that often adequately describe the process. This article lists a large number of such models and briefly describes their properties.
Subexponential Distributions
Authors: Klüppelberg Claudia
Published: September 2014

Subexponential distributions are a special class of heavy‐tailed distributions. The name arises from one of their properties that their tails decrease slower than any exponential tail (3). This implies that large values can occur in a sample with nonnegligible probability, which makes the subexponential distributions natural candidates for modeling situations in which some extremely large values occur in a sample compared with the mean size of the data. Such a pattern is often seen in insurance data, for instance, in fire, wind–storm, or flood insurance (collectively known as catastrophe insurance). Subexponential claims can account for large fluctuations in the surplus process of a company, increasing the risk involved in such portfolios.
Graphical Methods
Authors: Unwin Antony
Published: September 2014

Graphical displays are excellent for giving overviews of data. It is important to distinguish between categorical and continuous data in the choice of display and to avoid including unnecessary ‘chart junk’. Recent developments include parallel coordinate plots, mosaic plots, trellis graphics, and the development of interactive graphics for exploratory analysis.
Lundberg, Filip (1876‐1965)
Authors: Martin‐Löf Anders
Published: September 2014

Filip Lundberg (1876–1965) was a pioneer of the collective theory of risk that describes the surplus of, for example, a branch of an insurance company as a stochastic process. The purpose of the theory is to study the probability distribution of the surplus and of the time until ruin.
Estimation of Actuarial Quantities
Authors: Pitts Susan M.
Published: September 2014

We consider methods of parametric and nonparametric estimation for claim sizes and claim number distributions, and also for quantities of interest in risk theory such as compound distributions, the adjustment coefficient and the probability of ultimate ruin.
Censoring
Authors: Papaioannou Takis
Published: September 2014

Censoring is a process or a situation where we have partial information or incomplete observations. It is an area in statistics, engineering, and actuarial science, which has received widespread attention in the last 40 years, having been influenced by the increase in scientific computational power. The purpose of this article is to present the concept, the idea of censoring, to describe various types or kinds of censoring, and to point out its connections with survival analysis and
actuarial methods
. Censoring is closely related with censored data and is a major topic in
biostatistics
and reliability theory (life testing).
Poisson Processes
Authors: Grandell Jan
Published: September 2014

For a long time, Poisson processes have formed the most popular stochastic model for claim arrivals in an insurance portfolio. No wonder that in the course of time a wealth of generalizations have been constructed such as point processes, Cox processes and mixed Poisson processes. The essential ingredients of these processes are included.
Regenerative Processes
Authors: Wolff Ronald W.
Published: September 2014

A regenerative process is a stochastic process with the property that after some (usually) random time, it starts over in the sense that, from the random time on, the process is stochastically equivalent to what it was at the beginning.

In many applied fields such as telecommunications, finance, and actuarial science, important probability models turn out to be regenerative. Properties of regenerative processes and the mathematical methods used in their analysis are fundamental in the analysis and understanding of these models.

For
classical
regenerative processes, cycles and cycle lengths are i.i.d. (independent and identically distributed). This assumption has been weakened over time. Now, processes satisfying the first paragraph above are regarded as regenerative, without any independent assumptions.

This article introduces the classical case in the section ‘Classical Regenerative Processes’, presents their time‐average properties in the section ‘Time‐average Properties, Classical Case’, and briefly treats more advanced topics in the section ‘Existence of Limits; Combining Processes’.
Stationary Processes
Authors: Lindgren Georg
Published: September 2014

Stationary processes form a prime example of sets of not necessarily independent random variables, usually in the form of a time series. We collect the most important ingredients, in particular the spectrum and the spectral representation of such processes.
Itô Calculus
Authors: Steele J. Michael
Published: September 2014

This entry for the
Encyclopedia of Actuarial Sciences
provides an introduction to the Itô calculus that emphasizes the definition of the Itô integral and the description of Itô's formula, the most widely used result in the Itô calculus.
Logistic Regression for Credit Scoring
Authors: Dierckx Goedele
Published: September 2014

Logistic regression is a very flexible tool to study the relationship between several explanatory variables and a binary response. To fit and examine such a logistic regression model, some tools used with generalized linear models, as introduced by McCullagh and Nelder in 6, are useful. Once the model is fitted and the goodness‐of‐fit has been examined, the relationship between covariates and the response can be better understood by interpreting the coefficients in the logistic model in terms of odds ratios. The model can also be used to make predictions. As such, the logistic model provides a method to classify objects in two (or more) groups as well.
Dynamic Financial Modeling of an Insurance Enterprise
Authors: Hardy Mary R.
Published: September 2014

A dynamic financial insurance model is an integrated model of the assets and liabilities of an insurer. In the United Kingdom, these models may be called ‘model offices’. Modeling the insurer as a whole entity differs from individual policy or portfolio approaches to modeling in that it allows for interactions and correlations between portfolios, as well as incorporating the effect on the organization of decisions and strategies, which depend on the performance of the insurer as a whole. For example, profit distribution is most sensibly determined after consideration of the results from the different insurance portfolios that comprise the company, rather than at the individual portfolio level. The insurance enterprise model takes a holistic approach to asset–liability modeling, enabling synergies such as economies of scale, and whole insurer operations to be incorporated in the modeling process.
Cooperative Game Theory
Authors: Lemaire Jean
Published: September 2014

Game theory models situations of conflict and/or cooperation between economic agents. Cooperative games with transferable utilities and two‐person bargaining games, the two most important contributions of cooperative game theory to economic analysis, are reviewed and illustrated with examples.
Homeowners Insurance
Authors: Fry Martin
Published: September 2014

Homeowners insurance indemnifies owners against property damage arising from a number of insurable events. The insurance covers building costs and repairs, and rental costs if a property becomes uninhabitable. Factors affecting the premium for a homeowners policy are the sum insured, the construction materials of the building, the use of the building, and its location. Deductibles are often imposed.
Lapses
Authors: Fry Martin
Published: September 2014

A lapse is a failure by a policyholder to accept an insurer's offer to renew an expiring policy. Lapses differ from cancellations, which require specific action by a policyholder during the policy term. Insurers monitor lapse rates, as high lapse rates may indicate that an insurer's policies are uncompetitive. In practice, renewal rates are often monitored; they are calculated as (1‐lapse rates).
L
loyd's
Authors: Michaelson Robin
Published: September 2014

To understand Lloyd's, one has to realize what it is not. It is not an insurance company with shareholders or a mutual, nor does it accept liability for a risk as a trading entity under the name of ‘Lloyd's’. It is, in fact, a ‘society’, or group of individual and corporate members, who accept a share of a risk by operating through an underwriting syndicate, in which the individual members (called Names) are liable to the full extent of their personal private wealth, to supply the capital backup to meet the insurance liabilities, but the corporate organizations operate with a form of limited liability.
Audit
Authors: Coestier Bénédicte , Fombaron Nathalie
Published: September 2014

In an insurer–policyholder relation, insurees may use their informational advantage about the occurrence and/or magnitude of their losses to exaggerate the claims. Claims auditing may be a means to manage this type of insurance fraud. The economic analysis of audit has been developed in the literature principally using Costly State Verification models. After recalling the more basic results of CSV models, we discuss the major limitation of these auditing procedures, namely, the commitment assumption, and finally consider several solutions to the no‐commitment problem.
Underwriting Cycle
Authors: Klein Robert
Published: September 2014

The property‐casualty insurance industry is notorious for its pattern of rising and falling prices and supply of coverage, commonly known as the “underwriting cycle.” This article explains this phenomenon, reviews various theories about its causes, and discusses proposed government remedies. The “real cycle” in the price and supply of insurance is distinguished from the “accounting cycle” in reported performance ratios. Several hypothesized causes of the real cycle are examined, including adverse loss shocks, movements in interest rates, under‐pricing due to naivety or excessive risk taking, and greater uncertainty about the distribution of expected losses. Government policies that help to control claims costs will be the most effective in promoting greater market stability.
Deregulation of Commercial Insurance
Authors: Klein Robert
Published: September 2014

This article utilizes the US experience as a primary point of reference with some discussion of insurance deregulation in other countries. The concept of insurance deregulation contemplates a shifting of regulatory emphasis from prior approval of commercial lines rates and forms to a more competitive regulatory system coupled with more intensive regulatory monitoring of market competition and strategic intervention when required. It is important to stress that this does not involve an abrogation of regulatory oversight, but rather a restructuring of regulatory functions to facilitate more efficient and competitive markets combined with an array of regulatory activities, tools, and authorities to support strategic, proactive regulatory intervention if problems develop.
Frontier between Public and Private Insurance Schemes
Authors: Zweifel Peter
Published: September 2014

From an economic point of view, insurance coverage is very much like any other goods or service purchased by households and firms. One would therefore expect individually contracted insurance coverage provided by private firms to dominate. However, mandated coverage provided by public insurance is common for the provision for old age, disability, workers' compensation, health, long‐term care and unemployment. Contributions to public insurance amount to about 30% of the Gross Domestic Product (GDP) and are still rising in major industrialized countries whereas the premium revenue of personal lines of private insurance make up as little as 5% of GDP even in the United Kingdom, a stronghold of private insurance. This raises the question, what determines the frontier between public and private insurance? and, in a normative vein, would a shifting of this frontier be in the interest of the insured?
Insurability
Authors: Gollier Christian
Published: September 2014

We first describe the competitive equilibrium of frictionless insurance markets with symmetric information. Risks are insurable in this economy in the sense that all mutually advantageous risk exchanges are realized at equilibrium. We then provide various reasons why many risks cannot be efficiently shared in our decentralized economy. Transaction costs, adverse selection, moral hazard, insurance fraud, and the inexistence of an objective distribution function do generate an insurability problem that requires public intervention. The heterogeneity of beliefs and the difficulties in diversifying individual risks are other reasons why some risks are not insurable, but this does not mean that insurance markets are inefficient.
Pareto Optimality in Insurance
Authors: Dana Rose‐Anne
Published: September 2014

Any sequence of positive, independent and identically distributed random variables can be considered as a renewal process. Traditional examples are the interclaim times and the successive claims in a homogeneous portfolio. The article describes the most important quantities and results from renewal theory. Also defective, delayed and discrete‐type renewal processes are discussed and illustrated with examples from actuarial science.
Pooling Equilibria
Authors: Boyer Marcel , Martin Boyer M.
Published: September 2014

We present in this paper, different contexts under which pooling equilibria emerge in insurance economics. A pooling equilibrium may emerge when it is not optimal (or not feasible or not allowed) to offer different contracts to different agents. As a result, agents with different risk types are ‘pooled’ together even though the low‐risk agents end up subsidizing the high‐risk agents. This subsidy, quite like an externality imposed by the high‐risk types on the low‐risk ones, may lead low‐risk insureds to try to identify themselves and insurers to search for different ways to bypass the pooling equilibrium by identifying and luring away good risk types, thereby destabilizing the pooling equilibrium.
Black–Scholes Model
Authors: Henderson Vicky
Published: September 2014

The Black–Scholes model was the first, and is the most widely used model for pricing options. The model and associated call and put option formulas have revolutionized finance theory and practice, and the surviving inventors Merton and Scholes received the Nobel Prize in Economics in 1997 for their contributions.

Black and Scholes and Merton introduced the key concept of dynamic hedging whereby the option payoff is replicated by a trading strategy in the underlying asset. They derive their formula under log‐normal dynamics for the asset price, allowing an explicit formula for the price of European call and put options.

Remarkably their formula (and its variants) have remained the industry standard in equity and currency markets for the last 30 years. Despite the assumptions underpinning the formula being somewhat unrealistic, options prices computed with the formula are reasonably close to those of options traded on exchanges. To some extent, the agreement in prices may simply reflect the fact that the Black–Scholes model is so popular.
Catastrophe Derivatives
Authors: Muermann Alexander
Published: September 2014

Catastrophe derivatives are capital market instruments that allow investors outside of the insurance and reinsurance arena to invest in natural catastrophic risks. In this article, we describe the development of this market since the early 1990s, examine various stochastic models that have been proposed to model the underlying risk process, and address the pricing of these instruments.
Credit Scoring
Authors: Hand David J.
Published: September 2014

‘Credit scoring’ describes the formal statistical and mathematical models used to assist in running financial credit‐granting operations, primarily to individual applicants in the personal or retail consumer sectors. The range of applicability of such tools is vast, covering areas such as bank loans, credit cards, mortgages, car finance, hire purchase, mail order, and others.
Bailey‐Simon Method
Authors: Mildenhall Stephen J.
Published: September 2014

This article introduces the Bailey–Simon method for classification ratemaking and explains the connection between linear Bailey–Simon methods and generalized linear models.
Financial Pricing of Insurance
Authors: D'arcy Stephen P.
Published: September 2014

Financial pricing models bring together the underwriting and investment components of an insurance contract. These models are used to attempt to determine the appropriate rate of return for a line of business, the minimum premium level at which an insurer would be willing to write a policy, or target rate of return for an insurance company in aggregate.
Retrospective Premium
Authors: Meyers Glenn
Published: September 2014

Insurance is about the transfer of risk. If an entity, either a person or a business, wants to transfer all of its risk of loss to an insurer and the insurer is able to quantify the risk that the entity wishes to transfer, the price of the risk transfer is readily established by market forces and a deal is struck.

In many cases, the insurer is not confident that it can quantify the risk that the entity wishes to transfer. An entity sensing difficulty in getting a full transfer of risk may be willing to settle for a partial transfer of risk. The insurer would be more comfortable with a partial risk transfer because the entity has an incentive to keep its loss at a minimum.

This article describes a particular kind of risk‐sharing agreement called a retrospective rating plan. In these plans, the premium for an insurance contract is a function of the actual loss paid under the contract. The final premium is not known until after the contract has expired. This explains the name retrospective rating.
Pooling in Insurance
Authors: Aase Knut K.
Published: September 2014

Risk sharing resulting in pooling of risk is considered. We take the perspective of Pareto optimal risk sharing, originating from a model introduced by Karl Borch in the late 1950s, and discuss when pooling may result, and also what is needed for pooling not to be optimal. Finally, we illustrate by some examples, including mutual insurance schemes, and also a limited liability partnership.
Reinsurance, Reserving
Authors: Radtke Michael
Published: September 2014

The article deals with actuarial reserving techniques used in reinsurance. The impact of reinsurance on the actuarial reserving approach is discussed with a focus on the actuarial methods. In reinsurance, very often, the standard methods, that is, Chain‐Ladder or Bornhuetter Ferguson have to be modified because of specific reinsurance requirements. We introduce some methodical adjustments and illustrate the practical circumstances under which they have been taken into account. The paper ends with some comments on practical applications of reserving methods in reinsurance.
Cochrane, Archibald ('Archie') Leman
Authors: Elwood P. , Hughes C.
Published: September 2014

Born in 1909 in Galashiels, UK; died in 1988 in Dorset, UK. Cochrane is best known for his dedication to improving epidemiological methodology, and for being instrumental in establishing the Cochrane Collaboration, which facilitates access to the results of health care interventions.