bluuebunny/crossref_metadata_2025 huggingface dataset:
Box‐Behnken Designs
Authors: Robinson Timothy J.
Published: September 2014

Designs for second‐order response surface models play an important role in response surface methodologies. The central composite design and Box‐Behnken designs have served as popular choices for designs for second‐order models when design economy and precise prediction variance are desired. The Box‐Behnken design has been widely used in completely randomized experiments, split‐plot experiments, and within the robust parameter design setting. This article provides a historical background for the Box‐Behnken design, describes its construction, and reviews various contributions in the literature regarding the use of these designs.
Center Points
Authors: Borkowski John J.
Published: September 2014

In a designed experiment, center points can provide an estimate of experimental error, allow for lack‐of‐fit tests and for tests of curvature, or ensure orthogonal blocking and uniform precision. A review of these applications of center points will be given.
Rotatable Designs and Rotatability
Authors: Draper Norman R.
Published: September 2014

Choosing a suitable experimental design is an important step in the investigations of the factors that may influence one or more response variables. There are several criteria to keep in mind when the choice is made, one of which is
rotatability
. When a design is
rotatable
, it will produce information that predicts ŷ with the same precision at all points equidistant from the coded origin of the design. Another way of saying this is that the contours of
V
(ŷ), the variance of the predicted value, will be spherical about the design origin. In experimental practice,
exact
rotatability is not essential, but the knowledge of how to obtain it is useful in producing approximate rotatability while perhaps attaining other desirable design characteristics.
Performance Measures for Robust Design
Authors: Murphy Terrence E. , Tsui Kwok‐Leung
Published: September 2014

Despite their widespread use as performance measures in robust design, Taguchi's signal‐to‐noise ratios (SNRs) do not always minimize quadratic loss. The relationship between minimization of expected quadratic loss and Taguchi's SNR was articulated by León
et al.
1. Their performance measure independent of adjustment (PerMIA) is a general performance measure which justifies the use of the Taguchi two‐step procedures as a method of minimizing quadratic loss under certain models. We review the basic conceptual framework of the PerMIA and the literature related to this performance measure.
Robust Design
Authors: Ankenman Bruce E.
Published: September 2014

Robust design is a methodology that seeks to set the controllable factors of a system in order to achieve a consistent and desirable response from the system. The defining characteristic of robust design is the emphasis on achieving a consistently desirable response, not just a response that is desirable on average. The robust design procedure involves designing, conducting, and analyzing experiments. In this article, robust design methodology is explored for two typical cases. The first case is when the variability in the system is due to replication error. The second is when there are certain factors, callednoise factors, which can be controlled during an experiment, but will vary randomly when the system is put into its standard operating mode. Models for the response, data analysis techniques, and experimental design techniques will all be discussed and demonstrated through a simple manufacturing example.
Signal‐to‐Noise Ratios for Robust Design
Authors: Murphy Terrence E. , Tsui Kwok‐Leung , McShane‐Vaughn Mary
Published: September 2014

Taguchi introduced a collection of performance measures called
signal‐to‐noise ratios
(SNRs) as a core component of the robust design methods he introduced to US corporations in the 1980s. The SNR is the most controversial part of Taguchi's methods because it summarizes the quality information from the entire experiment in a single entity. While the use of a single performance measure provided a conceptual simplicity attractive to engineers, it also introduced certain statistical controversies. We review the strengths and limitations of this performance measure and the evolution of related research. Our discussion includes the use of the SNR for both static and dynamic robust design (
see
Robust Design
).
Disease and Clinical Trial Modeling
Authors: Abbas Ismail , Rovira Joan , Cobo Erik , Romeu Joan , Casanovas Josep
Published: September 2014

Introduction

The objective is to show how disease and clinical trial modeling can be applied to estimate the success probability, duration and cost that resulting from a certain trial design or from similar decisions.

Methods

Multidisplinar team has participated in the construction of the general simulation model of clinical trials. This model is constructed splitting the whole process into two main parts. The first part represents the recruitment sub‐model aiming at estimating the time and the number of included patients. The second part is based on the follow‐up sub‐model represented by disease progression.

Results

The model is applied to retrospective clinical trial.

Conclusion

Simulation modelling will optimise clinical trials whenever information from different disciplines, such as clinics, statistics, economics and informatics is integrated and used properly.
Process Capability Indices, Skewed
Authors: Chang Young Soon , Bai Do Sun
Published: September 2014

Conventional process capability indices (PCIs) are usually determined under the assumption that quality characteristics follow a normal distribution. If a process does not follow a normal distribution, however, conventional PCIs do not provide valid measures of process capability, especially in terms of the number of nonconforming parts. Methods to remedy the shortcoming of the conventional PCIs when the population is skewed can be divided into five categories; to use normalizing transformations like Box–Cox power transformation or Johnson transformation, to fit an empirical distribution or a known three‐ or four‐parameter distribution such as Burr or Pearson distribution to the original data and use the quantiles of the fitted distribution, to modify the standard definition of PCIs in order to increase their robustness to skewness, to construct PCIs with estimate of the process yield, and to develop heuristic methods adequate for skewed distributions. This article provides a compact survey and brief comments on the skewed PCIs.
Process Capability Indices,
B
ayesian Estimation of
Authors: Spiring Fred , Cheng Smiley
Published: September 2014

Practitioners often base inferences regarding the capability of a process on a point estimate of one of the common indices without examining the distributional properties of the estimator used. The practice is due, in part, to (a) the complexity of the indices developed and, at least initially, (b) the lack of stochastic development in the general area of process capability indices. Since the mid‐1980s the body of work addressing (a) estimation of and (b) drawing inference from process capability indices has grown steadily. Investigating process capability from a Bayesian perspective has mirrored this development. Much like the indices themselves, the Bayesian approach has seen two distinct patterns develop. One focus has been on examining parts nonconforming while a second examines the ability of a process to cluster around a target.
Process Capability Plots
Authors: Vännman Kerstin
Published: September 2014

A process is usually defined to be capable if a process capability index exceeds a stated threshold value. This definition can be expressed graphically as a region in the plane, defined by the process parameters, to obtain a process capability plot. Under the assumption of normality, safety regions can be plotted in the process capability plot to draw conclusions about process capability at a given significance level. Alternatively, an estimated process capability plot defined by the estimators of process parameters can be used. This article discusses these different kinds of plots and presents examples and interpretations.
Process Capability Indices for Multiple Stream Processes
Authors: Bothe Davis Ross
Published: September 2014

Multiple streams are created in a manufacturing process when its flow of parts is divided into several supposedly identical paths. Presumably, the quality of parts produced by each stream is identical but, in practice, there are usually differences between streams. The capability metric introduced in this article, called the
average C

pk

index
, is used when a practitioner desires a measure of capability for the combined output of all streams. Because this new index is derived from the average percentage of nonconforming parts expected in the mixed output of all streams, it works equally well with both variable‐type data (having either unilateral or bilateral specifications) and attribute‐type data. Two examples are provided: the hole size of parts produced by a four‐cavity mold in an injection‐molding operation; and the rejection rate of a food product made on six lines.
Measurement Systems Analysis, Attribute
Authors: Borror Connie M.
Published: September 2014

Methods for assessing the capability of a quantitative or continuous measurement system are well documented and include the tabular method and the analysis of variance approach. When the measurement system involves attribute data, the standard quantitative methods are not appropriate. An attribute gauge measurement system is one where the parts or objects under study are placed into one of two or more possible categories. The classification of the part is the measurement of interest in an attribute measurement system. Several commonly used statistics for “appraiser agreement” and attribute gauge repeatability and reproducibility are presented.
Warranty: Usage and Wear Process for
Authors: Wilson Simon P.
Published: September 2014

Many products, for which warranties are offered, are subject to wear and this can be a major factor in when the product fails. The process by which wear accumulates is best modeled as a stochastic process. In this article, I describe some stochastic processes for wear. Each process is defined, the ease with which its probability distribution can be computed is described, and its advantages and disadvantages as a wear process is discussed. I briefly discuss how these models may be applied to practical warranty problems such as for products whose warranty is defined in terms of time and some measure of usage (like kilometers traveled) to failure.
Warranty Modeling
Authors: Thomas Marlin U.
Published: September 2014

Manufacturer warranty costs vary with product quality, particularly reliability and failure characteristics that relate to warranty claims. These costs represent a significant portion of the total cost and are therefore important in product planning and manufacturing control decisions. In this article, models are presented for assisting manufacturers in analyzing and making economic decisions for product warranties. Methods are developed for predicting costs, determining the amount of reserve funds for covering warranty expenses, and determining optimum periods of warranty coverage.
Total Time on Test Plots
Authors: Bergman Bo , Klefsjö B.
Published: September 2014

In the 1970s the total time on test (TTT) plot, and its theoretical counterpart, the scaled TTT transform, was presented by R. E. Barlowet al. as a tool for model identification based on data representing lives of nonrepairable equipment. It has been used when analyzing different aging properties, optimising replacement policies and studying test statistics. Generalisations of the TTT plot have also been used for analysis of data from repairable units. It has also been suggested as a tool for the selection of active factors in design of experiments. In this paper we give an overview of TTT plotting and its practical and theoretical applications. A wide range of references are suggested for further reading.
Stationary Replacement Strategies
Authors: Bergman Bo
Published: September 2014

This paper gives a general overview of the idea of stationary replacement strategies and a general formulation of the objective function to be minimized is given. Some special cases are discussed. Finally, a comment critical to the usage of stationary replacement policies is given.
Maintenance Optimization in Random Environments
Authors: Özekici Süleyman
Published: September 2014

We consider reliability models that operate in a randomly changing environment. The random environment represents important factors that affect the stochastic and deterministic parameters of the reliability model under consideration. We focus, in particular, on the maintenance problem involving complex systems. We do not aim to report new results on recent ongoing research. Rather, the objective is to provide an overview of the models and results on reliability models in random environment. This will include mainly previous work done by the author.
Group Maintenance Policies
Authors: Wilson John G. , Benmerzouga Ali , Anderson Chris K.
Published: September 2014

This paper introduces a new group replacement policy for
n
independent identical machines operating in parallel. This policy is a generalization of the classes of
m
‐failure, (
m
,
T
) and
T
‐failure policies. The adaptive nature of this policy is its most attractive feature: the replacement rule varies according to the state of the system. Once the rule has been found, implementation is no harder than for other standard policies which do not incorporate this adaptive feature. An attractive feature of this approach is that no other policy that uses only the times of operations of the machines and the number of machines that have failed can do better. It is demonstrated that the classes of
m
‐failure, (
m
,
T
) and
T
‐failure policies are not generally the optimal.
Expert Opinion in Reliability
Authors: Sims Benjamin H. , Wiedlea Andrew Koehler , Wilson Gregory D.
Published: September 2014

Expert opinion can be a useful source of information for assessing reliability, provided it is obtained in a manner that minimizes common sources of bias and ambiguity. The term for obtaining expert opinion in this manner iselicitation. In reliability assessment, elicitation is most often directed at two distinct elements of expert opinion: expertjudgmentabout the value of a specific quantity or probability of interest, or expertknowledgeabout the dependency structure of a system.
Multivariate Age and Multivariate Renewal Replacement
Authors: Ebrahimi Nader
Published: September 2014

A large part of reliability theory deals with replacement of single‐component systems. Two of the popular replacement policies are (a) age‐replacement and (b) block‐replacement policies. As systems become more complicated and require new technologies and methodologies, more sophisticated maintenance policies are needed to solve the maintenance problems. For systems consisting of
k
related components, a legitimate question is when to replace the components. Obviously, the classical age‐and block‐replacement policies are unsuitable for such situations. This article deals with multivariate versions of age replacement policies that may be used for replacing components. Also, for planning purposes, the article describes several optimal age replacement policies.
System Availability
Authors: Gaver Donald P.
Published: September 2014

Availability
quantifies the propensity of a system to be functionally operative upon demand. It increases if operating times between failures (“uptimes”) are long, and decreases if, following failure or anticipatory removal, logistics delays and repair (“downtimes”) are protracted. This chapter summarizes the general availability concept and discusses the limitation of
operational availability
suggesting that
mission availability
is often more useful and appropriate.
Global and Dynamic Information Measures for Reliability
Authors: Ebrahimi Nader , Soofi Ehsan S.
Published: September 2014

In modeling a duration variable, such as the lifetime of an object as it ages, consideration of the age partitions the support of the lifetime distribution progressively and induces truncated distributions for the past and residual lifetimes. Global information measures of the distribution of the entire lifetime do not change with the age, and thus are static. Information measures of the past and residual lifetime distributions are functions of the age, and hence are dynamic. This article presents an overview of the global and dynamic Shannon entropy, Kullback–Leibler information, and mutual information. Examples include information measures for parallel and series systems, proportional hazard, exponential, and Pareto models.
Nonparametric and SemiparametricBayesian Reliability Analysis
Authors: Ghosh Kaushik , Tiwari Ram C.
Published: September 2014

In this article, we first provide an overview of some nonparametric Bayesian methods of inference using life‐history data. These methods include those that use the Dirichlet process, the gamma process, and the beta process as the prior. We then present a semiparametric Bayesian method for estimating the reliability of a component in a multicomponent system using lifetime data from several systems. This method assumes that the component lifetimes have a parametric distribution with a Dirichlet process prior on the distribution of the parameters.
Multicomponent Maintenance
Authors: Nicolai Robin P. , Dekker Rommert
Published: September 2014

In the past few decades the maintenance of multicomponent systems has become more and more complex and, as a consequence, it has got the attention of many scholars. Multicomponent maintenance is the problem of finding optimal maintenance policies for a system consisting of several units of machines or many pieces of equipment, which may or may not depend on each other. Generally, three types of interactions or dependencies can be distinguished: economic dependence, stochastic dependence, and structural dependence. Economic dependence implies that grouping maintenance actions either saves costs (e.g. because to economies of scale) or yields higher costs (e.g. because of manpower restrictions) compared to multiple individual maintenance actions. Stochastic dependence occurs if the condition of the components influences the lifetime distribution of other components. Structural dependence applies if components structurally form a part, so that maintenance of a failed component implies maintenance of working components as well.

On the basis of the planning aspect, we may distinguish between two types of models for multicomponent maintenance: stationary models and dynamic models. In stationary models, a long‐term stable situation is assumed and mostly these models assume an infinite planning horizon. In dynamic models, short‐term information can be taken into account. These models generate dynamic decisions that may change over the planning horizon.
M
arkov Renewal Processes in Reliability Modeling
Authors: Çekyay Bora , Özekici Süleyman
Published: September 2014

Renewal theory is one of the most useful tools used in reliability modeling and analysis. The stochastic structure of most models involve an embedded renewal process where the state of the system regenerates itself over these renewal times. This allows one to analyze various issues related to reliability, availability, maintenance, and repair using renewal theory. In this setting, we aim to explore this idea further by considering Markov renewal models. However, we propose to use a Markov renewal process to model a mission‐based system where the device is designed to perform a random sequence of phases or stages of the mission with random durations. The mission process is modeled as a Markov renewal process and different reliability measures are analyzed using Markov renewal theory. First, it is assumed that the system is replaced with a brand‐new one (maximal repair model) at the beginning of each stage. Under this hypothesis, the probability of survival until a predetermined time (system reliability) and the probability of completing a predetermined number of phases of the mission (mission reliability) are determined. Then, we consider cases without replacement (no repair model) and use intrinsic aging concepts to analyze mission reliability of a series system.
Burn‐In and Maintenance Policies
Authors: Mi Jie
Published: September 2014

It is always desired that products have high reliability, long life, and so on. There are basically three phases in which certain measures can be taken to achieve these goals. In the first phase the product has to be carefully designed, good materials have to be used, and so on. This phase will not be considered in this article. In the second phase, i.e. after the completion of production process and before shipment to customers, the burn‐in procedure can be applied to eliminate weak products and thus improve the quality of products before they are shipped. In the third phase, appropriate maintenance measures will keep the products properly functioning for long and accomplish the desired mission with low risk.
Dynamic Programming Methods in Repair and Replacement
Authors: Bhattacharjee Manish C.
Published: September 2014

Applications of dynamic programming to problems in reliability, with a specific emphasis on repair and replacement are surveyed. A brief summary of early classic work on such uses of dynamic programming is followed by a review of later approaches adopted by different researchers toward the problem of modeling plausible and pragmatic notions of imperfect repairs. We then provide a synthesis of how such different approaches for the study of repairable systems can be subsumed within a unified setting of a stochastic dynamic programming framework with some illustrative applications of such a formulation.
Accelerated Life Tests: Designs Comparison within a
B
ayesian Framework
Authors: Dorp Johan René , Mazzuchi Thomas A. , Garcidueñas Jorge E.
Published: September 2014

Accelerated life testing (ALT) is the set of procedures used to reduce the time needed to obtain information related to life characteristics of an item, material or part of interest. The importance of the design of these ALTs is paramount to obtain inferential life estimators with, for example, minimum variance. Typically, for a set ALT, step‐regimen optimal stress levels and duration are determined in the ALT design phase. Herein we focus on the comparison of different ALT designs (fixed stress, profile ALT, progressive step‐stress ALT, and regressive ALT) within a single Bayesian inference framework. We analyze the preposterior variance of the use stress reliability based on a single failure over the course of the ALT for these different ALT designs. To the best of our knowledge Miller and Nelson in their 1983 article titled “Optimum simple step‐stress plans for accelerated life testing” in
IEEE Transactions on Reliability
R–32
, 59–65, were among the earliest to claim similarity of asymptotic estimator variance when comparing step‐stress testing ALT with fixed stress ALT. The results in this article shed some light on this claim within a Bayesian context.
Accelerated Life Tests: Nonparametric Approach
Authors: Ebrahimi Nader
Published: September 2014

Many of today's products are capable of operating under extremes of environmental stress and for thousands of hours without failures. For a variety of reasons, manufacturers may wish to obtain reliability results for their products more quickly than they can with data obtained under normal operating conditions. Consequently, traditional life data analyses are no longer sufficient to identify design weaknesses or validate life prediction.

Accelerated life testing (ALT) is an approach for obtaining more information from a given test time than would normally be possible. It does this by subjecting items to test environment that is more severe than those experienced during normal use. ALT uses a model relating reliability (a life) measured under high‐stress conditions to that which is expected under normal operation to determine the reliability (or length of life). Various parametric and nonparametric models have been introduced to describe the relationship between the distribution functions of lifetimes for different stress levels. The parametric models assume a particular form of the distribution functions for different stress levels and the relationship between them. The approach in this article is nonparametric, where only a relationship between the distribution functions corresponding to any two different stress levels is assumed.
Density and Failure Rate Estimation
Authors: Müller Hans‐Georg , Wang Jane‐Ling
Published: September 2014

Density and failure rate estimation are valuable tools to assess and explore the occurrence and timing of failures in reliability and quality control. This article focuses on nonparametric approaches such as histograms, the kernel method, and other smoothing procedures. Nonparametric density and failure rate estimation is particularly valuable for exploratory data analysis and in situations where available information is insufficient to specify a parametric model, as these methods “let the data speak for themselves”, and no assumptions are needed beyond smoothness of the functions to be estimated. Issues specific for nonparametric approaches are finite bias behavior and choice of the necessary smoothing parameter. For failure rate estimation, available data are sometimes incompletely observed (censored) or available in aggregated form only, necessitating appropriate adjustments. Shape restrictions such as increasing failure rate (IFR) are also occasionally of interest in reliability.
Multiple Sampling Plans
Authors: Suresh Kodakanallur Krishnaswamy , Göb Rainer
Published: September 2014

Under a single sampling plan, the decision of rejection or acceptance is based on a unique sample. If product quality is extreme, either very good or very bad, the inspection amount can be reduced by
iterative sampling plans
: smaller sample portions are taken and evaluated successively so that extreme product quality is detected rapidly. Two kinds of iterative sampling procedures are distinguished: Under
multiple m‐stage sampling
a maximum number of
m
sample portions are selected, a definite decision is reached after evaluating the
m
th sample.
Sequential sampling plans
impose no upper limit on the number of samples taken. The procedure may continue until 100% inspection of a lot. The article describes the operation of iterative sampling plans, provides their essential performance measures, namely the operating characteristic function and the average cumulative sample size, and compares iterative against single sampling.
Skip Lot and Chain Sampling
Authors: Balamurali Saminathan , Jun Chi‐Hyuck , von Collani Elart
Published: September 2014

This article deals with sampling and inspection policies, which are located in the frontier area between process control and lot acceptance sampling. These methods show that from the beginning of statistical quality control the need was felt to consider lot acceptance not as an isolated problem, but in connection with the corresponding lot generating process. However, the methods described here are heuristic ones and do not allow reliable statements about their performance under realistic conditions. Therefore, future research in lot acceptance should focus on modeling the relation between lot quality and process quality for allowing the development of reliable and efficient procedures.
Prior Information in Sampling Schemes
Authors: Seidel Wilfried
Published: September 2014

The choice of a sampling scheme and the amount of inspection is guided at least informally by prior information on quality. We are concerned with formal models of prior information. The Bayesian approach is introduced in detail. Based on a prior distribution of submitted lots according to quality and a cost model, a Bayesian sampling plan minimizes the average costs. A special feature of sampling inspection is that the prior distribution (and consequently also posterior distributions and costs) may have a frequentist interpretation (in contrast to a subjective prior distribution). The cost model is not restricted to costs in the monetary sense. It only requires a numerical goal function that measures the consequences of possible decisions, examples are given.

Bayesian models may be used as a theoretical instrument for analyzing and comparing the performance of existing sampling schemes. In practice, assumptions like the stability of the prior may not be satisfied and full information on the prior distribution and the costs is often lacking. Modifications of the full Bayesian approach are necessary, including robust strategies and Γ‐minimax. Estimation of the prior distribution from past inspections and empirical Bayes is discussed. Adaptive sampling strategies are addressed.
Variables Sampling under Measurement Error
Authors: Wilrich Peter‐Th.
Published: September 2014

Single sampling plans for inspection by variables in the case of measurement error are presented that fulfill given requirements on their operating characteristic function. Three cases are considered: (a) measurement standard deviation and process standard deviation known, (b) measurement standard deviation and process standard deviation unknown and each sampled item measured once, and (c) measurement standard deviation and process standard deviation unknown and each sampled item measured more than once.
Acceptance Sampling in Modern Industrial Environments
Authors: Von Collani Elart , Göb Rainer
Published: September 2014

In the industrial mass production environments of the first half of the twentieth century, statistical product inspection (SPI) was a central tool of statistical quality control (SQC). Contemporary SQC emphasizes methods of provision and prevention such as experimental design or process control rather than inspection. To remain a valid tool of modern SQC, SPI has to be redefined in its purpose and in its procedures. This article analyzes important challenges for SPI in modern industrial environments: the adjunct role of SPI in product control, adaptiveness and flexibility of SPI, the role of prior information on product quality, the economic concern of SPI, and quality measurement as a purpose of SPI.
Sampling in Pharmaceutical and Chemical Industries
Authors: Melgaard Henrik
Published: September 2014

This article discusses the specific issues related to sampling in the pharmaceutical and chemical industry. The effect of measurement uncertainty in case of acceptance sampling by variables is one issue. The largest deterioration on the operating characteristics is seen from the low‐frequency error type. Sampling in bulk materials and retesting is also discussed. The trend in this industry is in the direction of faster measurement methods replacing off‐line by on‐line measuring and release.
Statistical Analysis of Survey Data
Authors: Ograjenšek Irena
Published: September 2014

After data collection and entry, survey data need to be prepared for analysis and analyzed. The data preparation stage involves three important components: data formatting, data editing, and computation of survey weights. The data analysis stage involves the choice of relevant statistical tools according to the measurement scale properties of survey variables.
Survey Quality and Survey Ethics
Authors: Djerf Kari
Published: September 2014

Producers of statistics have devoted considerable efforts to improve the quality of their products. Traditionally, surveys are annotated with quality descriptions providing the clients with support to interpret the results. Furthermore, there can be studies on the quality of the entire sample survey, calledquality reports. The clients often need more profound information on the organization, applied procedures and processes as well as the products. Thus, the approach is changing from a mere focus on product quality to total quality management (TQM).

This article describes various perspectives of survey quality, starting from traditional reporting and ending up with recent more comprehensive quality approaches.
Parallel, Series, and Series‐Parallel Systems
Authors: Agustin Marcus A.
Published: September 2014

This article will consider the system reliability of three different systems: series, parallel, and series–parallel systems. Interest is in finding the system reliability when the failure of each component depends on the length of time that the component is observed. Exponentially distributed failure times as well as Weibull failure times will be considered.
Reliability Optimization
Authors: Rigdon Steven E.
Published: September 2014

The goal of reliability engineering is to produce systems that have the highest reliability possible. In this article, we consider a number of ways that this optimization can be done, including design for reliability, reliability allocation, redundancy allocation, and system maintenance.
Repairable Systems: Statistical Inference
Authors: N. Agustin Ma. Zenia
Published: September 2014

This article discusses statistical inference procedures for a general class of models for repairable systems. In particular, estimation procedures as well as goodness‐of‐fit testing for an age‐dependent minimal repair model that incorporates covariates are presented. Examples involving real datasets are used to illustrate the applicability of the procedures.
Genetic Algorithms in Reliability
Authors: Coit David W. , Taboada Heidi A.
Published: September 2014

Genetic algorithms (GAs) have been effectively used to solve many difficult engineering problems and are particularly effective for solving combinatorial optimization problems with large, complex search spaces. The redundancy allocation problem (RAP) is perhaps one of the most common problems in design for reliability and it is known to be NP hard. Redundancy is used as a strategy to meet high reliability specifications in many system design engineering projects. In this material, we present an overview of some of the most relevant research that has been done on the use of GAs in the reliability optimization of redundant systems.
Intensity Functions for Nonhomogeneous Poisson Processes
Authors: McCollin Christopher
Published: September 2014

When analysing reliability data from a repairable system e.g. a car, a fridge, etc, reliability specialists are interested in the full life history of a system so that they may identify problems that have affected its life and apply solutions, if possible, to other new systems so that these new systems do not suffer from the same problems. The basis of reliability analysis is to understand how systems are failing by modeling their life history so that prediction of the likely future reliability of systems is possible. This is the basis of reliability growth (development) testing where systems under development are tested to find latent design and manufacturing defects so that they can be eliminated from the full‐scale production system.

The simplest way of identifying structure in the system's life history is to plot the data. Three plots are commonly used: plotting failures on a time line; plotting the failure number against cumulative time, and plotting an estimate of the intensity, the rate of occurrence of failures (ROCOF) against cumulative time. These plots appear in Ascher and Feingold [31] and Crowderet al. [61] among others. These plots will help to identify structure such as an increase or decrease in the interfailure times of a system over time (more commonly known as reliability growth and reliability decay); evidence of cycles in the data—these may be short or long cycles; periods of high or low reliability (again related to usage); gaps in the time stream (due to change in the reporting mechanism, management, etc) and outliers (possible abnormal operating conditions).

This review lists the intensity functions and their associated expected number of failures, which is the mean value parameter of the nonhomogeneous Poisson process (NHPP). The simplest and best known intensities, those based on mortality rates, those based on hazards of well‐known probability distributions, the software related intensities, and those based on differential equations and extensions are discussed under their appropriate classification headings.
Computational Issues in Network Reliability
Authors: Colbourn Charles J. , Shier Douglas R.
Published: September 2014

Systems of interconnected components can often be usefully represented by networks. It is practically important to calculate the reliability of such network systems when the components are subject to (statistically independent) failures. We define several commonly occurring reliability models and summarize the computational complexity of calculating their associated reliability measures. Some general techniques for exact and approximate calculation of network reliability are surveyed.
Cramér–Lundberg Asymptotics
Authors: Cai Jun
Published: September 2014

This article considers the Cramér–Lundberg asymptotics that include the Cramér–Lundberg asymptotic formula and the Lundberg inequality for ruin probabilities in various risk models. The generalizations of the Cramér‐Lundberg condition and asymptotics are discussed as well.
D
e
P
ril Recursions and Approximations
Authors: Sundt Bjørn
Published: September 2014

In this article, we present some recursive methods for exact and approximate evaluation of aggregate claims distributions in the individual model, that is, convolutions of distributions. We discuss the exact methods of De Pril and Dhaene–Vandebroek and the approximations of De Pril, Kornya, and Hipp. For the approximations, we give error bounds.
Heckman–Meyers Algorithm
Authors: Klugman Stuart A.
Published: September 2014

The collective risk model for aggregate losses states that total losses for a period comprise a random number of random payments where the payments have identical distributions and all variables are independent. Evaluating probabilities for this model can be difficult. The Heckman–Meyers Algorithm is one of several approaches to this problem. While computationally challenging, it is accurate and in many situations is extremely fast.
Lundberg Approximations, Generalized
Authors: Lin X. Sheldon
Published: September 2014

In this article, we briefly discuss generalizations to compound distributions of the classical Cramér–Lundberg approximation and bounds for the ruin probability.
S
undt and
J
ewell Class of Distributions
Authors: Panjer Harry H.
Published: September 2014

This article describes the Sundt and Jewell class of distributions and the related Panjer recursions.
Claim Number Processes
Authors: Garrido José
Published: September 2014

Risk theory models describe the uncertainty associated with the claims recorded by an insurance company for losses incurred by its policy holders. The claims frequency and the claims severity are two important components of these models. This article centers on models for the frequency of losses.

Even if an insurance company were able to maintain the exact same portfolio of policies over time, the number of claims recorded would still vary from year to year. Such natural fluctuations are modeled through the claim number random variable.

Over time, claim counts evolve according to a stochastic process: the claim number process. While other sections discuss specific claim number processes in greater detail, the general features are given here.
Claim Size Processes
Authors: Cheung Ka Chun , Yang Hailiang
Published: September 2014

This article is a survey of claim size processes. We present an overview of the renewal process model, and both the light‐tailed and the heavy‐tailed claim distributions are discussed. Recent developments in the insurance risk models in which the claim size processes are nonstationary or have dependence structure are also covered.
L
undberg Inequality for Ruin Probability
Authors: Yang Hailiang
Published: September 2014

This article surveys the main results and developments of Lundberg inequality for ruin probability. We briefly describe various insurance risk models in the literature, as well as the Lundberg inequality for ruin probability under these models. Finite time horizon insurance risk model and the effect of the invest income are discussed. We also mention some main results, including the Lundberg type inequality, for the severity of ruin, the distribution of surplus before ruin, and the joint distribution of surplus before and after ruin.
Seasonality
Authors: Stramer Osnat
Published: September 2014

This article considers development in estimating and removing seasonal components from an observable discrete‐time series.
Actuarial Control Cycle
Authors: Bellis Clare
Published: September 2014

The expression ‘Actuarial Control Cycle’ (ACC) is used in two ways: as a model to describe the fundamental nature of actuarial work, and as the name of a subject which since 1996 has formed Part 2 of the Australian actuarial education system. Its introduction as a subject was an important and influential educational innovation, and was the key to popularizing the ACC as a model of actuarial work. The development of the subject is recounted in this article.
Asset Shares
Authors: Forfar David O.
Published: September 2014

The article looks at asset shares, a concept primarily used in the United Kingdom in respect of with‐profits business but applicable to any policy where the bonus distribution is at the discretion of the insurance company.
Capital in Life Assurance
Authors: Forfar David O.
Published: September 2014

The article looks at the requirements for capital in a life company. The requirements for capital, over and above that are required to cover a valuation of the company's financial liabilities, depend on the strength of the valuation basis and the risks run by the company.
Disability Insurance
Authors: Pitacco Ermanno
Published: September 2014

We first describe types of disability insurance products and common policy conditions. Then a probabilistic model for insurance covers providing disability annuities is defined, adopting a time‐discrete approach. The construction of actuarial values, premiums, and reserves follows. A more general actuarial framework is finally sketched, using the multistate approach.
Life Insurance
Authors: Macdonald Angus S.
Published: September 2014

This article describes the main features and types of life insurance, meaning insurance against the event of death. Life insurers also transact annuity business.
Participating Business
Authors: David O'Brien Christopher
Published: September 2014

In participating life business, also referred to as ‘with profits’, there are policyholders with rights to share in the surplus (or profits) of the business. This means there are important issues in the management of such business, including how to price policies that contain such rights, how to determine the investments of the fund (given that the obligations to policyholders depend on the surplus that is earned), and how to assess the amount of surplus to be distributed. There is then the question of how to share surplus between the participating policyholders and, in a stock life insurer, the shareholders.
Social Security
Authors: Eriksen Tor
Published: September 2014

Social security is a concept that can be interpreted in many different ways and should therefore be used with the utmost caution.

Barr notes that in the United States, it refers to retirement pensions; in the United Kingdom, it refers to the entire system of cash benefits; and in mainland Europe (in accordance with the practice of the International Labor Organization), it refers to all cash benefits plus health care.

Barr chooses to describe the security system by examining the purpose of the various cash benefits.

Universal benefits awarded on the basis of a specified event, without regard to a person's income or contribution record. Examples include family allowance and free health care.

Social assistance awarded on the basis of an income test and the occurrence of a specified event, without a contribution test.

Consequently, social security can be seen as an accumulative concept for different systems that provide economical compensation in the case of illness, unemployment, old age, and so on.
Reserving in Non‐Life Insurance
Authors: Hesselager Ole , Verrall Richard
Published: September 2014

This article summarizes the issues in reserving for non‐life insurance. The basic terms are defined, and some of the most frequently used approaches are introduced. Introductions are given to further articles in this Encyclopedia on specific methods for reserving, and some of the practical issues are discussed.
Markov ChainMonteCarlo Methods
Authors: Roberts Gareth O. , Rosenthal Jeffrey S.
Published: September 2014

One of the simplest and most powerful practical uses of the ergodic theory of Markov chains is in Markov chain Monte Carlo (MCMC). Suppose we wish to simulate from a probability density π (which will be called thetargetdensity) but that direct simulation is either impossible or practically infeasible (possibly due to the high dimensionality of π). This generic problem occurs in diverse scientific applications, for instance, Statistics, Computer Science, and Statistical Physics.

Markov chain Monte Carlo offers an indirect solution based on the observation that it is much easier to construct an ergodic Markov chain with π as a stationary probability measure, than to simulate directly from π. This is because of the ingeniousMetropolis–Hastingsalgorithm, which takes an arbitrary Markov chain and adjusts it using a simple accept–reject mechanism to ensure the stationarity of π for the resulting process.
Simulation of Stochastic Processes
Authors: Asmussen Søren
Published: September 2014

In order to gain insight into the role played by the stochastic ingredients in insurance and finance, one is often forced to rely on simulation as no explicit analytic results are available. There exist a few general methods, but the generation on computer for most models requires non‐trivial and complicated operations that heavily depend on the specific structure of the underlying stochastic elements.
Simulation of Risk Processes
Authors: Burnecki Krzysztof , Härdle Wolfgang , Weron Rafał
Published: September 2014

The simulation of risk processes is a standard procedure for insurance companies. The generation of aggregate claims is vital for the calculation of the amount of loss that may occur. Simulation of risk processes also appears naturally in rating triggered step‐up bonds, where the interest rate is bound to random changes of the companies' ratings.
Beta Function
Authors: Drekic Steve
Published: September 2014

This article summarizes some of the key mathematical/computational properties associated with the beta function and incomplete beta function, which find use in applications to probability theory and parametric claims modeling.
Empirical Distribution
Authors: Klugman Stuart A.
Published: September 2014

When constructing probability models, it may be sufficient to let the data speak for itself. That is, the model is designed to look like the data, the assumption being that the data is of sufficient quantity and quality to adequately represent the population. Such models are called empirical distributions.
Esscher Transform
Authors: Yang Hailiang
Published: September 2014

This article surveys the main results and developments of Esscher transform. We first present the original idea of Esscher and its applications to the problem of approximating the tail probabilities. The Esscher transform applied to the premium calculation, the Esscher premium principle, is then discussed. Recently, the Esscher transform has been applied to finance to tackle the problem of option pricing. Following Gerber–Shiu's framework, we provide an overview on this interesting development.