bluuebunny/crossref_metadata_2025 huggingface dataset:
Calibration, issues in
Authors: Bzik Thomas J.
Published: September 2014

Calibration establishes and standardizes common units of measurement for commerce and scientific study. Through calibration the measured item or sample is related to items or samples with known properties, the standards. Statistical methods are typically used to identify and quantify the form of the relationship between sample measurements and one or more standards. They are also used to evaluate the accuracy and precision of the current as well as alternative measurement methods. Statistical tools are also used to determine the optimal frequency of recalibration as well as the frequency with which calibration should be checked. Calibration models can take the form of linear relationships or a nonlinear relationship. Two‐variable calibration models are often monotonic in their form. While many calibration models often involve only two variables, they can be multivariate in nature. Keeping bias out of calibration models requires not only selecting the correct model form but also ensuring that the model is fit, using an appropriate optimization criteria. Calibration models typically provide very high explanatory powers as compared to other typical scientific modeling applications such as plant or process optimization studies. Calibration models also typically yield extremely good levels of statistical significance. Current common statistical toolsets used in calibration studies are often not well structured for handling the actual, and sometimes complex, error structures that occur in routine application of calibration.
Life Cycle Costs and Reliability Engineering
Authors: Elsayed Elsayed A.
Published: September 2014

This chapter presents the life cycle cost (LCC) and relates it to product or system reliability. It discusses LCC through the product life phases beginning with the design phase and ending with warranty and field operation phase. It demonstrates how decisions in every phase directly or indirectly affect the LCC over the product life. Determinations of optimal process parameters or decision that minimize the LCC are demonstrated through examples in different phases of the product life cycle.
Multiattribute Warranty Policies
Authors: Chun Young H.
Published: September 2014

Warranties have been important elements in business planning and decision making for manufacturers of products and producers of services, and this will continue to be the case in years to come. In this article, we introduce various types of single‐attribute and multiattribute warranty policies, and review different modeling approaches with an emphasis on two‐attribute warranty plans. Some suggestions for future research are also provided.
Inspection Policies for Reliability
Authors: Baker Rose D.
Published: September 2014

The rôle of inspections in improving reliability is discussed, and a distinction is drawn between inspections of standby equipment, that “waits to work”, and inspections of equipment such as a production line that is in continuous use. Simple examples of both situations are given, and some of the complexities of the various models used are discussed and referenced. It is stressed that models are valueless for practical purposes without checking that they are appropriate, and without estimation of their parameters.
Replacement Strategies
Authors: Popova Elmira , Popova Ivilina
Published: September 2014

We define what is a replacement policy for a system that fails randomly in time and its main characteristics. There are several parameters that drive the structure of the optimal policy. We provide a detailed discussion of the time horizon, objective functions, and failure time distributions as part of any replacement policy.
Imperfect Repair
Authors: Hollander Myles , Samaniego Francisco J. , Sethuraman Jayaram
Published: September 2014

The notion of “imperfect repair”, as introduced by Brown and Proschan, is reviewed, and generalizations by Block, Borges and Savits and by Kijima are discussed. Basic properties of these models are highlighted, including the proportional hazards property of the time until first perfect repair and a number of preservation properties enjoyed by these models. The authors summarize the published work on statistical inference based on data assumed to follow an imperfect repair model (i.e., given failure times plus mode of repair indicators), including constrained and unconstrained nonparametric maximum likelihood estimation and estimation
via
nonparametric Bayes methods.
Load‐Sharing Models
Authors: Kvam Paul H. , Lu Jye‐Chyi
Published: September 2014

Load sharing describes how the failure probabilities of components within a system depend on the working status of the other components. For example, if a component fails in the system, the other components may experience an increase in failure rate by inheriting an extra “load” from the failed one. Load sharing has its roots in stress‐strength models for fiber bundles, but extends to many time‐to‐failure test environments, including software reliability and materials testing. Load‐share rules characterize how the load changes after a component within the system fails, and can be estimated if unknown.
Maintenance Optimization
Authors: Mazzuchi Thomas A. , Noortwijk Jan M. , Kallen Maarten‐Jan
Published: September 2014

Maintenance optimization is the problem of determining cost‐optimal maintenance decisions for a system or structure to ensure a safe and economic operation. An important concept in maintenance optimization is that of life‐cycle costing, where the total costs of design, building, maintenance, and demolition are considered over the entire life span of the system or structure in question. In optimizing maintenance, the uncertainties in the time to failure and/or the deteriorating condition should be taken into account. Proper stochastic deterioration models are Markov processes with independent increments (e.g., gamma processes) and Markov decision processes. This chapter reviews mathematical decision models to optimize time‐based maintenance (e.g., in terms of age‐ and block‐replacement intervals) and condition‐based maintenance (e.g., in terms of inspection intervals). Using renewal theory, optimal maintenance decisions under uncertain deterioration can be determined for which the expected nondiscounted cost per unit time or the expected discounted cost over an unbounded time horizon is minimal. Using Bayesian statistics, these optimal maintenance decisions can be adapted on the basis of observations.
Multivariate Imperfect Repair Models
Authors: Ebrahimi Nader
Published: September 2014

Brown and Proschan introduced univariate imperfect repair models, in which a system, upon failure, is replaced with a new one with probability α (perfect repair), and is minimally repaired with probability 1 − α (imperfect repair). This article deals with multivariate versions of imperfect repair models for systems ofkcomponents with dependent lifetimes.
General Minimal Repair Models
Authors: Aven Terje
Published: September 2014

Minimal repairs have been given considerable attention in the reliability literature. A minimal repair restores the system to the state it had just before failure. But the state just before failure depends on the information that is available about the system. This article presents general models for analyzing such repairs, using a point process framework and taking into account the information available about the state of the system. Several examples demonstrate the wide range of applications.
Multistate Reliability Theory
Authors: Natvig Bent
Published: September 2014

An inherent weakness of traditional reliability theory (
see
Coherent Systems
) is that the system and the components are always described either as functioning or failed. Early attempts to replace this by a theory of multistate systems for multistate components were made in the late 1970s. By the mid‐1980s the basic theory in this area was established. The objective of this article is to introduce concepts of multistate systems and present some upper and lower bounds for the availabilities and unavailabilities, to any level, in a fixed time interval. A series of applications of multistate reliability theory have been suggested during the last years. For example, the theory enables one to consider applications in electrical power generation systems, where the system state is the amount of power generated by the system or in offshore gas pipeline networks, where the system state is the amount of gas delivered.
Masked Failure Data: Competing Risks
Authors: Basu Sanjib
Published: September 2014

The competing‐risks model considers a setting when a system is exposed to multiple risks and a system failure can be caused by one of the multiple risks. The case of masked causes arises when the causes of failure for some of the systems are not completely identified but are narrowed down to a subset of the potential risks. This article provides a selective review of statistical models and methods for analysis of competing‐risks data with or without masking in the context of reliability applications. Latent failure times and cause‐specific hazards provide two parallel approaches to competing‐risks models; identifiability issues in these models in both nonparametric and parametric settings are discussed. For the case of masked data, recent developments in both likelihood‐based and Bayesian approaches are reviewed. A special emphasis is given to the treatment and models for the masking probabilities. The article concludes with a review of different reliability applications.
Age‐Dependent Minimal Repair and Maintenance
Authors: Sheu Shey‐Huei , Chien Yu‐Hung
Published: September 2014

This article presents and discusses two generalized maintenance replacement policies (policy 1 and 2) for a system with two types of failures, when it fails. Type I failure is assumed to be minor and can thus be rectified through minimal repair. Type II failure is catastrophic and can only be removed by replacement. Under policy 1, a system is replaced at the
n
th type I failure or first type II failure or at age
T
, whichever occurs first. Under policy 2, if an operating system fails before time
t
, it is either replaced by a new system (type II failure) or it undergoes minimal repair (type I failure); otherwise, the system is replaced when the first failure after
t
occurs or the total operating time reaches age
T
(0 ≤ 
t
 ≤ 
T
), whichever occurs first. Type I and type II failures are age dependent. The cost of the
i
th minimal repair of a system at age
y
depends on the random part
C
(
y
) and the deterministic part
c

i

(
y
). The expected cost rates for operating a system under policy 1 and 2 in the long run are obtained, respectively. The optimal (
n
*,
T
*) for policy 1 and optimal (
t
*,
T
*) for policy 2, which minimize the corresponding cost rate are derived and discussed. Various special cases are included and numerical examples are finally demonstrated. Because the models and its analysis are general, several existing results are shown to be subsumed by these two models.
Repair Data, Sets of: How to Graph, Analyze, and Compare
Authors: B. Nelson Wayne
Published: September 2014

Many products accumulate repeated repairs and repair costs over time. Analysis of such recurrence data requires special statistical models and methods not covered in basic reliability books. This article presents a simple and informative model and plot for analyzing data on numbers or costs of repeated repairs of a random sample of units. The plot is illustrated with transmission repair data from preproduction cars on a track test. This article also presents a method for comparing two such datasets, illustrated with automatic and manual transmissions. Computer programs that calculate and make the plots and comparisons with confidence limits are surveyed.
Accelerated Life Tests:Bayesian Design
Authors: Soyer Refik
Published: September 2014

In this article, the Bayesian decision theoretic setup for design of accelerated life tests (ALT) is presented. Some of the key contributions to the Bayesian design of ALT are reviewed. While doing so, approximate Bayesian designs based on linear Bayesian methods and Monte Carlo–based methods are discussed. Computational issues in the evaluation of expectation and optimization steps in the solution of the decision problem are considered and some recent Monte Carlo approaches that can reduce the computational effort in the design problem are discussed.
Accelerated Life Tests: Stress Step (Classical Methods)
Authors: Nikulin Mikhail
Published: September 2014

In this chapter we consider the accelerated models describing dependence of the lifetime distribution on the step stresses. Such models are often used in reliability and survival analysis to study the reliability of highly reliable, complex technical and biotechnical systems in dynamic environments.
Accelerated Life Tests: Analysis with Competing Failure Modes
Authors: Bunea Cornel , Mazzuchi Thomas A.
Published: September 2014

Most of the accelerated life tests (ALT) ignores the possibility of competing modes of failure. The literature that attempts to address this problem often does so by assuming independence among the competing failure modes. Rather, the failure modes display a highly dependent structure, which is usually influenced by the applied stress. The dependent ALT‐competing risks models available are based on multivariate distributions with specified marginals. However, multivariate exponential and Weibull distributions—dominant in literature—have properties not suited for all applications. This article investigates the applicability of existent independent and dependent models on a couple of datasets, and presents a new ALT model with dependent competing failure modes. The dependence structure is modeled by a copula given the rank correlation. The effects of the dependence degree of the competing failure modes are also studied.
Prediction of Expected Fatigue Lives of Fiber Reinforced Plastic Joints
Authors: Momenkhani Kourosh , Sarkani Shahram
Published: September 2014

This paper scrutinizes the accuracy of the application of the probability distribution functions for predicting the fatigue lives of different fiber reinforced plastic (FRP) joints under variable loading. Three different joint configurations (bonded, bolted, and bonded‐bolted) were tested under constant‐ and variable‐amplitude fatigue loading. The constant‐amplitude fatigue test results were analyzed in both log‐log and semi‐log scales. From there, Rayleigh approximation and Gaussian cumulative functions were used to predict expected fatigue lives. This study shows that even though Rayleigh approximation provides better fatigue lives than Gaussian cumulative function for higher root‐mean‐square (RMS) levels, it falls behind in predicting fatigue lives in lower RMS levels. However, both methods are weak in approximating the experimental fatigue lives.
Design for Reliability
Authors: Pecht Michael
Published: September 2014

Design for reliability (DfR) requires that certain practices be followed to ensure the appropriate level of product reliability is obtained. This chapter discusses some of the key DfR practices and their impact on life cycle reliability.
Software Failure Data Analysis
Authors: Kenett Ron S.
Published: September 2014

Effectively and efficiently analyzing software failure data is critical to competitive organizations developing software. This article covers several methods used to analyze such data, with examples. The methods covered include software reliability models for predicting the number of hidden faults, software trouble assessment for assessing the inspection process, Pareto charts of software errors, and control charts for tracking the weekly number of new and fixed bugs.
Life Testing from a
B
ayesian Perspective
Authors: Pulcini Gianpaolo
Published: September 2014

Life testing provides to the Bayesian analyst new information, which may lead to the revision of a belief held prior to observing the experimental data (
learning from experience
). The revised belief, expressed in terms of a posterior probability, constitutes the inferential result. Clearly, in a decision‐making approach, revising belief leads the expert to confirm or change the choice that would have been made among alternative courses of action on the basis of prior belief only. The way in which the observed data modify the current belief is formalized by Bayes theorem. As newer data is observed, today's posterior information becomes tomorrow's prior information, so that each time new observed data come in the current belief can be revised.

Clearly, the effect of life testing in updating expert belief depends on the size of the observed sample and on the manner in which the data have been collected, i.e. on the
design of life testing
. In a Bayesian perspective the choice of life testing design is made by optimizing the design with respect to a given overall loss function, which is the sum of a
decision loss
, associated with the need of making a decision under uncertainty, and a
sampling cost
, representing the cost of collecting life testing data.

Simple examples illustrate the Bayesian learning process and design optimization.
Resampling for Lifetime Distributions
Authors: Belyaev Yuri K.
Published: September 2014

In many applications, data sets contain lifetimes of occurred events, e.g., times of failures, diagnoses, censorings, and so on. If we want to use an estimator of a lifetime characteristic of interest, then it is necessary to evaluate the accuracy of this estimator. Resampling methods can be efficiently used to evaluate the accuracy of many estimators if the size of the data with lifetimes is sufficiently large. They are feasible for realization on personal computers. Correctly applied resampling methods give asymptotically consistent evaluation of the accuracy of estimators under certain assumptions as the size
n
of the data unboundedly grows. The basic tools of mathematical statistics, the likelihood and the central limit resampling theorem, are used to justify resampling methods.
Polya Trees and Their Use in Reliability and Survival Analysis
Authors: Hanson Timothy E.
Published: September 2014

The nonparametric Polya tree prior generalizes traditional parametric models such as the Weibull family. Relative to other well‐known priors, such as Dirichlet, gamma, and beta processes, Polya trees have seen more limited use. However, the Polya tree prior has several attractive features, including the existence of survival densities and the ability to be incorporated in different semiparametric models.
Sampling Inspection of Products
Authors: Göb Rainer
Published: September 2014

Product assessment by inspection is a traditional tool of industrial quality control. Statistical product inspection (SPI), also calledacceptance sampling, is product assessment by sampling inspection. Appropriately conceived, SPI continues to be a valid tool of quality control in modern industrial environments. The article analyzes the basics of SPI in several aspects: history, position of SPI in modern quality control, quality modeling, sampling and its statistical analysis, design of SPI schemes.
Sampling in Industrial Standards
Authors: Palcat Frank
Published: September 2014

This article reviews the history leading up to the development of the first sampling‐related standards from research in the 1920s following through to the very formative years of World War II and beyond. The transition in subsequent years from military‐specific standards to national standards and then to international standards is also covered. Finally, the array of sampling inspection standards currently available from the International Organization for Standardization (ISO) is briefly reviewed.
Rectification Sampling Schemes
Authors: Göb Rainer
Published: September 2014

Statistical sampling plans lead to a decision between accepting or rejecting a lot. Rejection calls for some extraordinary intervention into the routine business flow. A specific type of intervention consists in a more extensive inspection of the lot with the aim of
rectification
, i.e. removing or replacing detected items of inappropriate quality. Sampling schemes with a rectification interpretation of rejection are called
rectification schemes
. The article introduces the procedures and performance measures of rectification schemes. The well‐known
Dodge–Romig rectification scheme
is analyzed in detail.
Reliability Sampling
Authors: Hryniewicz Olgierd
Published: September 2014

Reliability sampling is a part of acceptance sampling dedicated to the control of those quality characteristics of a product, which are related to its functioning in time. Therefore, in reliability sampling we are interested in such quality characteristics of a product as: mean time to failure (MTTF), mean time between failures (MTBF), probability of good performance during a specified mission time, and so on. The aim of the reliability sampling procedures, known as
sampling plans
, is to provide means for testing requirements related to these characteristics. In the article we present reliability sampling plans by attributes and variables, which are useful in reliability practice. For sampling plans by variables, we present procedures valid in cases of the exponential and the Weibull distributions of lifetimes. We consider different types of sampling plans with different types of censoring. Special attention is devoted to procedures described in international standards related to reliability.
Attributes Sampling under Classification Error
Authors: Greenberg Betsy S.
Published: September 2014

Inspection, particularly acceptance sampling, is an important aspect of quality control. An acceptance sampling plan is one in which a specified number of units is sampled from each lot, with the lot being accepted if fewer than a fixed number of nonconforming items are found in the sample. However, inspection errors are inevitable. Inspection procedures may commit two types of errors. Items that are classified as nonconforming may be conforming (false positive) and conforming items may be classified as nonconforming (false negative). These errors affect the number of nonconforming items that are identified as well as the outgoing quality obtained from acceptance sampling plans.
Database Systems for Acceptance Sampling
Authors: Lenz Hans‐J.
Published: September 2014

Data collected in on‐line or off‐line quality control are no longer read into files owned by single departments but are stored in a database system. The data can be accessed according to the user's view (profile) and his read/write rights. The use of such operative data is called
on‐line transaction processing
(OLTP). It is of interest to low ranked officers responsible for administrative tasks and concerned with workflows like incoming batch inspection. Middle managers need data for planning and decisions, i.e., for “on‐line analytical processing” (OLAP), where grouped and aggregated data are mandatory. Such databases are called
data warehouses
and the managers' views are known as
data marts
. The main design ideas of such systems are presented.
Sampling from Virtual Populations
Authors: Polansky Alan M.
Published: September 2014

The increasing complexity of the problems addressed in modern statistical inference has created many situations where a closed‐form analytical solution is not available. For example, when constructing a rejection region for a hypothesis‐testing procedure, the sampling distribution of the test statistic under the null hypothesis may not have a closed form, even when the exact form of the population is known. In nonparametric situations where the population may not be known, estimates of the sampling distribution of a test statistic or parameter estimate computed using the bootstrap often do not have a closed form. The use of empirical approximations based on simulated realizations of the random process that produces the observed data have been implemented for many years. Almost universal access to computers has made such simulations easy to perform. The purpose of this article is to review the most common methodologies for performing these simulations.
Adaptive and Spatial Sampling Designs
Authors: Siegfried Gabler
Published: September 2014

On the one hand, spatial and adaptive sampling designs are informative since they depend on the characteristic of interest—in contrast to the classical sampling designs such as simple random sampling. On the other hand, better results can be obtained using adaptive designs for populations with special patterns. Dealing with spatial inferences, model‐based approaches are often used. The fixed‐population approach is replaced by a stochastic one. The characteristic of interest is defined for a continuous region of space and time that can be described by a spatial stochastic process.
Selection and Validation of Response Scales
Authors: Ograjenšek Irena
Published: September 2014

Measurement is defined as a set of rules for assigning either numbers or numerals to empirical properties of a concept under consideration. Concepts can be operationalized as variables with different properties of measurement scale: nominal, ordinal, interval, and ratio. The level of measurement determines which mathematical operations are possible on a variable, which, in turn, define the tools of statistical analysis at researchers' disposal.

Specific measurement tools applicable in the survey setting include list questions, category questions, ranking questions, and rating or scale questions. We want these measures to be reliable and valid, capturing what they are supposed to capture.

In the process of measurement, data can be obtained either in formal or informal settings and can represent verbal (oral and written) as well as nonverbal acts and/or responses. In order to minimize the possible effect of the chosen data collection method on the validity and/or scope of the research findings, researchers can use two or more methods of data collection to test hypotheses and measure variables; this is the essence of the so‐called triangulation.
Processing of Survey Data
Authors: Biemer Paul P.
Published: September 2014

Upon completion of data collection, the survey data must be converted from its raw and unedited state to a verified and corrected state that is ready for analysis and/or dissemination to the users. These steps may include questionnaire inspection, data entry, editing, coding, data preparation, documentation, and data analysis. This chapter discusses these steps as well as their potential effect on data quality.
Survey Error
Authors: Reiter Jerome P.
Published: September 2014

In survey samples, the primary objective usually is to estimate unknown population quantities, such as population means or totals. The estimates invariably do not exactly equal the population values, i.e. there are survey errors. This article reviews the main sources of survey errors and general approaches to reducing them.

Survey errors can be classified in two categories,
nonsampling
and
sampling
errors. Common sources of nonsampling error include measurement error, coverage error, mode effect error, nonresponse error, and process error. Measurement error occurs when respondents misinterpret, cannot answer, or inaccurately answer questions. Coverage error occurs when the list used to take the sample does not correspond to all units in the target population. Mode effect error occurs when the way the data are collected influences responses. Nonresponse error occurs when those who do not respond to a survey differ from those who respond to it. Process error occurs when edits, recodes, or other data processing steps go awry. Nonsampling errors are hard to detect and quantify. Their impact can be reduced by careful survey design. Sampling errors occur because only subsets of populations are measured, and estimates vary by sample. Sampling errors arise in every survey, but they are quantifiable.
HierarchicalMarkov ChainMonteCarlo (MCMC) forBayesian System Reliability
Authors: Wilson Alyson G.
Published: September 2014

Hierarchical models are one of the central tools of Bayesian analysis. They offer many advantages, including the ability to borrow strength to estimate individual parameters and the ability to specify complex models that reflect engineering and physical realities. Markov chain Monte Carlo (MCMC) is a set of algorithms that allow Bayesian inference in a variety of models. We illustrate hierarchical models and MCMC in a Bayesian system reliability example.
Path Sets and Cut Sets in System Reliability Modeling
Authors: Tortorella Michael
Published: September 2014

This article reviews the concepts of connectedness, path sets, and cut sets in the context of analyzing a system reliability block diagram described as a labeled random graph. The methods discussed also lend themselves to the development of bounds for system reliability. Directions for generalization to capacitated networks are given.
Component Reliability Importance
Authors: Rigdon Steven E.
Published: September 2014

The concept of reliability importance gives a measure of how much changes in the reliability of a particular component of a coherent system affects the reliability of the system. The definition of the importance of component
k
is
I
(
k
) = ∂
r
(

p

)/∂
p

k

, where

p

is the vector of component reliabilities and
r
(

p

) is the system reliability function. Examples of the reliability importance for common systems are given. The structural reliability importance is also given, along with its relationship to the reliability importance.
Reliability of Redundant Systems
Authors: Pham Hoang
Published: September 2014

This articles provides a brief concept of how to evaluate the reliability of redundant systems with various aspects including dynamic redundancy, imperfect coverage, fail‐safe redundancy, noncoherent systems, degradable redundancy, multiple failure modes,k‐out‐of‐nsystem redundancy, weighted systems, and load‐sharing redundancy.
Stress‐Strength Model
Authors: Basu Asit P.
Published: September 2014

In this paper, we consider estimation of reliability for stress‐strength models. Nonparametric, parametric, and Bayesian inferences are considered. The problems related to the exponential distribution are given in detail.
Fault Trees
Authors: Bartlett Lisa M.
Published: September 2014

The ability to analyze how failures occur and determine their likelihood of occurrence is fundamental in maximizing the functionality of a system. To achieve this, a technique such as fault tree analysis is required. The technique can be used to carry out a qualitative analysis, namely, identifying the failure events that contribute to the system failure, and a quantitative analysis, calculating numerical statistics relating to the system, for example, the probability of failure. This article provides an introduction to the technique and its analysis potential.
System Reliability:
M
onte
C
arlo Estimation
Authors: Rigdon Christopher J. , Rigdon Steven E.
Published: September 2014

Monte Carlo methods are useful for a number of situations in reliability. First, for very complex systems, it is difficult to determine the system reliability even if the component reliabilities are known. This can be done by simulating the performance (operating/failed) of each component, and determining the status of the system given the performances of these components. Second, the system reliability can be estimated when component reliabilities are estimated from pass/fail data. Uncertainties in the resulting estimate of system reliability can be obtained
via
Monte Carlo simulation. Third, many questions of availability (or other measures of system performance) can be treated using queuing theory. Since queuing models can become intractable, especially when times between events or repair times are not exponential random variables, Monte Carlo methods can be used.
System Reliability: Computational Algebra Methods
Authors: Leemis Lawrence M.
Published: September 2014

Computer algebra systems are useful in calculating system reliability. We use several diverse examples to illustrate how a computer algebra system can be helpful in determining system reliability. The examples presented here are (a) analyzing a
k
‐out‐of‐
n
system; (b) determining the mean time to failure of a parallel system with symbolic parameters; (c) determining the conditional survivor function for a system with a piecewise survival distribution; (d) determining the probability of mission success for a unit and two cold standby units; (e) determining a lower confidence bound on the system reliability from binary failure data collected on each of the independent components in a coherent system
via
bootstrapping; and (f) determining the exact distribution of a popular goodness‐of‐fit test statistic.
Reliability, Safety, and Risk Management
Authors: Cox Sue
Published: September 2014

The aim of this paper is to present a brief exposition on the connection between safety and reliability. The author adopts an approach that is described in full in the bookSafety, Reliability and Risk Management: An Integrated Approach. This book was designed to support students and practitioners in the development of their understanding of safety and its links to reliability. The text is structured around a systems approach to safety, reliability, and risk management and highlights a number of practical tools that practitioners have used to identify and manage risk. This approach is compatible with the current development of risk management theory, both in relation to public decision making and loss prevention strategies.
Block Replacement
Authors: Dekker Rommert
Published: September 2014

Block replacement is the replacement of a block of components at fixed time intervals. Its aim is to prevent failures, which can have severe negative consequences, both with respect to economics and safety. It is appropriate if components exhibit an increasing failure rate. A main problem is to determine the optimal replacement time. For this purpose the block‐replacement model has been formulated. We discuss how the optimum replacement time can be computed and we compare block replacement with some other policies.
System Downtime Distributions
Authors: Pievatolo Antonio
Published: September 2014

System downtime distributions are useful for determining economic or safety performance measures of a system. We consider system downtime in an interval and after a failure. We try to give expressions that can be readily programmed using only information on failure and repair time distributions of every single component of the system. For this reason, all such expressions are of asymptotic nature. We deal with systems of independent binary components in detail, whereas we mention only briefly (also indicating references) the tools that can be used for systems with multistate components.
Repairable Systems:
B
ayesian Analysis
Authors: Rigdon Steven E.
Published: September 2014

The Bayesian approach to analyzing data from repairable systems is presented in this chapter. Specifically, the homogeneous Poisson process and the power law process, a nonhomogeneous Poisson process with intensity equal to λ(
t
) = (β/θ)(
t
/θ)
β−1
,
t
 > 0, are studied. Other models, such as the renewal process, follow a similar pattern. Also, measures of system performance, such as availability, are discussed, where the Bayesian approach provides a convenient way to combine uncertainties. For multiple copies of a repairable system, we discuss empirical Bayes and hierarchical Bayes methods.
Queues in Reliability
Authors: Ausín M. Concepción
Published: September 2014

Queuing models can be useful in solving many complex reliability problems. Component failures are usually interpreted as the arrival of customers and the repair or replacement of failed components is typically associated with the service facility. A distinctive characteristic of queues in reliability is that requests for service are usually generated by a finite customer population because, in general, there are a limited number of units, e.g., machines which can fail, and when they are all in the system, being repaired or waiting for repair, no more can arrive. Thus the arrivals do not form a renewal process as they may depend on the number of units in the system. This is an essential difference from typical queuing systems, where the population of potential arrivals can be considered to be effectively limitless. This article gives an overview of the main queuing models used in reliability which are illustrated using the classical machine repairmen model. Some statistical methods to estimate the main quantities of interest in a queue are also discussed.
Imperfect Repair, Counting Processes
Authors: Rigdon Steven E.
Published: September 2014

Models for repairable systems are often categorized by the effect of a failure/repair on the subsequent performance of the system. This article looks at various assumptions regarding this effect. Models for minimal repair, renewal, imperfect repair, and various others are included.
Reliability Allocation
Authors: Malaiya Yashwant K.
Published: September 2014

A system is generally designed as an assembly of subsystems, each with its own reliability attributes. The overall system reliability is a function of the subsystem reliability metrics. The cost of the system is the sum of the costs for all the subsystems. This article examines possible approaches to allocate the reliability values such that the total cost is minimized. The problem is very general and is applicable for mechanical systems, electrical systems, and computer hardware and software. The problem involves expressing the system reliability in terms of the subsystem reliability values and specifying the cost function for each subsystem, which allows setting up an optimization problem. Software reliability allocation is examined as a detailed example. The article also examines some preliminary apportionment approaches that have been proposed. In some cases, it is possible to use exact optimization methods. In general, a complex case will require use of iterative approaches.
S
ix
S
igma Method
Authors: Does Ronald J.M.M. , De Mast Jeroen
Published: September 2014

Six Sigma is built on principles and methods that have proven themselves over the twentieth century. It has incorporated the most effective approaches and integrated them into a full program. It offers a management structure for organizing continuous improvement of routine tasks, such as manufacturing, service delivery, accounting, nursing, sales, and other work that is done routinely. Further, it offers a method and tools for carrying out improvement projects effectively.
Dependent Risks
Authors: Denuit Michel , Dhaene Jan
Published: September 2014

In risk theory, all the random variables (r.v.s, in short) are traditionally assumed to be independent. It is clear that this assumption is made for mathematical convenience. In some situations however, insured risks tend to act similarly. In life insurance, policies sold to married couples involve dependent r.v.s (namely, the spouses' remaining lifetimes). Another example of dependent r.v.s in an actuarial context is the correlation structure between a loss amount and its settlement costs (the so‐called ALAE's). Catastrophe insurance (i.e. policies covering the consequences of events like earthquakes, hurricanes or tornados, for instance), of course, deals with dependent risks.
Individual Risk Model: Overview
Authors: Dhaene Jan , Vyncke David
Published: September 2014

In the individual risk model, the total claims amount on a portfolio of insurance contracts is the random variable of interest. The total claims is modeled as the sum of all claims on the individual policies, which are assumed independent. We present several techniques, such as convolution and recursions, to obtain results in this model.
Stop‐Loss Premium
Authors: Cai Jun
Published: September 2014

This article considers stop loss premiums and related topics appearing in insurance.
Adjustment Coefficient
Authors: Kaas Rob
Published: September 2014

The adjustment coefficient is the number
R
appearing in the famous Lundberg upper bound: in a compound Poisson risk process with initial capital
u
 ≥ 0, the ruin probability, ψ(
u
), is bounded by e

−
Ru

. By changing the safety loading or the distribution of the individual claims that are involved in its definition, the value of
R
and with it the ruin probability can be adjusted.
Cramér‐Lundberg Condition and Estimate
Authors: Yang Hailiang
Published: September 2014

This article surveys the main results and developments of Cramér–Lundberg approximation. We present an overview of the classical results under the Lundberg–Cramér model, and the corresponding results in the cases of heavy‐tailed claim distribution are discussed. Recent developments in the diffusion perturbed insurance risk models and in the model in which an α‐stable Levy process is added to the compound Poisson process are covered.
Early Warning Systems
Authors: Wong Johnny
Published: September 2014

An early warning system provides information to insurers for monitoring their financial stability and soundness, and to regulators for identifying those insurers who may become insolvent so that early remedial actions can be taken. It normally uses a solvency measurement system, which values the excess of assets over liabilities. A dynamic solvency measurement system, which evaluates the insurers' ability to remain solvent in the future under varying conditions, is preferred over a static solvency measurement system, which determines solvency at a particular valuation date. A good early warning system should also balance the interests of consumers, policyholders, insurers, and shareholders.
Risk Minimization
Authors: Møller Thomas
Published: September 2014

Risk minimizationis a theory from mathematical finance that can be used for determining trading strategies. The theory of risk minimization was instituted by Föllmer and Sondermann who essentially suggested the determination of trading strategies for a given liability by minimizing the variance of future costs defined as the difference between the liability (or claim) and gains made from trading on the financial market.
Severity of Ruin
Authors: Tsai Cary Chi‐Liang
Published: September 2014

In this article, continuous‐time risk models are introduced; the time of ruin, and the surplus immediately before and at ruin caused by a claim are defined. Then the probability of ruin, the (discounted) moment of the severity of ruin caused by a claim, the joint moment of the severity of ruin and the time of ruin caused by a claim, and the (discounted) defective joint/marginal distribution and probability functions of the surplus immediately before and at ruin are studied.
Surplus Process
Authors: Schmidli Hanspeter
Published: September 2014

In this article, we discuss the ideas behind modeling actuarial surplus processes in continuous time. Several models that have been treated successfully in the literature are reviewed.
Time of Ruin
Authors: Tsai Cary Chi‐Liang
Published: September 2014

In this article, both classical discrete‐ and continuous‐time risk models are introduced; then the time of ruin and the severity of ruin are defined. The probability of ruin and some quantities concerning the time of ruin, such as the expectation of the present value of the time of ruin, the (discounted) moment of the severity of ruin caused by a claim, the joint moment of the severity of ruin, and the time of ruin caused by a claim, and the moments of the time of ruin due to oscillation and claim, respectively, are studied.
Assets in Pension Funds
Authors: Bowie David
Published: September 2014

In countries with large scale private and public funded pension arrangements, for example, the United States, Canada, Japan, the Netherlands, and the United Kingdom, one of the key decisions is how the contributions into the fund should be invested to best effect. The investment decision typically results in some form of risk sharing between members and sponsor in terms of (1) the level of contributions required to pay for all promised benefits, (2) the volatility of contributions required, and (3) the uncertainty of the level of benefits actually deliverable should the scheme be wound up or have to be wound up. Some of the risks associated with the pension benefits have a clear link with the economy and hence with other instruments traded in the financial markets. Others, such as demographic risks and the uncertainty as to how members or the sponsor will exercise their options, which are often far from being economically optimal, are less related to the assets held in the fund.

This article describes broadly what assets are available to the institutional investor, how an investor might go about deciding on an asset allocation, and explore what the possible consequences of an asset allocation might be.
Group Life Insurance
Authors: Akselsen Einar
Published: September 2014

The article describes group life insurance and the additional benefits written in conjunction or as riders, and the requirements that might apply.
Health Insurance
Authors: Bernet Patrick M. , Getzen Thomas E.
Published: September 2014

The health insurance industry differs from most other forms of insurance in that virtually all of the insured persons expect to make claims in most years, and those at highest risk expect to have their losses subsidized by the government or other parties. In this paper, the premium pricing process is used to highlight the many special features of health insurance with particular attention to frequency of loss, post‐loss price negotiation, adverse selection, tax benefits, social insurance, IBNR and reserve policies.
Life Insurance Mathematics
Authors: Norberg Ragnar
Published: September 2014

The subject matter and methodology of modern life insurance mathematics are surveyed. Standard insurance products with payments depending only on life history events are described and analyzed in the commonly used Markov chain model under the assumption of deterministic interest rates. The actuarial equivalence principle for determining premiums and reserves is motivated by risk diversification in large portfolios. Differential equations for reserves and other conditional expected values are obtained and proclaimed basic constructive and computational tools. The traditional method for managing nondiversifiable risk arising from changes in, for example, mortality rates and interest rates is outlined; premiums are calculated under prudent assumptions and systematic surpluses thus created are repaid as bonus. An alternative way of managing nondiversifiable risk is to link the contractual payments to the development of mortality, interest, and possibly other demographic or economic indexes. Examples of so‐called index‐linked products are given, and premiums and reserves are determined by combined use of classical actuarial principles and principles of pricing and hedging from financial mathematics. Transfer of nondiversifiable risk to the financial markets through creation of tradable insurance derivatives is outlined as an idea. Methods for estimation of mortality and other vital rates, formerly a major issue in life insurance mathematics, are fetched from modern statistical life history analysis and therefore only briefly described.
Long‐Term Care Insurance
Authors: Jones Bruce L.
Published: September 2014

It is well known that older adults become increasingly frail as they age. Even in the absence of a disease, one eventually loses the physical and/or mental ability to live independently. The kind of assistance required when this occurs is referred to as long‐term care (LTC). LTC is very different from the health care needed by individuals with injury or disease, and it requires a different set of services. Often, long‐term care services can be provided in a person's home, and this is the ideal situation. However, many cases require that the individual be institutionalized in an appropriate LTC facility.
Disability Insurance, Numerical Methods
Authors: Pitacco Ermanno
Published: September 2014

This article describes calculation methods used in actuarial practice for pricing disability annuity products. The following categories are dealt with: inception‐annuity models, models based on the probability of being disabled, models based on the expected time spent in disability, implementations of the multistate approach.