bluuebunny/crossref_metadata_2025 huggingface dataset:
Degradation Models
Authors: Bae Suk J. , Kvam Paul H.
Published: February 2008

Degradation models are used to relate a test item's estimated failure time with the wear and tear during its usage period. From a regression analysis of the degradation data, a test item's lifetime distribution can be inferred. We look at important examples of how an item's degradation rate relates to its lifetime distribution and outline statistical techniques used to analyze degradation data.
Burn‐In and Maintenance Policies
Authors: Mi Jie
Published: February 2008

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.
Warranty Cost Prediction Based on Warranty Data
Authors: Karim M. Rezaul , Suzuki Kazuyuki
Published: February 2008

This article discusses methods for predicting warranty cost to the manufacturer during a given future value(s) of the variable(s) defining the warranty terms. It models the predicted cost as a function of the lifetime distribution of the product and the average cost per claim based on observed costs of previous claims or costs from previous model years.
Single Sampling by Attributes and by Variables
Authors: von Collani Elart , Göb Rainer , Suresh Kodakanallur Krishnaswamy
Published: February 2008

Single sampling plans excel among statistical product inspection procedures. They are simple in structure, intuitive, and easy for implementation. The study of single sampling plans is illustrative for the understanding of acceptance sampling since single sampling plans exemplify all basic features of acceptance sampling in a particularly simple and transparent instance. Single sampling plans are sometimes theoretically inferior to more refined sampling algorithms like double, multiple, and sequential sampling plans. However, simplicity and ease in implementation have made single sampling the most widely used statistical product inspection procedure.
Rectification Sampling Schemes
Authors: Göb Rainer
Published: February 2008

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.
Continuous Sampling
Authors: Suresh Kodakanallur Krishnaswamy , von Collani Elart
Published: February 2008

This article considers the control of item‐by‐item production in contrast to the control of lot‐by‐lot production. The methods covered are the continuous sampling plan, CSP‐1, some of its extensions and the corresponding MIL‐STD‐1253C, each of them referring to attribute sampling. The situation, in which these methods can be applied, are for example conveyor and moving assembly lines. The mode of operation and the statistical and operational properties of continuous sampling plans are stated.
Skip Lot and Chain Sampling
Authors: Balamurali Saminathan , Jun Chi‐Hyuck , von Collani Elart
Published: February 2008

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.
Economic Sampling Schemes
Authors: von Collani Elart
Published: February 2008

The process of globalization has resulted in a situation where an increasing number of companies operate production locations all over the world and especially in the so‐called low‐cost countries. This trend has significantly increased the importance of outgoing and incoming quality inspection, normally by sampling inspection, because in many cases the inspection costs represent a considerable part of the total costs. Despite this situation, there is almost no research done on the application of economic sampling plans. The aim of this chapter is to give a short introduction into the state of the art with respect to economic sampling schemes to initiate further research in this important area of statistical quality control.
Prior Information in Sampling Schemes
Authors: Seidel Wilfried
Published: February 2008

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: February 2008

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.
Attributes Sampling under Classification Error
Authors: Greenberg Betsy S.
Published: February 2008

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.
Sampling Inspection of Products and Statistical Process Control
Authors: Hryniewicz Olgierd
Published: February 2008

Acceptance control charts, originally proposed by Freund, are the tools of statistical process control (SPC) that combine features of classical control charts and sampling plans used in acceptance sampling of products and services. In contrast with classical Shewhart control charts, their design is based on the requirements typical for acceptance sampling plans by variables. In the article, we present the design principles of the acceptance control charts. The similarity between acceptance control charts and acceptance sampling systems shows that the latter might be used for the purpose of SPC.
Sampling in Semiconductor Manufacturing
Authors: Barlović Robert , Holfeld Andre , Räbiger Jan
Published: February 2008

The task of sampling in state‐of‐the‐art semiconductor manufacturing is to provide relevant metrology data for a representative part of the population in order to monitor and maintain the process, thereby minimizing the risk of processing errors/faults. The decision process itself is restricted by certain expense criteria. Thus, sampling has to select the appropriate material for metrology based on manufacturing needs while fulfilling manufacturing constraints.
Sampling in Data Mining
Authors: Weiß Christian H.
Published: February 2008

After a brief review of basic terms and concepts of knowledge discovery in databases (KDD) and data mining, this article investigates aspects of sampling in data mining. A general scheme of sampling, and particular techniques used in data mining are discussed. The main objective of this article is to provide an overview on areas of KDD and data mining, where sampling approaches are applied.
Internal and External Quality Measures
Authors: Ograjenšek Irena
Published: February 2008

There are two distinct general approaches to the use of statistical methods in quality improvement. These are theproduction approachand themarketing approach. The production approach focuses on quality improvement from the management (internal) point of view using the statistical quality control (SQC) tools and producing predominantly internal quality measures. The marketing approach builds on the customer (external) assessment of quality using tools of survey research, producing predominantly external quality measures. One of the biggest challenges that companies face is a meaningful integration of these two groups of measures with the goal of facilitating continuous quality improvement.
Design and Testing of Questionnaires
Authors: Ograjenšek Irena
Published: February 2008

The questionnaire is the most frequently used data collection tool of survey research. It can be applied in personal, telephone, mail, and on‐line surveys. Two factors which determine the questionnaire design requirements to the largest extent are: the form of the questionnaire (paper
versus
electronic), and the mode of questionnaire administration (interviewer‐
versus
self‐administered questionnaire).

In order to test and evaluate a questionnaire, a wide range of methods can be used. Some (e.g., an expert panel or peer evaluation) are more applicable in the early stages of questionnaire design, other (e.g., a pilot study) should be used prior to the broad questionnaire distribution.
Survey Error
Authors: Reiter Jerome P.
Published: February 2008

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.
SERVQUAL
Surveys
Authors: Ograjenšek Irena
Published: February 2008

Service quality is often analyzed using rating scales to assess individual service attributes. The most widely used and most carefully scrutinized rating scale is SERVQUAL. The scale is a result of a systematic ongoing study of service quality that begun in 1983. The model defines quality as the difference between customer perceptions and expectations with regard to quality of delivered service. The respondents are asked to answer two sets of questions dealing with the same subject, one set at a general level, and one for a company in question. Respondents choose from a modified Likert scale which measures intensity of agreement or disagreement with any given statement. Response options range from “strongly agree” and lesser levels of agreement to “neutral” (neither agree nor disagree) and lesser levels of disagreement to “strongly disagree”. Although SERVQUAL has been widely used in business‐to‐business and business‐to‐customer settings, this does not mean the scale has not been subjected to reexamination and criticism. There are several well researched and documented objections to SERVQUAL. As a consequence of these critique, various alternative formulations of the service quality model have been suggested. The only one that, to date, seems to outperfom SERVQUAL is SERVPERF, the performance‐only measure of service quality.
Autocorrelation Function
Authors: Shore Haim
Published: February 2008

Assume that observations in a time series had been taken in fixed time intervals. In most cases (like for stationary time series), pairs of observations separated by a fixed number of intervals,
k
, will display a typical autocorrelation. This correlation is named
autocorrelation of lag k
, denoted as ρ

k

. The autocorrelation function displays ρ

k

as a function of
k
. It plays a central role in time‐series modeling. In this article, the autocorrelation function and the partial autocorrelation function are defined and their estimation procedures detailed.
Coefficient of Determination (

R

2
)
Authors: Di Bucchianico Alessandro
Published: February 2008

Coefficient of determination is a goodness‐of‐fit measure for models based on the proportion of explained variance. Variants of the coefficient of determination and pitfalls in the use of it are explained. The relation with the multiple correlation coefficient is explained.
Homogeneity of Variances
Authors: Koning Alex J.
Published: February 2008

The lack of homoscedasticity affects the validity of statistical tests, and has a negative effect on the coverage of confidence intervals and on the accuracy of estimators. Formal diagnostic tests and diagnostic plots are available for analysis of variance, the linear regression model and the nonparametric regression model. Box–Cox transformations are used to reduce the lack of homoscedasticity.
Leverage
Authors: Di Bucchianico Alessandro
Published: February 2008

Leverage is the measure of the influence of a given observation on a regression model. The importance of detecting leverage is described, as well as the major statistics used to detect observations with high leverage.
Measures of Location
Authors: Di Bucchianico Alessandro
Published: February 2008

Example of sample statistics that describe the center of gravity are given, together with some properties.
Nonparametric Tests
Authors: Koning Alex J.
Published: February 2008

Nonparametric tests do not rely on restrictive distributional assumptions, and hence are also known as
distribution‐free tests
. Examples are permutation methods, rank tests, and bootstrap tests.
Normal Distribution
Authors: Tong Y.L.
Published: February 2008

This article provides a description of the univariate normal distribution and a brief discussion on the bivariate and multivariate normal distributions.
Outliers
Authors: Di Bucchianico Alessandro
Published: February 2008

The concept of outliers and causes of outliers are explained. Graphical tools as well as some well‐known formal tests to detect outliers are described.
P
areto Chart
Authors: Di Bucchianico Alessandro
Published: February 2008

We present the ideas behind and some practical tips for performing a Pareto analysis, which is a technique to prioritize problems that need to be solved.
Sigma Metric (Sigma Level)
Authors: Does Ronald J.M.M. , De Mast Jeroen
Published: February 2008

The Greek symbol σ is used in statistics as a measure of variation. Since, especially in industry, many quality problems are related to excessive variation, the concept σ has become a basis for the definition of a measure for conformance quality: the
sigma metric
or
sigma level
. The sigma level indicates the performance of a process, namely: what percentage of products or service deliveries conforms to the specifications.
S
ix
S
igma Method
Authors: Does Ronald J.M.M. , De Mast Jeroen
Published: February 2008

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.
Variance
Authors: Shore Haim
Published: February 2008

The sections in this article are

Variance as a Property of a Distribution

Variance as a Population Parameter

The Sample Variance
Collinearity
Authors: Chen Gilad
Published: February 2008

Collinearity reflects situations in which two or more independent variables are perfectly or nearly perfectly correlated. In the context of multiple regression, collinearity violates an important statistical assumption and results in uninterpretable and biased parameter estimates and inflated standard errors. Regression diagnostics such as
variance inflation factor
(VIF) and
tolerance
can help detect collinearity, and several remedies exist for dealing with collinearity‐related problems.
Estimation
Authors: Van De Geer Sara A.
Published: February 2008

This paper is concerned with the relationship between sample data and the probability distribution (
P
), which is supposed to have generated it. The estimation of
P
using an empirically derived distribution is discussed along with specific estimators such as the sample mean, the sample median, and a histogram. Estimation by the method of moments and minimum χ
2
estimation are explained, as are the concepts of bias, mean square error, and sufficiency.
Expectation
Authors: Walwyn Rebecca
Published: February 2008

The expectation of a random variable with a particular probability distribution is its theoretical mean or average value. Expectations can also be calculated for functions of random variables.
Exploratory Data Analysis
Authors: Lovie Sandy
Published: February 2008

Exploratory data analysis (EDA) is one of the most influential recent developments in statistics. Led by John Tukey, EDA offered a new inductive orientation to the discovery of knowledge. In detail, this meant the invention of new graphical methods, the development of robust, outlier‐resistant measurements, and the modernization of regression analysis and related linear model approaches.
Heteroscedasticity
Authors: Morrison Donald F.
Published: February 2008

Homoscedasticity is the condition under which a series of observations have the same degree of variation. Heteroscedasticity is its negation. Homoscedasticity is assumed in the standard models for least‐squares linear regression, the two‐sample
t
test and the analysis of variance, and the effects of heteroscedasticity in these situations are discussed here.
Laws of Large Numbers
Authors: Kay Jim W.
Published: February 2008

The laws of large numbers concern when the average of
n
random variables converges to a fixed value as
n
tends to infinity. The
n
random variables could arise in various ways. They could, for example, be mutually independent and identically distributed and represent a simple random sample of observations taken from some fixed population, or they could represent a sequence of
n
realizations of a stationary stochastic process. The laws are defined under the assumptions that the random variables are mutually independent and follow the same probability distribution; generalizations obtained under more general conditions are mentioned. Illustrations are provided, which demonstrate the usefulness of the laws in providing theoretical justification for: the frequentist concept of probability; the strong consistency of the sample mean and variance estimators.
Moments
Authors: Walwyn Rebecca
Published: February 2008

Moments are expectations that are used to describe the probability distributions of random variables. The mean and variance of a random variable are the two most important examples of moments.
Probability Plots
Authors: Howell David C.
Published: February 2008

Probability plots are most often used to assess the shape of a distribution of data. Probability–probability plots display the cumulative percentage of the distribution against the cumulative percentages of a reference distribution (often the normal distribution). Quantile–quantile plots display the obtained and expected quantiles of the distribution.
Parametric Tests
Authors: Clark‐Carter David
Published: February 2008

Parametric tests derive their probability from probability distributions such as the normal distribution and the
t
distribution. They make more assumptions about the nature of the population from which samples have been drawn than their nonparametric equivalents. However, when the assumptions of a parametric test are met, the test will have more statistical power than a nonparametric equivalent.
Box and Cox TransformationArticle originally published in Encyclopedia of Statistical Sciences, 2nd Edition (2005, John Wiley & Sons, Inc.). Minor revisions for this publication by Jeroen de Mast.
Authors: Broemeling Lyle D.
Published: February 2008

The sections in this article are
Graphical Representation of Data
Authors: Snee Ronald D. , Pfeifer Charles G.
Published: February 2008

The sections in this article are

Exploratory Graphs

Data Condensation

Relationships between Two Variables

Relationships among More than Two Variables

Graphs Used in the Analysis of Data

Distribution Assessment and Probability Plots

Model Adequacy and Assumption Verification

Plots for Decision Making

Communication and Display of Results

Quantitative Graphics

Summary of Statistical Analysis

Graphical Aids
Missing Data and Imputation
Authors: Fuchs Camil , Kenett Ron S.
Published: February 2008

Handling missing data is a core requirement of data analysis. The assessment of the process that caused missing data and the approach for handling missing data can have significant impact on the results of the analysis. In this section, we address the issue of missing data and imputation, covering a wide variety of applications and solutions proposed in the recent literature.
Multivariate Analysis
Authors: Johnson Richard A. , Wichern Dean W.
Published: February 2008

Multivariate analysis is the body of statistical methodology used to analyze simultaneous measurements on several variables. We provide an overview of important methods for making inferences about mean vectors, analyzing covariance structure, and classifying and grouping items. In addition, there is a brief introduction to procedures for creating lower‐dimensional representations of items and/or variables. References and a list of sources for further reading are provided.
Probability Theory
Authors: Heyde Christopher. C.
Published: February 2008

The sections in this article are

Introduction

The Formal Framework

Important Concepts

Convergence

Other Approaches

The Literature
Overview of Statistics
Authors: Lehmann Erich L.
Published: February 2008

The sections in this article are

Introduction

Data Interpretation

Statistical Methodology

Data Analysis

Statistical Analysis Based on Probability Models

Exploration versus Verification

Bayesian Inference and Decision Making

TheBayesian/Frequentist Controversy

Data Acquisition

Measuring Single Units

Assessing Population Characteristics

Data from Experiments

Serial Data

Designing Experiments

Conclusion

Acknowledgments
Control Charts, Overview
Authors: Faltin Frederick W.
Published: February 2008

Control charts originated in the work of Dr. Walter Shewhart, the father of statistical process control, in the 1920s. Shewhart's groundbreaking insight was to apply statistical concepts to model the characteristic variability of a manufacturing process. His tool for doing so was the control chart, which was traditionally implemented graphically by having line workers plot production data over time. Corrective action would be taken when the plotted values fell outside of limits which were specified based on statistical properties of the process. Over the intervening decades, control charting techniques have been developed for monitoring and improving nearly all commonly encountered business processes, including nonmanufacturing processes such as supply chain/order fulfillment, human resource management, financial and accounting processes, call center management, and many others.
Control Charts for the Mean
Authors: Ryan Thomas P.
Published: February 2008

A Shewhart control chart for the mean is almost certainly the most frequently used control chart, due in part to its simplicity and ease of understanding. As with any statistical procedure, however, it must be used properly to be most effective, and this entails recognizing the assumptions upon which the chart is based and the importance of checking those assumptions in each application.
Cumulative Sum (CUSUM) Chart
Authors: Fatt Gan Fah
Published: February 2008

The use of the cumulative sum (CUSUM) charting procedure in process monitoring is first described. The strengths and weaknesses of the CUSUM charting procedure, with respect to the Shewhart charting procedure, are then illustrated with simulated data sets. Various other aspects of the CUSUM chart are also discussed. These include derivation of run‐length distribution, estimation of process mean using the CUSUM, weighting of samples for signaling, fast initial response for a newly start‐up process, simultaneous CUSUM schemes, design of the CUSUM chart, and multivariate CUSUM schemes.
Moving Range and

R

Charts
Authors: Champ Charles W. , Shepherd Deborah K.
Published: February 2008

Control charts for controlling the process mean are affected by changes in the process standard deviation. Therefore it is important to also control the process standard deviation. Various control charting methods have been developed for this purpose. Two commonly recommended statistical methods for controlling the process standard deviation are the moving range (
MR
) and the range (
R
) charts. The designs of
MR
and
R
charts are discussed in this article and each is illustrated with an example.
Control Charts for the Standard Deviation
Authors: Mitra Amitava
Published: February 2008

Control charts are graphical tools to monitor the activity of a process. They are used to determine if the variation in a process is due to the presence of common causes (those that are inherent to the process) or special causes (those that are not part of the process as designed). A process is said to be in statistical control when it is under a system of common causes. A standard deviation control chart monitors process variation, as measured by the standard deviation of observations, through subgroups collected over a period of time. Typically, three lines are depicted on a control chart—the centerline (CL), the upper control limit (UCL), and the lower control limit (LCL). Rules for determining out‐of‐control conditions are defined, the most commonly used one corresponds to a point falling outside the control limits. Some parameters for the construction of the standard deviation control chart are the subgroup size, frequency of sampling, and placement of the control limits from the CL, based on the choice of an acceptable level of a false alarm rate.
Multivariate Control Charts Overview
Authors: Runger George C.
Published: February 2008

Multivariate statistical process control is used to simultaneously monitor multiple measurements from a process. Similar to the case for a single variable, the objective is to detect assignable causes of variation. Multiple measurements are quite common in modern processes. This overview presents a brief summary of the advantages of an integrated solution for multiple measurements, types of applications, structure of the data, assignable causes, characteristics of charts, and signal interpretation.
H
otelling's

T

2
Chart
Authors: Sullivan Joe H.
Published: February 2008

Often referred to as a
Shewhart‐type control chart
, Hotelling's
T
2
control chart is based on a multivariate generalization of the Student's
t
statistic for univariate observations. As is the case of the univariate Shewhart chart, Hotelling's
T
2
chart is a good, general purpose tool that is sensitive to outliers and sustained shifts in the mean vector, although not effective in detecting quality improvements that might be reflected in decreased dispersion about the in‐control mean vector. Compared with the alternative of monitoring the measurement variables separately, this method takes into account the in‐control correlation among the measurements in detecting shifts in the mean vector resulting from special causes of variation, which is considered an advantage.
Multivariate Cumulative Sum (
CUSUM
) Chart
Authors: Testik Murat C. , Runger George C.
Published: February 2008

Cumulative sum (CUSUM) control charts are important tools for the real‐time, on‐line monitoring of production processes. There are several multivariate extensions to the univariate CUSUM control chart. This work discusses the multivariate extensions to the CUSUM control chart and their uses. Basic formulas and notation are provided and the advantages and disadvantages of each are compared. References are given to allow the interested reader to investigate further.
Multivariate Charts for Variability
Authors: Lin Dennis K.J. , Yeh Arthur B.
Published: February 2008

In this article, we discuss two multivariate control charts for monitoring changes in a covariance matrix. The |
S
| chart is applicable when the subgroup size
n
is larger than the dimensionality
p
. The multivariate exponentially weighted moving squared‐deviation (MEWMS) chart is specifically designed for the case when
n
 = 1. Examples are given and discussed to demonstrate how each chart can be used in practice. Related issues and potential future research are also discussed.
Autocorrelated Data
Authors: Wardell Don G.
Published: February 2008

Traditional statistical process control methods assume that consecutive observations on a control chart are statistically independent. Often observations from actual processes are serially correlated. In such cases, the use of traditional control charts often leads to misleading conclusions as to whether or not the process is under control. We illustrate the problems of using traditional control charts and review several methods that have been proposed to handle the autocorrelation. Some of the methods are model based while others are model free. The majority of the methods are improvements over traditional control charts, but none is able to completely overcome the inherent difficulty of monitoring autocorrelated data. Hence there are some cases where traditional charts, which are simpler to implement, should be considered even when the process is autocorrelated.
Control Charts for Short Production Runs
Authors: Elam Matthew E.
Published: February 2008

This article presents control charts for short production runs. The existing research can be placed into four categories. They are pooled data control charts, control charts with greater sensitivity, control charts for process inputs, and control charts with modified limits. This article also presents advantages and disadvantages of each. Control charts with greater sensitivity include exponentially weighted moving average (EWMA), cumulative sum (CUSUM), and economically designed control charts. Control charts with modified limits include Q charts and two‐stage short‐run control charts. The particular focus of this article is the two‐stage short‐run control charting methodology. This article concludes with future research opportunities in two‐stage short‐run control charts.
Control Charts for Batch Processes
Authors: Lewis Donald K.
Published: February 2008

Applying control charts successfully to batch processes requires the recognition of some distinguishing features of batch processing
versus
single‐unit processing. Traditional Shewhart‐type charts can be modified for use in batch‐processing practitioners of statistical process control (SPC); however, entirely different control chart methods and practices will often be required. This article reviews the common features of batch processing and the data available to control chart practitioners from typical batch processes and suggests alternatives to standard Shewhart charts for effective process monitoring and control.
Precontrol
Authors: Ledolter Johannes
Published: February 2008

Precontrol monitors the acceptability of a process by comparing individual process values against their specification limits. Its goal is the prevention of nonconforming units. This article reviews precontrol and discusses its strengths and weaknesses.
Economic Design of Control Charts
Authors: Saniga Erwin M.
Published: February 2008

Control charts are designed by using a heuristic, or meeting statistical constraints or minimizing cost. The latter two design methods are called
statistical design
and
economic design
. A combination of them, called
economic statistical design
, is a related criterion. In this chapter I discuss these methods and their relative strengths and weaknesses. I then review some literature that addresses the choice of an optimal economic process control policy and subsequently discuss how one can design the optimal economic control chart. I also review and address some of the criticism of economic design.
Profile Monitoring
Authors: Woodall William H.
Published: February 2008

In many practical situations the quality of a process or product can be characterized and summarized by a functional relationship between a response variable and one or more explanatory variables. Profile monitoring is used to understand and check the stability of this relationship over time. At each sampling stage one observes a collection of data points that can be represented by a curve (or profile). In some calibration applications, the profile can be represented adequately by a simple straight‐line model, while in other applications more complicated models are needed. In this article, we discuss some of the general issues involved in using control charts to monitor such process and product quality profiles.
Control Charts, Selection of
Authors: Adams Benjamin M.
Published: February 2008

The control chart is an essential tool in the area of statistical process monitoring. As the applications of control charts become more varied, control charts are continuously being adapted to meet the new data environments. Many types of control charts and monitoring schemes are now available to practitioners. This article provides general guidelines for selecting appropriate control charts for a given application.
Engineering Process Control
Authors: He Bin , Adams Benjamin M.
Published: February 2008

This article addresses the similarities and distinctions between traditional statistical process control (SPC) methods (
see
Control Charts, Overview
) and engineering process control (EPC) methods (
see
Feedback Control
). Both techniques share a primary goal of reducing process variation while maintaining target values. The strategic and mathematical foundations for the techniques are, however, quite different. These differences have led to confusion surrounding the appropriate choice of control method when both SPC and EPC appear to be viable quality tools. This article provides a brief overview of SPC and EPC methods and seeks to clarify the relationship between these two complementary methods.
Feedback Control
Authors: Mastrangelo Christina , Kumar Naveen
Published: February 2008

Previously, it has been held that statistical process control (SPC) and engineering process control (EPC) were two distinct domains for process improvement. This paper focuses on the latter and presents an introduction to the simple methods of feedback adjustment. It shows how these techniques can be used where there is a manipulated variable that affects the output of a process, and how SPC and EPC may be integrated.
Change‐Point Methods
Authors: Hawkins Douglas M. , Qiu Peihua , Zamba Kokou D.
Published: February 2008

Change‐point methodologies applied to statistical process control are predicated on the possibility that a special cause induces a shift from an in‐control statistical model to an out‐of‐control statistical model, and so are particularly attractive for persistent special causes. Along with indications of a loss of control, they provide estimates of when the shift occurred, and (if needed) of the before‐ and after‐shift process parameters. A less obvious advantage is that some change‐point proposals allow for the near‐universal situation that the in‐control distribution of process readings is not known exactly. This feature largely removes the need for extensive phase I calibration studies, and allows phase II production use to start early. In addition to the stand‐alone use of change‐point methodologies for both signaling and diagnosing the effects of special causes, they have been proposed as tools for following up signals given by other charting methods, when their likelihood properties lead to good estimators of the time of occurrence and effect of the special cause.
Process Capability Indices, Skewed
Authors: Chang Young Soon , Bai Do Sun
Published: February 2008

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, Multivariate
Authors: Fuchs Camil , Kenett Ron S.
Published: February 2008

Process capability is determined by comparing the actual performance of a process with required specifications. Several indices have been proposed to report the capability of a process in the univariate case. When performance is tracked in several dimensions, an extension of these indices is required. We present several multivariate capability indices, and extend the idea of multivariate tolerance regions for assessing the capability of a process.
Multivariate Process Capability Indices, Comparison of
Authors: Wang Fu‐Kwun
Published: February 2008

In this article, some methods of evaluating the process capability of products with multiple quality characteristics are reviewed. Multivariate process capability indices are introduced and a summary is made systematically. An example is used to demonstrate the performance of different multivariate process capability indices.
Process Capability Indices, Comparison of
Authors: Spiring Fred
Published: February 2008

The most common process capability indices are examined from several perspectives. A brief historical review outlines recent developments from simple variability measures to today's more sophisticated indices. The behavior of the indices
C

pk

,
C

pm

, and
C

pmk

is compared with
C

p

for processes that are not necessarily centered at target, illustrating the relationships among the various indices. A weight function is presented that allows the functional form of a variety of indices to be examined. A discussion of process yield and the resulting interpretation from a quality loss perspective is presented and the differing philosophies represented by the competing indices are highlighted.
Yield Surface Modeling
Authors: Maass Eric Charles
Published: February 2008

Yield Surface Modeling™ (YSM) has been used to perform multiple‐response optimization for over 60 new products with high yields and first‐pass successes. The approach expands on response surface modeling (RSM), using the Generation of System Moments method to forecast the mean and variance, and then the process capability index (
C

pk

), and yield for each response—effectively replacing the expected value of the response with the expected value of the
C

pk

and yield for each combination of settings of factor levels. Composite
C

pk

and composite yield surfaces are generated for those combinations of settings of factor levels. The method is illustrated with a case study for an integrated alternator regulator (IAR) (integrated circuit). The strengths and limitations of the approach are discussed, including the value of the sensitivity analyses that come from the use of the Generation of System Moments method.
Control Charts and Process Capability
Authors: Lovelace Cynthia R.
Published: February 2008

Statistical process control (SPC) charts play a very important role in the determination of process capability. It is important that SPC be achieved
via
the use of appropriate control charts before process capability indices are calculated, so that the indices reflect the long‐term capability of a process to produce product within specification. A significant portion of the theoretical research dedicated to process capability indices has focused on those index estimators that utilize a pooled estimator of process variance, but data collected in subsamples from an in‐control SPC chart, most likely an

X

 − 
R
or

X

 − 
s
chart, is preferred in practice for index estimation to insure process stability. This article is focused on the significant work published to date on process capability indices estimated using subsamples, including confidence bounds and hypothesis testing procedures for the primary indices
C

p

,
C

pk

, and
C

pm

.
Process Capability Indices for Multiple Stream Processes
Authors: Bothe Davis Ross
Published: February 2008

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.
Gauge Repeatability and Reproducibility (
R
&
R
), Variance Components in
Authors: Borror Connie M. , Burdick Richard K. , Montgomery Douglas C.
Published: February 2008

Traditionally, a standard gauge repeatability and reproducibility (R&R) study consisted of a two‐factor crossed design with operators and parts; with each operator measuring each part say
r
times. There are numerous situations where there are more than two factors, the design is not crossed but possibly nested, or the appropriate design is crossed and nested. In this article, variance components for gauge R&R studies are presented for these more complex experimental situations.
Gauge Repeatability and Reproducibility (
R
&
R
) Studies, Misclassification Rates
Authors: Burdick Richard K.
Published: February 2008

To properly monitor and improve a manufacturing process, it is necessary to measure attributes of the process output. Measurements of these attributes are taken by a gauge that has associated measurement variability. Gauge R&R studies are used to determine if the measurement system variability is harmfully large. The approach for evaluating the goodness of the measurement system based on a gauge R&R study is to determine the probability that a part is misclassified. The better a measurement system, the less likely it is to classify a “good” part as “bad”, and a “bad” part as “good”. References are provided for computing bounds on the probabilities of these misclassifications.
Gauge Repeatability and Reproducibility (
R
&
R
) Studies, Confidence Intervals for
Authors: Chiang Andy Kok Leong
Published: February 2008

Gauge repeatability and reproducibility (R&R) studies are often conducted to determine the capability of a gauge for monitoring a manufacturing process. In this paper, we discuss common measures of gauge capability as well as established confidence intervals for them, based on the modified large sample and generalized confidence interval methods.
Measurement Error and Uncertainty
Authors: Borror Connie M.
Published: February 2008

In this article, some very basic definitions and concepts concerning measurement error and uncertainty are provided. The information provided in this article is an introduction to the differences between uncertainty and error. Measurement error and uncertainty are defined and several resources are provided for discussions and critiques of the uses of these terms and how they are applied in various situations.
Measurement Systems Analysis, Capability Measures for
Authors: Larsen Greg A.
Published: February 2008

There are two “families” of measurement capability metrics in common use. There are those that compare measurement variation to total or part variation, and there are those that compare to the tolerance or specification width. These capability metrics are all functions of the variance components in the statistical model used to describe the response of interest. In addition to these capability metrics, it is also often useful to estimate the misclassification rates that arise from using the measurement system to discriminate between “good” and “bad” items being tested. An additional capability metric is obtained from the ratio of the estimated misclassification rates to the rates that would occur purely due to random chance. This section will define several capability measures, how they are related to one another, and give some common criteria for capability. Additional topics discuss the effect of the unit of measure and present a situation where none of the aforementioned metrics are particularly useful in quantifying the capability of a measurement process.