bluuebunny/crossref_metadata_2025_split huggingface dataset:
Sigma Metric (Sigma Level)
Authors: Does Ronald J.M.M. , De Mast Jeroen 
Published: February 2008

Abstract

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

Abstract
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.
Collinearity
Authors: Chen Gilad 
Published: February 2008

Abstract

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

Abstract

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.
Exploratory Data Analysis
Authors: Lovie Sandy 
Published: February 2008

Abstract
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

Abstract

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

Abstract

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.
Graphical Representation of Data
Authors: Snee Ronald D. , Pfeifer Charles G. 
Published: February 2008

AbstractThe sections in this article areExploratory GraphsData CondensationRelationships between Two VariablesRelationships among More than Two VariablesGraphs Used in the Analysis of DataDistribution Assessment and Probability PlotsModel Adequacy and Assumption VerificationPlots for Decision MakingCommunication and Display of ResultsQuantitative GraphicsSummary of Statistical AnalysisGraphical Aids
Multivariate Analysis
Authors: Johnson Richard A. , Wichern Dean W. 
Published: February 2008

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

AbstractThe sections in this article areIntroductionData InterpretationStatistical MethodologyData AnalysisStatistical Analysis Based on Probability ModelsExploration versus VerificationBayesian Inference and Decision MakingTheBayesian/Frequentist ControversyData AcquisitionMeasuring Single UnitsAssessing Population CharacteristicsData from ExperimentsSerial DataDesigning ExperimentsConclusionAcknowledgments
Control Charts, Overview
Authors: Faltin Frederick W. 
Published: February 2008

Abstract
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.
Cumulative Sum (CUSUM) Chart
Authors: Fatt Gan Fah 
Published: February 2008

AbstractThe 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

Abstract

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

Abstract
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

Abstract
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

Abstract

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

Abstract
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

Abstract

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

Abstract
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

Abstract
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

Abstract

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.
Economic Design of Control Charts
Authors: Saniga Erwin M. 
Published: February 2008

Abstract

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

Abstract
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.
Engineering Process Control
Authors: He Bin , Adams Benjamin M. 
Published: February 2008

Abstract

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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
Process Capability Indices, Comparison of
Authors: Spiring Fred 
Published: February 2008

Abstract

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

Abstract

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

Abstract

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

Abstract

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.