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The Half-Half (HH) plot is a new graphical method to investigate qualitatively the shape of a regression curve. The empirical HH-plot counts observations in the lower and upper quarter of a strip that moves horizontally over the scatterplot. The plot displays jumps clearly and reveals further features of the regression curve. We prove a functional central limit theorem for the empirical HH-plot, with rate of convergence . In a simulation study, the good performance of the plot is demonstrated. The method is also applied to two case studies. The proofs and one more case study are deferred to a supplement, which is available online. [ABSTRACT FROM AUTHOR]

The analysis of screening experiments based on nonregular designs can lead to a model selection problem in which the number of variables is large, the number of trials is small, and there are constraints on model structure. Common subset selection methods do not perform well in this setting. We propose a new approach particularly well suited to screening. The method uses an intentionally nonconvergent stochastic search to generate a large set of well-fitting models, each with the same number of variables. Model selection is then viewed as a feature extraction problem from this set. An easy-to-use graphical method and an automatic approach are proposed to determine the best models. Computer code and additional supplementary materials are available online. [ABSTRACT FROM AUTHOR]

Proposes a graphical method for assessing parametric transformation of the response in a linear regression model. Examples of response formations using data from an experiment on the behavior of worsted yarns; Details of the proposed method; Application of the linearity condition to the marginal distribution of the predictors.

This paper presents theory and applications of a simple graphical method, called hazard plotting, for the analysis of multiply censored life data consisting of failure times of failed units intermixed with running times on unfailed units. Applications of the method are given for multiply censored data on service life of equipment, for strength data on an item with different failure modes, and for biological data multiply censored on both sides from paired comparisons. Theory for the hazard plotting method, which is based on the hazard function of a distribution, is developed from the properties of order statistics from Type II multiply censored samples. [ABSTRACT FROM AUTHOR]

Measures of the quality of prediction at locations on the surface of a hypersphere are presented. These measures are used to form a graphical method of assessing the overall prediction capability of an experimental design throughout the region of interest. A plot of the spherical variance and the maximum and minimum prediction variances for locations on a sphere against the radius of the sphere, a variance dispersion graph, is used to give a comprehensive picture of the behavior of the prediction variances throughout a region and hence of the quality of the predicted responses obtained with a particular design. Such plots are used to investigate and compare the prediction capabilities of certain response surface designs currently available to the researcher. [ABSTRACT FROM AUTHOR]

The sorted binary plot is a graphical method for identifying and displaying patterns in multivariate data sets. The construction requires calculation of the median for each variable measured, followed by subtraction of the medians from the values for each sample. The signs of the residuals represent a binary number for each sample. The list of binary numbers is sorted and converted to a graph by assigning distinctive symbols to 1 and 0. The sorting operation causes samples with the same binary number to form clusters. The method can be extended to three or more quantiles. It has been applied to several kinds of data. [ABSTRACT FROM AUTHOR]

A dynamic graphical method is one in which a data analyst interacts in real time with a data display on a computer graphics terminal. Using a screen input device such as a mouse, the analyst can specify, in a visual way, points or regions on the display and cause aspects of the display to change nearly instantaneously. Brushing is a collection of dynamic methods for viewing multidimensional data. It is very effective when used on a scatterplot matrix, a rectangular array of all pairwise scatterplots of the variables. Four brushing operations-highlight, shadow highlight, delete, and label--are carried out by moving a mouse-controlled rectangle, called the brush, over one of the scatterplots. The effect of an operation appears simultaneously on all scatterplots. Three paint modes--transient, lasting, and undo--and the ability to change the shape of the brush allow the analyst to specify collections of points on which the operations are carried out. Brushing can be used in various ways or on certain types of data; these usages are called brush techniques and include the following: single-point and cluster linking, conditioning on a single variable, conditioning on two variables, subsetting with categorical variables, and stationarity probing of a time series. [ABSTRACT FROM AUTHOR]

This paper presents theory and applications of a simple graphical method, called hazard plotting, for the analysis of multiply censored life data consisting of failure times of failed units intermixed with running times on unfailed units. Applications of the method are given for multiply censored data on service life of equipment, for strength data on an item with different failure modes, and for biological data multiply censored on both sides from paired comparisons. Theory for the hazard plotting method, which is based on the hazard function of a distribution, is developed from the properties of order statistics from Type II multiply censored samples. [ABSTRACT FROM AUTHOR]

A graphical method for examining the assumptions of covariance analysis is presented. A plot of the response residuals (y - ŷ) versus the covariate residuals (χ - &χcirc;) provides a useful method for studying the relationship between the covariate and the response. It also aids in the detection of abnormal observations. [ABSTRACT FROM AUTHOR]

Because of the exponential distribution assumption, many reliability databases recorded data in an aggregate way. Instead of individual failure times, each aggregate data point is a summation of a series of collective failures representing the cumulative operating time of one component position from system commencement to the last component replacement. The data format is different from traditional lifetime data and the statistical inference is challenging. We first model the individual component lifetime by a gamma distribution. Confidence intervals for the gamma shape parameter can be constructed using a scaled χ2approximation to a modified ratio of the geometric mean to the arithmetic mean, while confidence intervals for the gamma rate and mean parameters, as well as quantiles, are obtained using the generalized pivotal quantity method. We then fit the data using the inverse Gaussian (IG) distribution, a useful lifetime model for failures caused by degradation. Procedures for point estimation and interval estimation of parameters are developed. We also propose an interval estimation method for the quantiles of an IG distribution based on the generalized pivotal quantity method. An illustrative example demonstrates the proposed inference methods. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

Critical to any regression analysis is the identification of observations that exert a strong influence on the fitted regression model. Traditional regression influence statistics such as Cook's distance and DFFITS, each based on deleting single observations, can fail in the presence of multiple influential observations if these influential observations “mask” one another, or if other effects such as “swamping” occur. Masking refers to the situation where an observation reveals itself as influential only after one or more other observations are deleted. Swamping occurs when points that are not actually outliers/influential are declared to be so because of the effects on the model of other unusual observations. One computationally expensive solution to these problems is the use of influence statistics that delete multiple rather than single observations. In this article, we build on previous work to produce a computationally feasible algorithm for detecting an unknown number of influential observations in the presence of masking. An important difference between our proposed algorithm and existing methods is that we focus on the data that remain after observations are deleted, rather than on the deleted observations themselves. Further, our approach uses a novel confirmatory step designed to provide a secondary assessment of identified observations. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

Pipeline integrity is important because leaks can result in serious economic or environmental losses. Inspection information from a sample of locations along the pipeline can be used to estimate corrosion levels. The traditional parametric model method for this problem is to estimate parameters of a specified corrosion distribution and then to use these parameters to estimate the minimum thickness in a pipeline. Inferences using this method are, however, highly sensitive to the distributional assumption. Extreme value modeling provides a more robust method of estimation if a sufficient amount of data is available. For example, the block-minima method produces a more robust method to estimate the minimum thickness in a pipeline. To use the block-minima method, however, one must carefully choose the size of the blocks to be used in the analysis. In this article, we use simulation to compare the properties of different models for estimating minimum pipeline thickness, investigate the effect of using different size blocks, and illustrate the methods using pipeline inspection data. [ABSTRACT FROM PUBLISHER]

This article systematically investigates the inverse Gaussian (IG) process as an effective degradation model. The IG process is shown to be a limiting compound Poisson process, which gives it a meaningful physical interpretation for modeling degradation of products deteriorating in random environments. Treated as the first passage process of a Wiener process, the IG process is flexible in incorporating random effects and explanatory variables that account for heterogeneities commonly observed in degradation problems. This flexibility makes the class of IG process models much more attractive compared with the Gamma process, which has been thoroughly investigated in the literature of degradation modeling. The article also discusses statistical inference for three random effects models and model selection. It concludes with a real world example to demonstrate the applicability of the IG process in degradation analysis. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

We propose a candidate-list-free exchange algorithm that facilitates construction of exact, model-robust, two-level experiment designs. In particular, we investigate two model spaces previously considered in the literature. The first assumes that all main effects and an unknown subset of two-factor interactions are active, but that the experimenter knows the number of active interactions. The second assumes that an unknown subset of the main effects, and all associated two-factor interactions, are active. Previous literature uses two criteria for design construction: first, maximize the number of estimable models; then, differentiate between designs equivalent in estimability by choosing the design with the highest average -efficiency. We adopt a similar strategy, but (1) do not impose orthogonality or factor level balance constraints, resulting in generally equal or larger numbers of estimable models, and (2) use a flexible secondary criterion that maximizes the minimum -efficiency. We provide results for many situations of interest. We also provide online supplementary material that includes algorithmic details, designs, and MATLAB code. [ABSTRACT FROM AUTHOR]

The article discusses the insights of the authors on the comments of other authors regarding their article on the analysis of reliability growth. It says that the authors did not develop a maximum likelihood estimation (MLE) for the variable k since limiting metrics provide finite k estimates. It tells that the authors agree to use the Bayesian strategy to deal with the fix effectiveness factors. The authors concede that the analysis of n and x as pseudo trials and failures was needless.

This paper studies the maximum likelihood estimation of a class of inverse Gaussian process models for degradation data. Both the subject-to-subject heterogeneity and covariate information can be incorporated into the model in a natural way. The EM algorithm is used to obtain the maximum likelihood estimators of the unknown parameters and the bootstrap is used to assess the variability of the maximum likelihood estimators. Simulations are used to validate the method. The model is fitted to laser data and corresponding goodness-of-fit tests are carried out. Failure time distributions in terms of degradation level passages are calculated and illustrated. The supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]

Sufficient dimension-reduction methods provide effective ways to visualize discriminant analysis problems. For example, Cook and Yin showed that the dimension-reduction method of sliced average variance estimation (SAVE) identifies variates that are equivalent to a quadratic discriminant analysis (QDA) solution. This article makes this connection explicit to motivate the use of SAVE variates in exploratory graphics for discriminant analysis. Classification can then be based on the SAVE variates using a suitable distance measure, If the chosen measure is Mahalanobis distance, then classification is identical to QDA using the original variables. Just as canonical variates provide a useful way to visualize linear discriminant analysis (LDA), so do SAVE variates help visualize QDA. This would appear to be particularly useful given the lack of graphical tools for QDA in current software. Furthermore, whereas LDA and QDA can be sensitive to nonnormality, SAVE is more robust. [ABSTRACT FROM AUTHOR]

Variable selection, the search for j relevant predictor variables from a group of p candidates, is a standard problem in regression analysis. The class of 1D regression models is a broad class that includes generalized linear models. We show that existing variable selection algorithms, originally meant for multiple linear regression and based on ordinary least squares and Mallows's Cp, can also be used for 1D models. Graphical aids for variable selection are also provided. [ABSTRACT FROM AUTHOR]

People that the author would like to thank for their assistance in his designation as the editor of the journal are mentioned.

Variable selection, the search for j relevant predictor variables from a group of p candidates, is a standard problem in regression analysis. The class of 1D regression models is a [...]

We present graphical and numerical methods for assessing the adequacy of the log-linear model for variances. The proposed methods are derived from the cumulative sum of residuals over the covariate [...]

Data in statistical practice often consist of nonnegative measurements that exhibit positive skewness. The inverse Gaussian (IG) family of distributions provides a versatile and flexible model for analyzing such data. [...]

We consider the problem of selecting appropriate [2.sup.m-p] designs when some two-factor interactions are important. Current methods in the literature select designs that permit estimation of the postulated model consisting [...]

The terms curvature and interaction traditionally are not defined or used in the context of mixture experiments because curvature and interaction effects are partially confounded due to the mixture constraint [...]