We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Introduction to Mathematical Statistics. By R.V. Hogg and A. T. Craig. Pp. ix, 245. 47s. 1959. (The Macmillan Company, New York)

Control chart limits are often calculated using parameter estimates from an in-control Phase I reference sample. In Phase II monitoring, statistics based on new samples are compared with the estimated control limits to monitor for departures from the in..

Effects of Parameter Estimation on Control Chart Properties; A Literature Review

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.

/pdf/multivariate-statistical-process-control-charts-an-overview-1vbmsl9ae7.pdf

Multivariate statistical process control charts: an overview

There are many applications of control charts in health-care monitoring and in public-health surveillance. We introduce these applications to industrial practitioners and discuss some of the ideas that arise that may be applicable in industrial monitoring. The advantages and disadvantages of the charting methods proposed in the health-care and public-health areas are considered. Some additional contributions in the industrial statistical process control literature relevant to this area are given. There are many application and research opportunities available in the use of control charts for health-related monitoring.

/pdf/the-use-of-control-charts-in-health-care-and-public-health-3gpbuh1ni4.pdf

The Use of Control Charts in Health-Care and Public-Health Surveillance

The use of control charts is considered for situations in which the quality of a process or product is better characterized by a relationship between a response variable and one or more explanatory variables than by use of a univariate quality character..

Using Control Charts to Monitor Process and Product Quality Profiles

Human tactile perception is studied through digitized images of hand-drawn curves generated by subjects treated with various facial preparations The drawings represent their subjective assessment of a small brush moving across the face In this study, exploratory data analysis is carried out through a functional data analog of principal components analysis and curve decomposition based on Fourier representations In addition, high-dimensional analysis of variance is adapted for mixed-model functional data and applied to test whether preparation effects are significant

Mixed-Model Functional ANOVA for Studying Human Tactile Perception

Performance evaluation of social network anomaly detection using a moving window–based scan method

The detection of clusters of events occurring close together both temporally and spatially is important in finding outbreaks of disease within a geographic region. The Knox statistic is often used in epidemiology to test for space-time clustering retrospectively. For quicker detection of epidemics, prospective methods should be used in which observed events in space and time are assessed as they are recorded. The cumulative sum (CUSUM) surveillance method for monitoring the local Knox statistic tests for space-time clustering each time there is an incoming observation. We consider the design of this control chart by determining the in-control average run length (ARL) performance of the CUSUM chart for different space and time closeness thresholds as well as for different control limit values. We also explain the effect of population density and region shape on the in-control ARL and discuss other distributional issues that should be considered when implementing this method.

Use of the local Knox statistic for the prospective monitoring of disease occurrences in space and time

We consider a $\psi$-irreducible, discrete-time Markov chain on a general state space with transition kernel $P$. Under suitable conditions on the chain, kernels can be treated as bounded linear operators between spaces of functions or measures and the Drazin inverse of the kernel operator $I - P$ exists. The Drazin inverse provides a unifying framework for objects governing the chain. This framework is applied to derive a computational technique for the asymptotic variance in the central limit theorems of univariate and higher-order partial sums. Higher-order partial sums are treated as univariate sums on a `sliding-window' chain. Our results are demonstrated on a simple AR(1) model and suggest a potential for computational simplification.

https://projecteuclid.org/download/pdf_1/euclid.ecp/1465224956

Dan J. Spitzner

Papers

Using Control Charts to Monitor Process and Product Quality Profiles

Mixed-Model Functional ANOVA for Studying Human Tactile Perception

Performance evaluation of social network anomaly detection using a moving window–based scan method

Use of the local Knox statistic for the prospective monitoring of disease occurrences in space and time

Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.