E. S. Page

Bio: E. S. Page is an academic researcher from University of Cambridge. The author has contributed to research in topics: Control chart & Score test. The author has an hindex of 6, co-authored 6 publications receiving 5018 citations.

Cumulative Sum Charts

Abstract: This paper, presented orally to the Gordon Research Conference on Statistics in Chemistry in July 1960, traces the development of process inspection schemes from the original methods of Shewhart to the new charts using cumulative sums, and surveys the present practice in the operation of schemes based on cumulative sums. In spitc of the completely different appearance of the visual records kept for Shewhart and cumulative sum charts, a continuous sequence of development from the one type of scheme to the other can be established. The criteria by which a particular process inspection scheme is chosen are also developed and the practical choice of schemes is described.

An improvement to wald's approximation for some properties of sequential tests

Abstract: SUMMARY A SIMPLE modification of the Wald approximations to the operating characteristic and average sample number of a sequential test is given which provides estimates of their values for starting points of the test near the boundaries and an improved approximation for general starting points. In his book Sequential Analysis Wald (1947)gives an approximate formula for the operating characteristic of a sequential test or, equivalently, for the probability that a particle performing a linear random walk between two absorbing barriers is absorbed by a specified barrier. This formula is valid for starting points of the test not near either boundary and for mean paths inclined at not more than a small angle to the boundaries so that the overlap of the boundary at the end of the test is negligible. In this note we give a simple modification of Wald's formula which provides a better approximation and gives some information about values at the boundaries. Suppose that a Wald sequential test is to be carried out on a population for which the scores, xi, assigned to the observations are independent variates from a population with a continuous frequency functionf (x). Let the boundaries of the test be a, b (a 1). With this scoring system the boundaries in the Wald inspection diagram (Wald, 1947, p. 120) are the horizontal lines with ordinates a, b; in terms of the linear random walk, a, b are the positions of the two point boundaries. By considering expectations conditional upon the first observation, we find that the probability that the test ends at the lower boundary, P (Z), satisfies the equation (e.g., Kemperman, 1950) b

Techniques for Testing the Constancy of Regression Relationships Over Time

Abstract: Methods for studying the stability over time of regression relationships are considered. Recursive residuals, defined to be uncorrelated with zero means and constant variance, are introduced and tests based on the cusum and cusum of squares of recursive residuals are developed. Further techniques based on moving regressions, in which the regression model is fitted from a segment of data which is moved along the series, and on regression models whose coefficients are polynomials in time are studied. The Quandt log-likelihood ratio statistic is considered. Emphasis is placed on the use of graphical methods. The techniques proposed have been embodied in a comprehensive computer program, TIMVAR. Use of the techniques is illustrated by applying them to three sets of data.

Detection of abrupt changes: theory and application

Abstract: This book is downloadable from http://www.irisa.fr/sisthem/kniga/. Many monitoring problems can be stated as the problem of detecting a change in the parameters of a static or dynamic stochastic system. The main goal of this book is to describe a unified framework for the design and the performance analysis of the algorithms for solving these change detection problems. Also the book contains the key mathematical background necessary for this purpose. Finally links with the analytical redundancy approach to fault detection in linear systems are established. We call abrupt change any change in the parameters of the system that occurs either instantaneously or at least very fast with respect to the sampling period of the measurements. Abrupt changes by no means refer to changes with large magnitude; on the contrary, in most applications the main problem is to detect small changes. Moreover, in some applications, the early warning of small - and not necessarily fast - changes is of crucial interest in order to avoid the economic or even catastrophic consequences that can result from an accumulation of such small changes. For example, small faults arising in the sensors of a navigation system can result, through the underlying integration, in serious errors in the estimated position of the plane. Another example is the early warning of small deviations from the normal operating conditions of an industrial process. The early detection of slight changes in the state of the process allows to plan in a more adequate manner the periods during which the process should be inspected and possibly repaired, and thus to reduce the exploitation costs.

A survey on concept drift adaptation

Abstract: Concept drift primarily refers to an online supervised learning scenario when the relation between the input data and the target variable changes over time. Assuming a general knowledge of supervised learning in this article, we characterize adaptive learning processes; categorize existing strategies for handling concept drift; overview the most representative, distinct, and popular techniques and algorithms; discuss evaluation methodology of adaptive algorithms; and present a set of illustrative applications. The survey covers the different facets of concept drift in an integrated way to reflect on the existing scattered state of the art. Thus, it aims at providing a comprehensive introduction to the concept drift adaptation for researchers, industry analysts, and practitioners.