Since the work of Page in the 1950s, the problem of detecting an abrupt change in the distribution of stochastic processes has received a great deal of attention. In particular, a deep connection has been established between Lorden’s minimax approach to change-point detection and the widely used CUSUM procedure, first for discrete-time processes, and subsequently for some of their continuous-ti...

Exponential CUSUM charts are used in monitoring the occurrence rate of rare events because the interarrival times of events for homogeneous Poisson processes are independent and identically distributed exponential random variables. In these applications, it is assumed that the exponential parameter, i.e. the mean, is known or has been accurately estimated. However, in practice, the in-control m...

An efficient sequential nonparametric multichart (multichannel) CUSUM-type detection test for detecting changes in multichannel sensor systems is proposed. While there is a wide spectrum of applications where it is necessary to consider multichannel generalizations and general statistical models in change-point detection problems, the study in this paper is motivated by network security. Many k...

This correspondence considers the problem of detecting abrupt changes in the mean of a multivariate Gaussian random signal. A fixed sample size -test is compared against the optimum sequential tests ( -CUSUM and -GLR).

Generalizing a result of Furstenberg, we show that for every infinite discrete group $G$, the Bernoulli flow $2^G$ is disjoint from minimal $G$-flow. From this, deduce algebra generated by functions $\mathfrak{A}(G)$ proper subalgebra $\ell^\infty(G)$ and enveloping semigroup universal $M(G)$ quotient $\beta G$. When $G$ countable, also prove any metrizable, $G$-flow, there exists free, it exis...

In particular, the values at x = 0 are called Bernoulli numbers of order k, that is, Bn (0) = Bn k) (see [1, 2, 4, 5, 9, 10, 14]). When k = 1, the polynomials or numbers are called ordinary. The polynomials Bn (x) and numbers Bn were first defined and studied by Norlund [9]. Also Carlitz [2] and others investigated their properties. Recently they have been studied by Adelberg [1], Howard [5], a...

Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart cumulative sum (CUSUM) chart. In addition, new schemes proposed based on alternative weighting of past data, usually put greater emphasis data less weight current recent data. other cases, output one method, EWMA statistic, is used input another ...