Abstract: Suppose that we are monitoring incoming observations for a change in mean via a cusum test statistic. The usual nonparametric methods give first and second order approximations for the one- and two-sided cases. We show how to improve the order of these approximations for linear statistics.

We develop an empirical approximation to the null steady-state distribution of the cumulative sum (CUSUM) statistic, defined as the distribution of values obtained by running a CUSUM with no upper boundary under the null state for an indefinite period of time. The derivation is part theoretical

of conservativeness is based on the relationship between the in-control ARL and the false alarm probability function by regarding the Cusum statistic as a Markov process. The comparison shows that standard Cusum charts are conservative in contrast to FIR Cusum charts. Moreover, the concept of false alarm probability

In this paper we consider the problem of testing for a scale change in the infinite order moving average process, for the parameters in unstable models, and for those of regression models with ARCH errors. For performing the test, the cusum of squares test analogous to Inclán and Tiao (1994)’s

Although optimality of sequential tests for the detection of a change in the parameter of a model has been widely discussed, the test parameter tuning is still an issue. In this communication, we propose a learning strategy to set the threshold of the GLR CUSUM statistics to take a decision with a

We consider statistical process control when measurements are multivariate. A CUSUM procedure is suggested in detecting a shift in the mean vector of the measurements, which is based on the cross-sectional antiranks of the measurements. At each time point, the measurements are ordered

This paper will review and compare five multivariate CUSUM techniques. Two of these are proposed by Crosier (1986), the multivariate CUSUM and the CUSUM of T (COT). It will also compare two proposed by Pignatiello (1986), the multivariate CUSUM #1 (MCl) and the multivariate CUSUM #2 (MC2

and upper one-sided CUSUM schemes with a 50 % head start are also carried out, leading to – what we believe – surprising results. Key Words: Statistical process control; control scheme; run length. 1

This paper develops a model for the analysis and design of a CUSUM chart for monitoring the process mean in short production runs and proposes statistical measures of performance that are appropriate when the process is not operating indefinitely. The model can be used to evaluate the performance

of the work published deal with shifts in the location of correlated processes. In this paper, the ARL performance of a CUSUM chart for process dispersion is analyzed, when the process does not comply with the assumption of independence. The ARL performance of the CUSUM chart for dispersion derived assuming