A change point estimator in monitoring the parameters of a multivariate IMA(1, 1) model

Abstract

Abstract Modern production process is a very complex structure combined observations whichare correlated with several factors. When the error signal occurs in the process, it isvery dicult to know the root causes of an out-of-control signal because of insucientinformation. However, if we know the time of the change, the system can be controlledmore easily. To know it, we derive a maximum likelihood estimator (MLE) of thechange point in a process when observations are from a multivariate IMA(1,1) processby monitoring residual vectors of the model. In this paper, numerical results show thatthe MLE of change point is e ective in detecting changes in a process.Keywords: Change point, maximum likelihood estimator, multivariate exponentiallyweighted moving average control chart. 1. Introduction Statistical process control (SPC) charts are utilized for the purpose of monitoring for pro-cess changes by nding the special causes of variation. A control chart statistic is comparedto one or more control limits with data are gathered from a process. If the control chartstatistic exceeds a control limit, then special causes exist in the process. Although the qual-ity of products is characterized by several variables correlated in real industrial processes,most previous studies of process have been implemented in one variable process. If qualitycharacteristics are inuenced by several factors, one variable process control chart is usefulno longer. The objective of multivariate SPC charts is nding the special causes of variationlike those of univariate SPC. The charts send a signal, when the mean vector shifted, orwhen the covariance matrix perturbed, or when both the mean vector and the covariancematrix are shifted simultaneously.Hotelling’s T2 charts only take into account the present information of the process, thusbeing little powerful for detecting small changes. To improve eciency in the case of smallchanges in the process, mulitivariate the exponentially weighted moving average (EWMA)control chart was developed. The advantage of the chart is that it can give considerationto the present and past information of the process. Therefore, it is more powerful to detectsmall changes than Hotelling’s T2.