Phase II control charts for autocorrelated processes

A large amount of SPC procedures are based on the assumption that the process subject to monitoring consists of independent observations. Chemical processes as well as many non-industrial processes exhibit autocorrelation, for which the above-mentioned control procedures are not suitable. This paper proposes a Phase II control procedure for autocorrelated and possibly locally stationary processes. A time-varying autoregressive (AR) model is proposed, which is capable of dealing with the autocorrelation as well as with local non-stationarities of the temporal process. Such non-stationarities are induced by the time-varying nature of the AR coefficients. The model is optimized during Phase I when it is assured that the process is in control and as a result the model describes accurately the process. The Phase II proposed control procedure is based on a comparison of the current time series model with an alternative model, measuring deviations from it. This comparison is carried out using Bayes factors, which help to establish the in-control or out-of-control state of the process in Phase II. Using the threshold rules of the Bayes factors, we propose a binomial-type control procedure for the monitoring of the process. The methodology of this paper is illustrated using two data sets consisting of temperature measurements at two different stages in the manufacturing of a plastic mould.