Modeling autocorrelated process control with industrial application

In past literature, a primary solution to deal with autocorrelated process data consists of two steps, namely (i) time series model building and (ii) control charting based on the residuals. However, it requires some sophisticated statistical skills to build a satisfactory model during the first step. This has motivated us to propose a new procedure of time series model building. If traditionally time series model building is based on autoregressive integrated moving average (ARIMA) models, in this paper we show that a great number of time series data are governed by geometric Brownian motion (GBM) law. If the process is governed by GBM law, the appropriate model is directly derived from the properties of that law. Otherwise, the model is constructed by using the standard practice. An industrial example is presented to illustrate the advantages of the proposed method.