Monitoring simple linear profiles in the presence of within‐ and between‐profile autocorrelation

Abstract

AbstractThe current study investigates the effect of within‐profile and between‐profile autocorrelations on the performance of four monitoring methods of simple linear profiles in Phase II. To this end, a general correlation model between error terms is considered such that the correlation structure of within‐profiles errors and the error terms between consecutive profiles follow an autoregressive (AR) times series model of order one. Extensive simulations have been done to assess the effect of both autocorrelation types and the profile size on the estimations of the model parameters as well as the performance of control charts. The performance of the monitoring schemes is investigated and compared with respect to the average run length (ARL) metric. The simulation study results show that the autocorrelation within and between profiles has a negative impact on the monitoring technique's performance. It reduces the control chart's ability to detect process shifts compared to no or weak autocorrelation cases. Moreover, the performance of all the methods is improved by increasing the profile size. An illustrative example is also provided to demonstrate the use of the proposed methods for monitoring the stability of profiles in the chemical industry.