Methods for Monitoring Process Control and Capability in the Presence of Autocorrelation.

When standard control charts are applied to a process whose measurements of quality exhibit autocorrelation, the performance of those charts can be considerably different than that expected when no autocorrelation is present. To model this performance, the existing definitions of assignable and chance causes of variation are extended to account for the variation induced by the autocorrelation structure. The application of statistical thinking toward continuous process improvement using the proposed taxonomy is discussed. A method to select control limits which yield a specified average run length in the absence of assignable causes of variation and which is suitable for use on processes whose behavior can be modelled as an ARMA1,1 process is developed. The current paradigm for process improvement is centered around monitoring the state of statistical control. A new paradigm, based upon monitoring process capability, is proposed. The time varying aspects of capability are highlighted. A capability monitoring system for stationary ARMA1,1 processes is developed and compared to other standard methods. The benefits of additional knowledge are demonstrated by simulating the response of capability monitoring systerns tailored to independent normal and mixed ARMA1,1 models to shifts in the mean and variance.