On control charts for monitoring the variance of a time series

• Several new control charts for monitoring the variance are introduced.
• Our results cover all ARMA processes with Gaussian white noise.
• The charts are derived by using the LR, SPRT and Shiryaev–Roberts procedures.
• Generalized control charts are derived as well.
• An extensive comparison study is provided.

In this paper we derive control charts for the variance of a Gaussian process using the likelihood ratio approach, the generalized likelihood ratio approach, the sequential probability ratio method and a generalized sequential probability ratio procedure, the Shiryaev–Roberts procedure and a generalized modified Shiryaev–Roberts approach. Recursive presentations for the calculation of the control statistics are given for autoregressive processes of order 1. In an extensive simulation study these schemes are compared with existing control charts for the variance. In order to asses the performance of the schemes both the average run length and the average delay are used.