Executive Summary Because of its excellent property, the cumulative sum (CUSUM) control chart has been widely used in practice. The traditional CUSUM control chart is designed to optimally detect a pre-specified shift in process mean/variance. However, in most cases, it is not easy to predict the magnitude of the shift to be occurred in the future. The CUSUM control chart designed as such may perform poorly as the actual shift is possibly different from the pre-specified. To meet this limitation in part, this thesis proposes an adaptive CUSUM (ACUSUM) control chart for monitoring process variance, which originates from the likelihood ratio test and has a concept similar to the adaptive CUSUM (ACUSUM) control chart for monitoring process mean. Compared to the traditional one, the basic idea of the ACUSUM control chart for monitoring process mean is to replace δ in the CUSUM increment I, by its estimate. In this thesis, Monte Carlo simulation is performed to investigate the effects of three parameters, δ⁺min, n, λ, on the ACUSUM control chart for monitoring process variance and the design procedure of ACUSUM control chart is proposed as well. In addition, the average run length (ARL) performance is compared between the ACUSUM control chart and the traditional CUSUM control chart. The comparison results show that the ACUSUM control chart for monitoring process variance proposed in this thesis can perform well on average over a range of shifts rather than the traditional CUSUM control chart only optimizing a particular shift when the pre-specified shift is equal to the actual shift.