A mixed model with a white noise process and an IMA(0,1,1) process is considered as a process model. It is assumed that the process is a white noise in the absence of a special cause and the process changes to an IMA(0,1,1) due to a special cause. One useful scheme in measuring the process level is to use the variable measurement interval (VMI) between measurement times according to the value of the previous chart statistic. The advantage of the VMI scheme is to measure the process level infrequently when in control to save the measurement cost and to measure frequently when out of control to save the off-target cost. This paper considers the VMI scheme in order to detect changes in the process model from a white noise to an IMA(0,1,1). The VMI scheme is shown to be effective compared to the standard fixed measurement interval (FMI) scheme in both statistical and economic contexts.