Abstract: As we know, CUSUM and Shewhart control charts have good performance of detecting 
small and large shifts from the target value, respectively. And for a given shift $\delta$, the CUSUM 
chart with reference value $k=\delta/2$ is the optimal one in terms of out-of-control ARL. However, 
we do not know how big the shift will be taken in practice. For this situation, we have enough reasons
 to assume the shift locates in a interval. Obviously, for this kind of shift, CUSUM scheme with a given 
reference value is not the optimal control chart. In this paper, we firstly propose two criteria of comparing 
the performance of two control charts for detecting the interval shift, that are: the integral difference of the 
two charts' out-of-control ARL's (IDARL) and the integral ratio of the two charts' out-of-control ARL's 
(IRARL). And then we propose a new control chart-dual CUSUM (DCUSUM) control chart, which is 
combined from two independent CUSUM charts. Thirdly, using Markov chain method, we obtain the 
formula for evaluating the ARL of one sided DCUSUM scheme. Finally, we compare the performance 
of DCUSUM control chart with CUSUM, combined Shewhart-CUSUM control charts. From the view of 
out-of-control ARL, we can observed that DCUSUM scheme has better performance than that of 
CUSUM and combined Shewhart-CUSUM schemes uniformly. Moreover, two kinds of design for 
DCUSUM's reference values and the ratio between the two CUSUM's in-control ARL is considered 
in this paper.