In this paper, we define first, two-dimensional run by elaborating the concept of the traditional definition of run (one-dimensional run) and then propose a new statistical test with two-dimensional run which judges whether a process is under control or not. Second, a new multiple decision procedure for (x^^-, s) simultaneous control chart with two-dimensional run is designed to identify a type of change in a process when the run judges the process as out of control. Finally, the integrated multiple decision procedure for the (x^^-, s) simultaneous control chart is designed with control limits and two-dimensional run. The probability of the first kind of error and the power of this procedure obtained by the Markovian analysis is discussed.
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