There are a couple of options that might do what you want.
In the Process Properties dialog, try checking "One project per job" Assuming you have multiple projects for this one process, it should allow you to have one job that fails while another runs successfully (instead of the failure halting the successful job).
There is also a setting in the Project properties (When opened with XPRJ Editor) under the input tab, set the "File Existence criteria" to "not required". When used in combination with the above setting this should allow you to have multiple projects that run under a single process and do not throw errors when one of them doesn't have a source file (that project will just be skipped).
Thanks for your information. It is possible to run one project in a process which contains multiple projects? As per your instruction I tried the second option "File existence Criteria" to " Not required" and ran the process. It ran successfully. But it is possible to run the skipped project alone? I do not find an option to run the skipped project alone. Could you please advise.
It's not possible to do this via the interface with DataPump v9.
Creating a new process with one project in it is easy, but recreating export distributions can be a pain. DataPump v10, I believe, has the option to copy a process, and this would allow you to then delete the redundant projects and just keep the one you need, with scripts and distributions preserved.