1. A computer program product for monitoring processor characteristic information of a processor using run-time-instrumentation, the computer program product comprising: a non-transitory tangible storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method comprising: executing an instruction stream on a processor; detecting a run-time instrumentation sample point of the executing instruction stream on the processor; storing a reporting group in a run-time instrumentation program buffer based on the run-time instrumentation sample point, the reporting group including processor characteristic information associated with the processor; detecting a subsequent run-time instrumentation sample point of the executing instruction stream; checking current processor characteristic information prior to storing a subsequent reporting group in the run-time instrumentation program buffer based on the subsequent run-time instrumentation sample point; determining whether processors in a current configuration are configured to operate with a common CPU capability; and based on determining that a difference exists in CPU capability between the processors in the current configuration: reading a suppression control of a run-time instrumentation control; and suppressing storage of the subsequent reporting group in the run-time instrumentation program buffer based on the suppression control indicating that reporting group storage for a processor having a corresponding CPU capability is to be suppressed.