You could specify the following values for the parameters of the DFH$STED program if:
EODDRIFT=5 (5 minutes maximum drift time)
EODTIME=FIXED (a new end-of-day time)
EODFIXED=X'000000' (end-of-day time is midnight)
This would vary the statistics intervals by a pseudo-random amount, from midnight, up to maximum of five minutes:
Region 1 - statistics taken at 12.00.00
Region 2 - statistics taken at 12.04.10
Region 3 - statistics taken at 12.01.45
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Region n - statistics taken at 12.00.27