You appear to have many irregular ripples when your V+ is not stable going up or down. Each logic interface can react differently.
Therefore you must decide what state your logic should be in or have an uninterrupted power supply.
If V+ is interrupted or AC is lost or brownout , you must define the sequence of events in a controlled manner or even if multiple supplies exist.
I would suggest, without knowing these details a "Power Good" detector is required for !OE.
How you define this, depends on previous details.
One example may be if V+< (Nom-10%) then OE= high.(off)
This could be done with Programmable zener chip. You may need to add an appropriate time delay for ON and instant for OFF.