Zic A i think comes with 2 ratings... 5W-20 and 5W-30. this oil is used in newer engines and also in old engines during cold weather for easier starting.
Try a different oil with rating of 10W-40 / 15W-40 / 20W-40.
the higher the numbers the thicker the oil. Your piston rings may be slightly weak therefore allow a very small amount of oil to leak into the combustion chamber.
you say there is no smoke in the exhaust but i think there would be very little smoke now, which would not be visble until the matter gets worse.
thicker oil should solve your problem.