The dielectric strength of transformer oil is a measure of the oil's ability to withstand electrical stress without failure.
Water, sediment and conducting particle reduce the dielectric strength of transformer oil. Combination of these tends to reduce the dielectric strength to a greater degree.
Clean dry oil has an inherently high dielectric strength but this does not mean the absence of all contaminants, it may merely indicate that the amount of contaminants present is not large enough to affect the break down voltage of oil.
Careless sampling and testing techniques is the source of 99% of bad dilectric strength.
If the dielectric strength of the oil is too low, the normal remedy is to recycle the oil.