Smudging the eye pencils over the eyelid and on the water line is a common issue.
You can prevent the pencil eyeliner from smudging by applying a powder eye shadow over the pencil. The eye shadow will set the eyeliner in place and prevent it from smudging or smearing.
You can choose matching or slightly darker shade eye shadows to create more depth in the shade.
Below is an example of an eye pencil / eye shadow combination that can be used.