Odd behaviour?

One of my chickens ~ Felicity ~ is doing something rather odd (well odd for me as I am a novice).  She is the one that has never laid an egg besides the shell-less one.  
She follows the same routine as Penny before going to lay and egg, i.e eats pellets, drinks quite a bit of water then goes into the nesting box to lay and egg.  The exception being that Felicity doesn't lay an egg.  When she comes out she then goes around picking up long bits of grass or twigs and throws them on her back.  Could she have a problem with her vent?  She seems otherwise happy eating, drinking and foraging in the grass and she looks healthy.  
I saw her doing this about a week ago and then again this morning, which prompted me to make this post for advice.

I followed the advice given in my previous post and stopped giving them treats and they went back to eating their pellets quite happily with one treat in the late afternoon.

I would appreciate any help on this as I am totally clueless as to what she is up to.  

Thanks in advance

Carol

I have one that does this from time to time but only when she's broody and has been chucked out of the nest. Has Felicity never laid an egg?

Only the one that was shell-less.  She just goes into the nesting box and comes out again a while later without laying an egg.

We got our 2 chickens on the Friday (3 weeks ago) and Penelope gave us our first egg on the Monday and all her eggs are a good size with a nice shell, but Felicity has never given us an egg. 
They are both the same age ~ around 18 months I am told) and the come from the same stock so I am really at a loss as to why one is laying whilst the other isn't.
Felicity was a bit shy when she first arrived and spent the first day roosting, but she has come out of her shell (pardon the pun  ) and appears to be as happy and healthy as Penny.

Thanks themagicaltoad 
I do believe she was laying before we got her.  I will just let her do own thing and hopefully she will start laying soon.  They both have access to grit with oyster shell and are back to eating their pellets so as you said, she is probably just taking longer to adjust.

Thanks again 

When my Barnevelder settles to lay her egg she tosses bits of straw on her back.  She is the only one I have observed closely when laying so the only one I can comment on.  She walks around making a bit of a fuss, then goes to her nest in the corner of the garden (despite me supplying a perfectly good nest box in the coop!) 

Then she snuggles down into her specially-prepared dent under the nasturtium plant, pulls extra leaves and straw in around her, and picks up bits of straw one at a time to toss over har back.  After sitting quietly for a while she lays her egg.   

It sounds to me like your Felicity is just doing all the usual egg-laying behaviour, perhaps in preparation for laying an egg soon.  As others have advised, I wouldn't worry about it.  She sounds happy and healthy so just enjoy her funny ways, while you wait and see what happens.