I'm guessing that you're referring to Josephine Cochrane, the woman who invented the dishwasher. Josephine Cochrane was a wealthy Chicago-area socialite who loved to entertain. She was very proud of her fine china, which had been in her family since the 17th century. Unfortunately, her household staff didn’t share her pride and were most careless when washing and drying her prized plates. Cochrane was tired of finding chips and cracks in her best dishes, she decided there must be a more efficient way of cleaning them.
If I am correct in my guess, then the proper phrase would be:
tired of her servants chipping her plates
Because it wasn't just one member of her staff who was careless with her plates, it was many different people so the plural "servants" would be used.