It doesn't work like that. Most PC "manufacturers" (including Apple) don't make PCs, and they all use the same Taiwanese OEMs/ODMs and Chinese factories. The main ones are Quanta, Compal, Pegatron (spun out of Asus), Foxconn (Hon Hai), Wistron (spun out of Acer), Inventec etc.
Quanta is probably the biggest notebook manufacturer, followed by Compal and Pegatron. Compal and Pegatron probably have the best quality overall.
Most PC suppliers use several manufacturers, sometimes as many as five (Dell, I think). Asus currently uses Pegatron, Compal and Wistron, so it's average quality should be pretty good.
It's a tough business because the number of viable contract manufacturers is growing while the number of viable PC OEMs is shrinking. (No more Gateway, Compaq, TI, IBM etc, except as brands.)
In addition, companies with large volume sales can afford to offer several product ranges aimed at different markets. Dell, for example, has different ranges for consumers (Inspiron is low end, XPS is high end) and for businesses (Latitude, Optiplex, Precision), plus Vostro for the SO/HO market.
So, it doesn't really make a lot of sense to compare, for example, Dell with HP with Lenovo. They all have multiple ranges made in different factories -- and they could all be using the same factories!
You'd really need to compare the same types of laptop (low-end, mid-range, high-end / consumer, business, enterprise) across different PC manufacturers.
If you don't do this, the "worst" brand is likely to be whichever company makes the biggest volumes of really cheap consumer laptops, especially if they don't support them particularly well. This used to be Acer. Today, it's probably Lenovo.
Conversely, the "best" brand is likely to be whichever company makes the smallest volumes of really expensive laptops ;-)