How can I specify a color so that manufacturers the world over will use the same color paint?
Yes, there is a standard way to match your color. What you want is a colorimetric specification and tolerance. Typical specifications are in terms of CIELAB coordinates of L*, a*, and b* and tolerances are normally set around the desired color in terms of some color difference equation. When the paint manufacturers matched your samples in the past, it is likely they measured existing samples and then matched those CIELAB coordinates. Perhaps you can get those values from one of the paint manufacturers to set your standards. Alternatively you can choose a standard sample and send it to a paint supplier and they can measure it. Regardless, it is always good practice to have a physical sample as a standard to allow visual checks of the instrumental color matches.