A good way to start would be to see the rate of photo-oxidation of polymers. You would have to see the chemical kinetics of this reaction to identify the rate. Then, you would need to know the surface area of the polymer which is exposed to UV as I guess the most damage happen on the surface. However, for a complete study, you would need to know the penetration of UV rays inside the material. With this information, you should be able to calculate the number of chains that are breaking per unit time. In an amorphous plastic, you should be able to calculate an expected value of chains per unit volume. Crystalline polymer(though uncommon) can be predicted to very high accuracy. As the volume of chains present decrease with time due to photo-oxidation, you will obtain a differential equation with respect to time in terms of number of chains. You can solve this to get the half life.