An easy test to begin with could be to just leave some of your suspension in an upright clear container and come back some time later. Has it phase separated/ sedimented/creamed?
Particle size analysis such as by laser diffraction could be used to monitor quantitively any aggregation or agglomeration of your sample, either over time or under different conditions.
Essence is given by Alexander. Stability is a complex issue because it includes stability against different processes of destabilization - separation based on gravity (Stokes), agglomeration, coalescence, Ostwald ripening, phase inversion, microbial and chemical processes.
One approach is to test several properties as function of time, single properties as particle size or properties affected by several individual properties, e.g. viscosity and separation behaviour (e.g. settling velocity will increase when agglomeration happened but also if external phase viscosity increased).
Tendency to separate based on gravity can be enhanced by temperature or centrifugation, where you have to check whether stress applied leads to structural changes of dispersion.
Alexander Malm , I did the first test but i need something with more information and less time range is there is one. For the laser diffraction analysis i don't have the tools for it.
Titus Sobisch , the main problem is sedimentation, the particles are 500 micro meter, i think i need to concentrate on the viscosity.
For the test based on gravity and enhanced by temperature, if i find that the product is stable for 1 month or 3 how much time can i consider it to be stable at room temperature?
for that you need the temperature function of viscosity for the continuous phase. Similar if you use centrifugation as first approximation you would correct velocity obtained by acceleration (linear approximation). For more precision you would have to check, how settling velocity depends on acceleration.