No stability testing challenges the formula to see if it is stable for the emulsion, changes in odor, color and any number of factors under a certain protocol. There is no mandated protocol but most follow the guidance of the PCPC.
Challenge testing only assesses the preservative, not the physical factors.
Go to the site for Microchem, a testing Lab in Texas. They answer some of these questions.
You can NOT do these tests yourself unless you have expensive equipment and the knowledge. Send it out to someone like Microchem.