"We always think of semiconductors failing because of heat"
That is still correct, however, which is why the Arhenius equation is so widely used for electronics. Also in answer to the OP's question, you need to perform an accelerated life test, assuming you want to spend the money. You'd need to run at least two batches of parts at different temperatures to failure, and the failure rates as a function of temperature can then be determined, as well as identifying which components are the weakest. There are a series of military standards that describe how life testing is performed.
160ºF = 71ºC, which is already at the upper limit of commercial component temperature ratings; when you factor in the thermal resistance of the components within the supply to that ambient temperature, you could be easily at 85ºC. which is the temperature limit for many industrial temperature range components. Given that, you definitely need to run a few supplies at a minimum of 85ºC ambient, with instrumentation on the components to determine what the induced case temperatures are. I suggest the higher ambient temperature because it's almost invariably true that a "measured" ambient temperature is taken where it's convenient, and may not reflect the true thermal environment. We once ran a life test in an oven with 125ºC ambient temperatures, but the test engineer didn't do any thermal calculations to predict that the 1.5 kW being dissipated by the components might raise the local ambient temperatures above 180ºC, resulting in junction temperatures in excess of 200ºC. Naturally, we got failures almost immediately.
As far as the duration is concerned, therefore, if the part is truly that susceptible, you might try three supplies at 70ºC, 85ºC, and 100ºC, and run them to failure, since that's the actual objective, to determine the weakest component(s) within the power supply. This may become and iterative process, as you may have multiple weak links. As a first step, though, you may need to revisit the parts list of the supply and determine whether all the components are rated for at least 85ºC ambient. Note, also, your supplies may not necessarily have permanent failures,; they may just be operating outside of the design conditions and may regain operability when cooled down.
TTFN
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