I am in ICU rotation.  Oftentimes I need interpret low cortisol level.  There is a test to diagnose adrenal failure.  The cosyntropin stimulation test: cosyntropin, 250 mcg, IV or IM, plasma cortisol is measured 30 minutes later.  The normal response is a stimulated plasma cortisol > 20 mcg/dL. (reference: Washington Manual of Therapeutics, page 634)

After diagosing adrenal failure, primary or secondary adrenal failure need be differentiated.  It could be achieved through clinical manifestation, other lab tests, please see details in Washington Manual.

In terms of management, hydrocortisone 100 mg IV q8h, as well as D5NS infusion to correct hypotension.  Tapering hydrocortisone afterwards.