Final answer:
The depreciation method not based on the passage of time is the Activity method, which allocates an asset's cost based on actual usage rather than time.
Step-by-step explanation:
The depreciation method that is not based on the passage of time is the Activity method (also known as the units of production method). Unlike the Sum of the Year's Digits, Straight-line, and Declining balance methods, which are time-based and depreciate an asset over its useful life, the Activity method depreciates an asset based on its actual usage or output.
In the Activity method, an asset's cost is allocated over its expected usage units, which could be miles driven, hours used, or units produced. As the asset is utilized, depreciation expense is recorded in direct proportion to the usage. This approach reflects the economic wear and tear on the asset more closely than just the passage of time.