Dimensional analysis of airline quality

Dimensional analysis is widely used in physics and engineering to contribute to modeling systems in which variables are measured in incompatible units. I used dimensional analysis to rank the airlines in overall quality based on US Department of Transportation data: on-time arrivals, denied boardings, mishandled baggage, and customer complaints. The results conflict with the well-known airline quality rating (AQR), published annually since 1991 by Bowen and Headley. Weighted averages of quality data in the AQR are dimensionally incorrect and produce ranking that are virtually independent of on-time arrivals. For example, the 2001 AQR ranks Alaska Airlines first in overall quality, despite the worst on-time performance in the industry. Dimensional analysis places Alaska Airlines near the bottom of the industry, seventh in overall quality.