Example 1.1 Illustrates the Fundamental Nature of Variation in Estimates

An engineer is performing an analysis of warranty costs for drive train repairs within the fi  rst  year of ownership of luxury cars purchased in the United States. He found the average cost (to  the nearest dollar) to be $570 per repair from data taken over a 5-year period.

What range of repair costs should the engineer use to ensure that the analysis is sensitive to  changing warranty costs?

Solution

At  first glance the range should be approximately –25% to 15% of the $570 average cost to  include the low of $430 and high of $650. However, the last 3 years of costs are higher and  more consistent with an average of $631. The observed values are approximately ±3% of this  more recent average.

If the analysis is to use the most recent data and trends, a range of, say, ± 5% of $630 is recommended. If, however, the analysis is to be more inclusive of historical data and trends, a range  of, say, ± 20% or ± 25% of $570 is recommended.