1. Defining Target Tolerances

2. Expressing Target Requirements At Least X: –Target value has a lower bound of X –No upper bound –Example: each box will hold at least 500 nails At most X: –Target value has an upper bound of X –No lower bound –Example: temperature in a system must not be over 15ºC Between X and Y: –Target value has an upper bound of Y –Target value has a lower bound of X –Example: length of widget must be between 9 cm and 9.5 cm Exactly X: –Target value is exactly X (i.e. upper bound equals lower bound of X) –Example: 100 g calibration weights for a balance must be exactly 100 g

3. Targeting with Confidence? Tolerances define the acceptable deviations from target values Example: at least X: –90% of all boxes will hold at least 500 nails

4. Targeting with Tolerances Example: at most X: –95% of the time, the temperature in a system is less than or equal to 15ºC

5. Targeting with Tolerances Between X and Y: –Example: length of widget must be between 9 cm and 9.5 cm

6. Targeting with Tolerances Exactly X: –Most of product will fall within the range X±δ –Ex: 99.9% of 100 g calibration weights for a balance will weigh 100±0.0005 g.

7. Example: Bicycle Wheel The weight and cost of a bicycle wheel depend on: –Material properties and material volume Density (7850 kg/m 3 ) Spoke Thickness (2+/-0.01 mm) Material cost ($1.00+/-0.05 per 1000 cm 3 ) Fig: Distribution of Spoke Thickness

8. Example: Bicycle Wheel The lifetime of the wheel depends on: –Number of cycles to failure –Average riding speed (20+/-5 mph) –Roughness of terrain (waves per unit length) –Usage time (10+/-10 hours/week) –Rider weight (165+/-70 lb)