Defining Target Tolerances Expressing Target Requirements At Least

Expressing Target Requirements • At Least X: – Target value has a lower bound

Targeting with Confidence? • Tolerances define the acceptable deviations from target values • Example:

Targeting with Tolerances • Example: at most X: – 95% of the time, the

Targeting with Tolerances • Between X and Y: – Example: length of widget must

Targeting with Tolerances • Exactly X: – Most of product will fall within the

Example: Bicycle Wheel • The weight and cost of a bicycle wheel depend on:

Example: Bicycle Wheel • The lifetime of the wheel depends on: – Number of

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Defining Target Tolerances

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

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

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

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

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.

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 Fig: Distribution of Spoke Thickness (2+/-0. 01 mm) • Material cost ($1. 00+/-0. 05 per 1000 cm 3)

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)