Loss Function n n Losses begin to accrue

Loss Function n n Losses begin to accrue as soon as a quality characteristic of a product or service deviates from the nominal value Under the Taguchi Loss Function the continuous reduction of unit-to-unit variation around the nominal value is the most economical course of action, absent capital investment Slide 1

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¡ ¡ ¡ L(y) = k(y-m)2 = loss of deviating (y-m) units from the nominal value of “m” y= the value of the quality characteristic for a particular item of product or service m = the nominal value for the quality characteristic k = a constant, A/d 2 A = the loss (cost) of exceeding specification limits (e. g. , the cost to scrap a unit of output) d = the allowable tolerance from “m” that is used to determine specification limits. Slide 3

n Example ¡ Returning to the production of stainless steel ball bearings. Every millimeter higher or lower than 25 mm causes a loss that can be expressed by the following Taguchi loss function: L(y) = k(y-m)2 = (A/d 2)(y-m)2 = ($1. 00/5 mm 2)(y-25 mm)2 = (. 04)(y-25 mm)2 Slide 4

Diameter of Ball Bearing (y) Value of Taguchi Loss Function L(y) 18 1. 00 19 1. 00 20 1. 00 21 0. 64 22 0. 36 23 0. 16 24 0. 04 25 0. 00 26 0. 04 27 0. 16 28 0. 36 29 0. 64 30 1. 00 31 1. 00 32 1. 00 Slide 5

Robust parameter design An engineering method for product or process design that focuses on minimizing variation and/or sensitivity to noise. Provide a powerful and efficient method for designing products that operate consistently and optimally over a variety of conditions. Slide 6

The primary goal n n n find factor settings that minimize response variation, while adjusting (or keeping) the process on target. make the product insensitive to changes in uncontrollable (noise) factors produce more consistent output. Slide 7

Source : n Gitlow HS, AJ Oppenheim, R Oppenheim, DM Levine, Quality Management, Third Edition, Mc Graw Hill, Boston, 2005 [GIT] n Minitab Reference Manual Slide 8