Taguchi Loss Function vs. Traditional Goal Post

[b]APPLET DESCRIPTION[/b] A virtual manipulatives (interactive model) comparing Quality Yields using the Traditional Goal Post (Step Function) method vs. the Taguchi Loss Function method. Graphs include: [list] [*] Traditional Goal Post [*]Taguchi Loss Function [*]3 Scenarios for the Taguchi Loss Function [/list] [color=#0a971e]*** [i]This is just a functional prototype. Expect an improved version soon.[/i][/color] _____________________________________________________________________________________ [b]LITERATURE[/b] Traditionally, quality is viewed as a[b] Step function[/b] or [b] Traditional Goal Post (TGP)[/b] . A product is either good (within specifications) or bad (outside specifications). This view assumes a product is uniformly good between the specifications - the lower specification limit (LSL) and the upper specification limit (USL). If your data fits between the LSL & USL, then you are meeting your customer's requirements. However, a product's performance may fall within spec but will not produce close to the target. Several of these "[color=#c51414]good parts[/color]" may [b]not assemble well[/b], or may require [b]recall[/b], or may come back under [b]warranty[/b]. The vertical (y) axis represents the degree of displeasure the customer has with the product's / service's performance. [b]Genichi Taguchi[/b] believes that the customer becomes increasingly dissatisfied as performance departs farther away from the target and when it does, there's a [b]loss [/b]incurred by society. This loss may involve [b]delay[/b], [b]waste [/b][b]scrap [/b]or [b]rework[/b]. He suggests a quadratic curve to represent a customer's dissatisfaction with a product's performance (Quality Characteristic / Metric / KPI). The quadratic curve [b] target is set equal to zero[/b]. The [b] curve is centered on the target value[/b], which provides the best performance in the eyes of the customer. The [b]Taguchi Loss Function (TLF)[/b] uses both the process average and the variation as critical measures of quality. In essence, the Taguchi Loss Function measure quality. The vertical (y) axis represents the amount Loss ($) due to the product's / service's poor performance and high variation. The Taguchi Loss Function formula is: [b][math] L = k (y- m)^2 [/math][/b] where, [math]L[/math] = monetary loss ($) [math]k[/math] = loss coefficient [math]y[/math] = quality characteristic (metric / kpi) [math]m[/math] = target value for [math]y[/math] _____________________________________________________________________________________ [b]ASSUMPTIONS[/b] (for the Comparison between Traditional Goal Post vs. Taguchi Loss Function graphs) The 2 Normal Curves represent: [list] [*]same Value of a Characteristic (Metric / KPI) [*]the exact / same Averages [*]came from the same data set [*]taken on the same time period [*]check box for Show [b][color=#1551b5]∩[/color][/b] of Functions is based on the Intersection ([b][color=#1551b5]∩[/color][/b]) points of the functions (Normal Distribution & Taguchi Loss) [/list] [color=#0a971e]***[/color] [i]To [b]Reset [/b]the Graph (click the upper-most right corner) or Refresh your browser (F5) to initialize the default settings of the graphs.[/i] _____________________________________________________________________________________ [b]WALKTHROUGH (Part 1) [color=#1551b5]Comparison between Traditional Goal Post vs. Taguchi Loss Function[/color][/b]. [i]Default Settings for WALKTHROUGH (Part 1)[/i]: [list] [*]average = 5 [*]target = 5 [*]deviation = [color=#c51414][b]-[/b][/color]2.9 [/list] [i]We will now compare and contrast Quality via the Taguchi Loss Function (TLF) and Traditional Goal Post (TGP). [/i] [b][color=#198f88]Step 1[/color][/b]. Click the [b]Go to Student Worksheet[/b] button (or graph image) [b]below[/b] this page. [b][color=#198f88]Step 2[/color][/b]. Click the [b]Traditional Goal Post (TGP)[/b] check box. Note that: [list] [*][color=#1551b5]Yield [/color](within spec) =[color=#1551b5] 77.5%[/color] [*][color=#c51414]Defect [/color](out of spec) = [color=#c51414]22.5%[/color] [/list] [b][color=#198f88]Step 3[/color][/b]. Click the[b] Taguchi Loss Function (TLF) [/b]check box. Note that: [list] [*][color=#1551b5]Yield [/color](within spec) =[color=#1551b5] 62%[/color] [*][color=#c51414]Defect [/color](out of spec) = [color=#c51414]38%[/color] [/list] _____________________________________________________________________________________ [b]QUESTIONS[/b]: Q1. Which one has the highest Yield (TGP or TLF)? Q2. Based on your answer in Q1, does the [b]highest [/b] Yield (%) (TGP or TLF?) reflect our real performance in the eyes of our customers? Q3. If both TGP & TLF graphs have the same average and came from the same data set, why to they have differing Yields (%). Q4. Which one has the lowest Defect (TGP or TLF)? Q5. Based on your answer in Q4, does the [b]lowest [/b] Defect (%) (TGP or TLF?) reflect our real performance in the eyes of our customers? Q3. If both TGP & TLF graphs have the same average and came from the same data set, why to they have differing Defects (%). Q7. As a measure of your quality characteristic (metrics / kpi), would you prefer: [list] [*]A. Having your performance within the goal posts (Traditional Goal Post method) or [*]B. Trying to keep your performance as close to the target as possible (Taguchi Loss Function method). Explain why you chose A or B. [/list] _____________________________________________________________________________________ [b]WALKTHROUGH (Part 2)[/b] [b][color=#1551b5]3 Scenarios for the Taguchi Loss Function[/color][/b]. [i]Default Settings for WALKTHROUGH (Part 2)[/i]: [list] [*]average = 5 [*]target = 5 [*]deviation = [color=#c51414][b]-[/b][/color]2.9 [/list] [i]We will now compare and contrast Quality via 3 Scenarios for the Taguchi Loss Function (TLF).[/i] [b][color=#198f88]Step 4[/color][/b]. Click the Scenario 1 (TLF) check box. The configuration for [b]Scenario 1 is: On-Target vs. Off-Target (≠μ, =σ)[/b]. Q8. Two Quality Metrics are being compared here having different average but the same variation. Which one has better quality? Explain why. [list] [*]A. [b][color=#888]Gray [/color][/b]Normal Curve [*]B. [b][color=#b20ea8]Purple [/color][/b]Normal Curve [/list] [b][color=#0a971e]***[/color][/b][i] Hint: Compare the shaded areas. Shaded areas = Yield (within spec).[/i] [b][color=#0a971e]***[/color][/b][i] Before you answer, think about these factors as they affect the Yield: process average, variation (deviation), & target.[/i] ............................................................... [b][color=#198f88]Step 5[/color][/b]. Click the Scenario 2 (TLF) check box. The configuration for [b]Scenario 2 is : On-Target (=μ, ≠σ)[/b]. Q9. Two Quality Metrics are being compared here having the same average but different variation. Which one has better quality? Explain why. [list] [*]A. [b][color=#888]Gray [/color][/b]Normal Curve [*]B. [b][color=#198f88]Green [/color][/b]Normal Curve [/list] [b][color=#0a971e]***[/color][/b][i] Hint: Compare the shaded areas. Shaded areas = Yield (within spec).[/i] [b][color=#0a971e]***[/color][/b][i] Before you answer, think about these factors as they affect the Yield: process average, variation (deviation), & target.[/i] ............................................................... [b][color=#198f88]Step 6[/color][/b]. Click the Scenario 3 (TLF) check box. The configuration for [b]Scenario 3 is: On-Target vs. Off-Target (≠μ, ≠σ)[/b] Q10. Two Quality Metrics are being compared here having different average and different variation. Which one has better quality? Explain why. [list] [*]A. [b][color=#888]Gray [/color][/b]Normal Curve [*]B. [b][color=#d69210]Orange [/color][/b]Normal Curve [/list] [b][color=#0a971e]***[/color][/b][i] Hint: Compare the shaded areas. Shaded areas = Yield (within spec).[/i] [b][color=#0a971e]***[/color][/b][i] Before you answer, think about these factors as they affect the Yield: process average, variation (deviation), & target.[/i] _____________________________________________________________________________________ [b]References & Inspirations[/b]: [i][url=http://elsmar.com/Taguchi.html]elsmar.com[/url] [url=http://www.terninko.com/loss.htm]terninko.com[/url] [url=http://www.qimacros.com/lean-six-sigma-articles/taguchi-loss]qimacros.com[/url][/i] _____________________________________________________________________________________ applet created & shared by [color=#1551b5][url=http://www.geogebratube.org/user/profile/id/37538]daRny[/url][/color].

 

Randolph Abelardo

 
Resource Type
Activity
Tags
function  loss  probability  sigma  six  statistics  taguchi 
Target Group (Age)
19+
Language
English (United States)
 
 
 
© 2018 International GeoGebra Institute