Lab #2 Loss Function

Objective:

To better understand how to calculate loss with an actual data set.  How to interpret the results using the Taguchi Loss Function and comparing these to traditional methods.

Overview:

Devise a process to cut a series of one-inch length parts from a three-foot long wooden dowel.  Use the formulas below in your calculations.  The failure cost for each peg is 20 cents.  That is, when a peg falls outside of the specification limits it must be discarded or reworked, which costs 20 cents.  The specification limit for the peg is 1.000 +/- .005 inches.

To calculate Taguchi Loss Function:

            Loss at a point (x) is L(x) = k (x-m) 2

            Loss of the sample set is L = k (s2 + (pm – m)2)

              Where:

k = the loss coefficient (a scaling factor)

x = a measured value (i.e. 0.992²)

m= the target value (i.e. 1.000²)

s= the standard deviation of the sample s =   [S (x-pm)2]/(n-1)

pm= process mean (average length)

Equipment:

Calipers

Wooden dowel, 3 foot long

Safety glasses

A process to cut the parts

Procedure:

Perform the following tasks in any shop available: using the band saw, the cut-off saw, any hand tool, a pocketknife, or plastic spoon.  You design the process!

With the wooden dowel, measure a one-inch piece.

Cut the one inch piece and number it.

Repeat the operation 32 more times.

Be sure to use the same process for all the parts being measured and cut!!

 Results:

After all parts are cut, measure each part length to .001² accuracy.

Record below the measurements of 11 samples, each with a sample size (n) of 3.

Calculate the mean and standard deviation of the sample.

Calculate the loss for each manufactured peg (loss at a point)

Sketch traditional and Taguchi loss curves using all data point losses.

Calculate the overall loss of the sample set (traditional and Taguchi).

Sample Number

N size

1

2

3

4

5

6

7

8

9

10

11

1

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 Discussion:

How can loss function data be used to improve your process?

Why are there losses attributed to a part that is within specification limits?

Compare the costs of traditional and Taguchi loss functions?

If a part is in spec, where is the lost money coming from?

What do your calculations tell you in regards to your process and your parts?