lect13 - IE 410: Design of Experiments Lecture 13: Latin...

Info iconThis preview shows pages 1–16. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: IE 410: Design of Experiments Lecture 13: Latin Squares We have seen that in some cases, several noise factors can often be blocked at the same time (e.g. age, gender, weight of subjects are all blocking factors) Treatment 1 2 3 4-------------- X X X X Block 1: Young, female, 10-30 overweight X X X X Block 2: Middle aged, male, not overweight X X X X Block 3: Young, male 30-50 overweight etc. In other cases this is not physically possible: Recall the Car example: Blocking factor 1: Car (1,2,3,4) Blocking factor 2: Position (LF,LR,RF,RR) There is no way to handle both of these together. That is, we can't do this: Treatment (Tire Brand) A B C D--------------------- X X X X Block 1: Car 1 and LF X X X X Block 2: Car 2 and LR X X X X Block 3: Car 3 and RR . . . Example : Test 5 Chemical recipes Blocking factor 1: batches of raw material (each batch contains only enough raw material to make 5 recipes). Blocking factor 2: Operator who prepares the recipe from the raw materials For this example, one might use a RCBD. Treatment (Recipe) A B C D E------------------ X X X X X Block 1: Batch 1, Operator 1 X X X X X Block 2: Batch 2, Operator 2 X X X X X Block 3: Batch 3, Operator 3 X X X X X Block 4: Batch 4, Operator 4 X X X X X Block 5: Batch 5, Operator 5 Etc. . For both this example, and the car example, the Latin Square design can be used. A 5x5 Latin Square is: Block i ng Facto r 1 (e .g . opera to r s ) | 1 2 3 4 5- - | - - - - - - - - - - - - - - - - 1 | A B C D E Block i ng 2 | B C D E A Facto r 2 3 | C D E A B e.g . Batch 4 | D E A B C 5 | E A B C D The treatments (recipes) are given by A,...,E Compare and contrast the two designs above. Should Montgomery use this example as the prototypical example for Latin Squares? Note that each treatment appears exactly once in each batch (row) and exactly once in each operator (column). Thus the effects of both "batch" and operator" are "averaged out" for each treatment. Note that we have 5 treatments and 5 levels for each blocking factor, thus there are a total of 5x5x5 = 125 possible combinations. We run only 25, thus the design is not fully crossed. (it is more than 5 combinations as in the RCBD above) The design is fairly efficient in its use of runs. Of course the design has to be square. Cutting our example down to a 3x3 latin square, another way to depict the design is: Trea tments A B C- - - - - - - - - - - - - - - - - | - - - | - - - | - - - | Batch 1 | X | | | Oper 1 Batch 2 | | X | | Batch 3 | | | X |- - - - - - - - - - - - - - - - - | - - - | - - - | - - - | Batch 1 | | X | | Oper 2 Batch 2 | | | X | Batch 3 | X | | |- - - - - - - - - - - - - - - - - | - - - | - - - | - - - | Batch 1 | | | X | Oper 3 Batch 2 | X | | | Batch 3 | | X | | The RCBD above would look like this: Trea tments A B C- - - - - - - - - - - - - - - - - | - - - | - - - | - - - | Batch 1 | X | X | X | Oper 1 Batch 2 | | | | Batch 3 | | | |- - - - - - - - - - - - - - - - - | - - - | - - - | - - - | Batch 1 | | | | Oper 2 Batch...
View Full Document

This note was uploaded on 08/06/2008 for the course IE 410 taught by Professor Storer during the Fall '04 term at Lehigh University .

Page1 / 81

lect13 - IE 410: Design of Experiments Lecture 13: Latin...

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online