Design of experiment related to Taguchi Method.

1. PRESENTATION ON
ORTHOGONAL ARRAY TESTING
SUBMITTED TO:
DR. JAGTAR SINGH
SUBMITTED BY:
ATUL RANJAN
KAMINI SINGH
UTTAM KUMAR
VIPIN Kr. SINGH

2. Contents:
 Introduction.
 Orthogonal Array.
 Terminology of OATS.
 Why OATS..??
 Conventional testing issues.
 Example
 Application
 Advantage & disadvantage
 Degree of freedom

3. Introduction:
 Orthogonal Arrays (often referred to Taguchi
Methods) are often employed in industrial
experiments to study the effect of several control
factors.
 Popularized by G. Taguchi. Other Taguchi
contributions include:
 Model of the Engineering Design Process
 Robust Design Principle
 Efforts to push quality upstream into the engineering
design process.

4. Orthogonal Array
• Theoretically-
An orthogonal array is a type of experiment where the
columns for the independent variables are “orthogonal” to
one another.
• Analytically-
An N x k array A with entries from some set S with v
levels, strength t within the range 0 ≤ t ≤ k and index λ
where every N x t sub array of A contains each t-tuple
based on S exactly λ times as a row.

5. Why Orthogonal Array Testing (OATS)..??
 Systematic, statistical way to test pair-wise interactions.
 Interactions and integration points are a major source of
defects.
 Most defects arise from simple pair-wise interactions.
 “When the background is blue and the font is Arial and the layout
has menus on the right and the images are large and it’s a Thursday
then the tables don’t line up properly.”
 Exhaustive testing is impossible.
 Execute a well-defined, concise set of tests that are likely
to uncover most (not all) bugs.
 Orthogonal approach guarantees the pair-wise coverage of
all variables.
5

6. Taguchi OATS Approach

7. For OA, Must be identify:
1. Number of factors(K) to be studied.
2. Levels(V) for each factor
3. The specified Strength (t)
4. The special difficulties that would be encountered in
running the experiment

8. Terminology for working with OA’s
OA’s are commonly represented as :
OA(Runs, Factors, Levels, Strength)
OAλ(Runs(N); Factors(k), Levels(v), Strength(t))
is an N × k array on v symbols such that every N × t sub-array contains all
tuples of size t from v symbols exactly λ times.
Runs (N) – Number of rows in the array, which translates into the
number of Test Cases that will be generated.
Factors (k) – Number of columns in the array, which translates into
the maximum number of variables that can be handled by the
array.
8

9. Continued..
 Levels (v) – Maximum number of values that can be taken
on by any single factor.
 Strength (t) – The number of columns it takes to see
all the possibilities equal number of times.
ƒNo of runs= λvt
t is the strength, v is the number of levels
λ -1 for software testing and is often omitted

10. Conventional Testing Issues:
 Conventional Test Cases:
 Variables:3
Input: 3
Possible cases: 27=33
 Variables: 3
Input: 5
Possible Cases: 243 = 35
 …
 Variables: 5
Input: 5
Possible Cases: 3125 = 55
10
 Orthogonal Test Cases
 Variables:3
Input: 3
Possible cases: 9
 Variables: 3
Input: 5
Possible Cases: 11
 …
 Variables: 5
Input: 5
Possible Cases: 21

11. OATS - Example
A B C
1 1 1 3
2 1 2 2
3 1 3 1
4 2 1 2
5 2 2 1
6 2 3 3
7 3 1 1
8 3 2 3
9 3 3 2
TABLE1 Sample Array using OA
Total cases = 9 which cover all
pair-wise combinations of the 3
variables.
Applying
OATS
3 Parameters – A,B,C
3 Values – 1,2,3
All possible cases
involving 3
parameters:
3*3*3 = 27 cases
11

12. Conventional Test Cases
Example:
 If we have three variables
(A,B,C), each can have 3
values say (Red, Green, and
Blue).
 The possible combinations
in conventional test cases
would be 27 i.e. 33
12

13. By OATS:
Example:
 If we have three variables
(A,B,C), each can have 3
values say (Red, Green, and
Blue).
 The possible combinations
in OATS test cases would
be 9.
13

14. Example
14
A Web Page has three distinct sections
(Top, Middle, Bottom) that can be individually shown or
hidden from userNo.of Factors=3 (Top,middle,Bottom)
No.of Levels =2 (Hidden or shown)
Array Type = OA(4,3,2,2)
If we go for exhaustive testing we need :2 x 2 x 2 = 8 Test Cases
OA(Runs, Factors, Levels, Strength)

15. contd..
15
Fixed Level Array: L4(2 3)
F1 F2 F3
Run1 0 0 0
Run 2 0 1 1
Run 3 1 0 1
Run 4 1 1 0
L423-OA with 4 Runs
3 factors with 2 levels
Top Middle Bottom
Test 1 Hidden Hidden Hidden
Test 2 Hidden Visible Visible
Test 3 Visible Hidden Visible
Test 4 Visible Visible Hidden
The Four Test Scenarios (4 Vs. 8)
1 - Display the home page and hide all sections.
2 - Display the home page and show all except Top section.
3 - Display the home page and show all except Middle section.
4 - Display the home page and show all except Bottom section.

16. APPLICATIONS OF OA
 They are essential in statistics and they are used in
computer science and cryptography.
 Orthogonal array are used in automobile design.
 They are immensely important in all areas of human
investigation: for example in medicine, agriculture and
manufacturing.
 orthogonal arrays are related to combinatorics, finite
fields, geometry and error-correcting codes.

17. OATS advantage to select a test set:
 Guarantees testing the pair-wise combinations of all the
selected variables.
 Creates an efficient and concise test set with many fewer test
cases than testing all combinations of all variables.
 Creates a test set that has an even distribution of all pair-wise
combinations.
 Exercises some of the complex combinations of all the
variables.
 Is simpler to generate and less error prone than test sets
created by hand.
17

18. Disadvantages of OATS:
 Can only be applied at the initial stage of the
product/process design system.
 Arrays can be difficult to construct.
 With so many possible combinations of components or
settings, it is easy to miss one.
 It covers 100% (9 of 9) of the pair-wise combinations, 33%
(9 of 27) of the three-way combinations and 11% (9 of 81) of
the four-way combinations.

19. Degrees of Freedom
The number of degrees of freedom is very important
value because it determines the minimum number of
treatment conditions.
It is equal to:
Number of factors(no. of levels-1)+no. of
interactions(no.of levels-1)(no.of levels-1)+one of the
average.

20. EXAMPLE:
Given four two level factors A,B,C,D and two suspected interactions, BC
and CD,determine the degree of freedom,df . What is the answer if the
factors are the three levels
1: df =4(2-1)+2(2-1)(2-1)+1=7 (for two level)
2:df=4(3-1)+2(3-1)(3-1)+1=17 (for three levels)

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