What are Orthogonal Arrays

The quality engineering methods of Dr. Taguchi, employing design of experiments (DOE), is one of the most important statistical tools of TQM for designing high quality systems at reduced cost. Taguchi methods provide an efficient and systematic way to optimize designs for performance, quality, and cost.

The Taguchi approach essentially covers four steps:

§  Formulate the problem  

§  Plan the experiment

§  Analyze the results

§  Confirm the experiment

§  Adopting the new design

While planning the experiment, which is essentially the design of test case, Taguchi analysis uses a concept called Matrix experiment using Orthogonal Arrays. It is an efficient way to study the effect of several factors simultaneously.

Orthogonal arrays are two dimensional arrays of numbers which possess the interesting quality that by choosing any two columns in the array you receive an even distribution of all the pair-wise combinations of values in the array.1 Here is some terminology for working with orthogonal arrays followed by an example array in Figure 1

Runs: the number of rows in the array. This directly translates to the number of test cases that

will be generated by the OATS technique.

Factors: the number of columns in an array. This directly translates to the maximum number of variables that can be handled by this array.

Levels: the maximum number of values that can be taken on by any single factor. An orthogonal array will contain values from 0 to Levels-1.

Strength: the number of columns it takes to see each of the Levels. Stength possibilities equally

Figure 1: An L9(34) orthogonal array with 9 runs,

4 factors, 3 levels, and strength of 2.

Factors

Runs

0 0 0 0

0 1 1 2

0 2 2 1

1 0 1 1

1 1 2 0

1 2 0 2

2 0 2 2

2 1 0 1

2 2 1 0

Orthogonal arrays offer many benefits. The conclusions arrived at from such experiments are valid over the entire experimental region spanned by the control factors and their settings

There is a large saving in the experimental effort

The data analysis is very easy

Benefits of OA in improving testing productivity

Lower implementation time due to lower test cases.

Execution time is less due to lower test cases.

Result analysis takes less time due low lower number of test cases and lesser number of lines of code. High code coverage: The OA methodology coveres close to 95% of the feature code compared to the usual method.

Increase in overall productivity: Implementation time, test execution time and the result analysis time is less compared to the other methods.