Discussions of the various aspects of Orthogonal Arrays(OA) can be found in the following links:
The Approach of OA
Comparison to the Conventional Approach
Application of OA
Advantages and Disadvantages of OA
The Approach of Orthogonal Arrays
An experiment during the product design stages, involves the materials used in manufacturing the experimental product which affects the final quality outcome. Factors such as variations in the chemical ratio, the level of ingredients used, and how the product is formed together, will contribute to the variation in the targeted value of the final product.
Orthogonal Arrays(OA) are a special set of Latin squares, constructed by Taguchi to lay out the product design experiments. By using this table, an orthogonal array of standard procedure can be used for a number of experimental situations. Consider a common 2-level factors OA as shown in table 1 below :
The OA facilitates the experimental design process by assigning factors to the appropriate columns. In this case, referring to table 1, there are at most seven 2-level factors, these are arbitrarily assigned factors A, B, C, D, E, F, and G to columns 1, 2, 3, 4, 5, 6, 7 and 8 respectively, for an L8 array. From the table, eight trials of experiments are needed, with the level of each factor for each trial-run as indicated on the array. The experimental descriptions are reflected through the condition level. For example, 0 may indicates the factor is not applied, and 1 represents the factor that is fully applied. The factors may be variation in chemical concentration, material purity, mechanical pressure and so on. The experimenter may use different designators for the columns, but the eight trial-runs will cover all combinations, independent of column definition. In this way, the OA assures consistency of the design carried out by different experimenters. The OA also ensures that factors influencing the end product's quality are properly investigated and controled during the initial design stage.
Comparison to the Conventional Approach
The method of investigating all possible combinations and conditions in an experiment(involving multiple factors) is traditionally known as factorial design. The factorial design is based on the theory, that for a full factorial design, the number of possible designs, N (number of trails), is :
N = Lm
where L = number of levels for each factor
m = number of factors involved
Thus, if the qualities for a given product depended on three factors, the variation of 2-level conditions can be limited to a number of design experiments of 23, which equals 8 trials. If the same method is carried out on the conditions based on table 1, for 27, then 128 trials would be needed. Moreover, the method of level combinations laid out is not specified in the factorial design process. This may lead to different results on the same experimental subject each time a trial is conducted. Thus, Taguchi's Orthogonal Array is able to simplify and standardised the factorial designs, in a manner that will yield consistent data results and similar outcomes, even though the trials are carried out by different experimenters. Thus, two different investigators will have similar conclusion and a standard design methodology.
The concept of standard design methodology and uniform results through OA analysis is very important, since it allows the manufacturer to produce two products of the same quality standards, using the same materials, but with differences in the manufacturing process. This is possible since, through OA experimental analysis, the quality influencing factors of a product can be identified, controlled, and hence compensated during the early product design stage. Thus, the quality of the product itself, rather than depending on the manufacturing process, is able to "adapt" to the manufacturing process.
Taguchi's OA is considered to be more superior than the traditional factorial design method since :
Taguchi's OA experiments, on a product design yield similar and consistent results, although the experiment can be carried out by different experimenters.
The OA table allows determination of the contribution, of each quality influencing factor.
OA allows easy interpretation of experiments with a large number of factors.
To gain the best, or optimum, condition for a process, or a product, so that good quality characteristics can be sustained.
To approximate the response of the product design parameters under the optimum conditions.
There are two different methodologies in carrying out the complete OA analysis. A common approach is to analyse the average result of repetitive runs, or a single run, through ANOVA analysis as discussed. Another approach, which is a better method for multiple runs, is to use signal (S) to noise (N) ratio (S/N) for the same steps in the analysis. The objective of S/N analysis, is to determine the most optimum set of the operating conditions, from variations of the influencing factors within the results. The signals, in this case, will be those factors which are invariant. The noise are those influencing factors which are active. Details regarding the methods of OA results analysis using ANOVA and signal-to-noise ratio can be referred to article .
Application of Orthogonal Array
Taguchi's OA analysis is used to produce the best parameters for the optimum design process, with the least number of experiments. The OA manages to transform a quality concept into the product design. The OA method is able to treat quality influencing factors at discrete levels, and often this method save time, and indirectly reduces the cost of hardware testing. Thus, the OA is usually applied in the design of engineering products, test and quality development, and process development. All applications involved have a common objective, that is to use Taguchi's OA method to build the quality into a product at the initial design stage.
Advantages and Disadvantages of Orthogonal Array
The advantages of OA, are such that they can be applied to experimental design involving a large number of design factors. The OA design experiments, analysis, and cost guidance based on the loss function have made this approach more attractive. The limitation of OA is that it can only be applied at the initial stage of the product/process design system. There are some situations whereby OA techniques are not applicable, such as a processes involving influencing factors that vary in time and cannot be quantified exactly.