Design of Experiments via Taguchi Methods: Orthogonal Arrays

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Design of experiments via Taguchi methods: orthogonal arrays


The Taguchi method involves reducing the variation in a process through robust design of experiments. The overall objective of the method is to produce high quality product at low cost to the manufacturer. The Taguchi method was developed by Dr. Genichi Taguchi of Japan who maintained that variation. Therefore, poor quality in a process affects not only the manufacturer but also society. He developed a method for designing experiments to investigate how different parameters affect the mean and variance of a process performance characteristic that defines how well the process is functioning. The experimental design proposed by Taguchi involves using orthogonal arrays to organize the parameters affecting the process and the levels at which they should be varied; it allows for the collection of the necessary data to determine which factors most affect product quality with a minimum amount of experimentation, thus saving time and resources. Analysis of variance on the collected data from the Taguchi design of experiments can be used to select new parameter values to optimize the performance characteristic. In this article, the specific steps involved in the application of the Taguchi method will be described and examples of using the Taguchi method to design experiments will be given.

Summary of Taguchi Method

The general steps involved in the Taguchi Method are as follows: 1. Define the process objective, or more specifically, a target value for a performance measure of the process. This may be a flow rate, temperature, etc. The target of a process may also be a minimum or maximum; for example, the goal may be to maximize the output flow rate. The deviation in the performance characteristic from the target value is used to define the loss function for the process. 2. Determine the design parameters affecting the process. Parameters are variables within the process that affect the performance measure such as temperatures, pressures, etc. that can be easily controlled. The number of levels that the parameters should be varied at must be specified. For example, a temperature might be varied to a low and high value of 40 C and 80 C. Increasing the number of levels to vary a parameter at increases the number of experiments to be conducted. 3. Create orthogonal arrays for the parameter design indicating the number of and conditions for each experiment. The selection of orthogonal arrays will be discussed in considerably more detail. 4. Conduct the experiments indicated in the completed array to collect data on the effect on the performance measure. 5. Complete data analysis to determine the effect of the different parameters on the performance measure.

A detailed description of the execution of these steps will be discussed next.

Taguchi Loss Function

The goal of the Taguchi method is to reduce costs to the manufacturer and to society from variability in manufacturing processes. Taguchi defines the difference between the target value of the performance characteristic of a process, τ, and the measured value, y, as a loss function as shown below. [pic]

The constant, kc, in the loss function can be determined by considering the specification limits or the acceptable interval, delta. [pic]
The difficulty in determining kc is that τ and C are sometimes difficult to define.

If the goal is for the performance characteristic value to be minimized, the loss function is defined as follows: [pic]
If the goal is for the performance characteristic value to maximized, the loss function is defined as follows: [pic]
The loss functions described here are the loss to a customer from one product. By computing these loss functions, the overall loss to society can also be calculated.

Determining Parameter Design Orthogonal Array

The effect of many different parameters on the performance characteristic in a condensed set of experiments can be...
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