The method, based on the design techniques developed by Genichi Taguchi, Ph.D., seeks to create products and pro-cesses that are robust against all sources of undesirable external influences. Using design of experiments (DOE) can determine the optimal levels of process or design parameters that can alleviate the affects of so-called "noise" factors. But finding these optimal levels is not always easy. Industrial experiments do not always go as planned because a nonsystematic approach is often taken by the experimenters.

The following is a 10-step plan that helps users plan experiments, conduct them, analyze results and implement solutions. The planning phase makes up the first seven steps.

Step 1: Recognition and formulation
The first step is to recognize the problem, because not completely understanding the problem makes it difficult to find the best answer. A clear and succinct statement of the problem can create a better understanding of what needs to be done. The statement should contain an objective that is specific, measurable and that can yield practical value to the company.

Some manufacturing problems that can be addressed using an experimental approach include:

• Development of new processes or products; improvement of existing processes or products.
  
• Improvement of the performance of a product and process relative to customer needs and expectations.
  
• Improvement of low process yields, due to the process not operating at the optimum condition.
  
• Correction of excessive process variability, which leads to poor process capability.

After the problems and the objective of the experiment are decided upon, a team can be formed. Diverse teams are important because they lead to unbiased objectives of the experiment. This team may include a DOE specialist, process engineer, production engineer, quality engineer, machine operator and a management representative.

Step 2: Quality characteristics
The selection of quality characteristics to measure the experiment's output influences the number of experiments that will have to be carried out to be statistically meaningful. These outputs can be variable or attribute in nature. Variable characteristics such as dimensions, efficiency, viscosity and strength, generally provide more information than attribute characteristics such as "good or bad," "pass or fail." Variable characteristics require fewer experiments or samples than characteristics that are attribute in nature to achieve the same level of statistical significance.

The quality characteristic for the experiment should be related as closely as possible to the product's basic engineering mechanism. In Taguchi methods of experimental design, the following five types of quality characteristics are generally considered:

• Smaller-the-better quality characteristics: This is used to measure characteristics such as tool wear, surface finish, porosity, shrinkage and other defects.
  
• Larger-the-better quality characteristics: This measures characteristics such as efficiency, hardness and strength.
  
• Nominal-is-the-best quality characteristics: This is used to measure characteristics such as length, thickness, diameter, width, force and viscosity.
  
• Classified attribute quality characteristics. This type is selected for the experiment when the data is classified into good and bad or by grades such as a, b, c or d.
  
• Dynamic characteristics. This is used when the strength of a particular parameter, called a signal factor, has a direct effect on the output quality characteristics.

Experimenters should define the measurement process including understanding what, where and how to measure the test widget prior to the experiment in order to understand the contribution of variation accounted for by the measurement system. Every measurement has some uncertainty that can be attributed to key inputs such as gages, parts, operators, methods and environment. These sources of variation may bias the experiment, and so the measurement system must be capable, stable, robust and insensitive to operator or environmental changes.

Step 3: Selecting parameters
Brainstorming, flowcharts, and cause and effect analysis are useful tools for determining which design and process parameters to include in the initial experiments. This step is the most important step of the experimental design procedure. If important factors are left out of the experiment, then the results may be inaccurate or questionable.

A screening experiment can identify the most important parameters. In a screening experiment, the number of levels is kept as low as possible, usually at two.

Step 4: Classifying factors
Having selected the design and process parameters, the next step is to classify them into control, noise and signal factors. Control factors are those factors that can be controlled by a design engineer in the design of a product or process, or by a manufacturing process or production engineer in a production environment.

Noise factors are those factors that cannot be controlled, are difficult to control or are too expensive to control in actual production environments. Noise factors include ambient temperature and the machine operator skill levels.

Signal factors are those that affect the target performance of the characteristic but generally have no influence on variability in the performance characteristic of the product or process. In an injection molding process, the dimension of the die will have a direct influence on the dimension of the injected part. The dimension of the die is a signal factor.

Step 5: Determining levels
Determining the number of levels for the design and process parameters is the fifth step of the planning phase. A level is the value that a factor holds in an experiment. For example, a car's gas mileage is affected by such levels as engine design, tire pressure and speed. The number of levels depends on the nature of the design and process parameter and whether or not the chosen parameter is qualitative or quantitative.

For quantitative parameters such as pressure and speed, two levels are generally required, especially in the early stages of experimentation. However, for qualitative parameters such as type of material and type of supplier, more than two levels may be required in initial experiments.

The levels need to be in an operational range of the product or process. Taguchi recommends the use of three levels if nonlinearity is expected in the main effect of control factor on the quality characteristic. The following example shows Taguchi's principle for selecting the test levels of noise factors:

Suppose the mean and standard deviation or the distribution of noise factor (Ni) are mi and si respectively. If Ni is assumed to have a linear effect on the quality characteristic, then it should have two test levels: (mi - si) and (mi + si). On the other hand, if Ni is assumed to have a curvilinear effect on the quality characteristic, then it should have three test levels:

(mi - si . =(3/2) ), mi, (mi + si . = (3/2) )

These choices of test levels are based on the assumption that noise factors have approximate symmetrical distributions. If noise factors cannot be studied, repeat the experiment randomly to capture variation caused by unknown sources.

Step 6: Interactions
Interaction between two design and process parameters exists when the effect of one parameter on the quality characteristic is different at different levels of the other parameter. Determine which interaction should be studied. If the interactions between control factors need to be studied, then list the potential interactions of interest. The questions to ask include: "Should an interaction be replaced by an additional factor?," and, "Do we need to study the interactions in the first phase of the experiment?"

Interactions among the noise factors or signal factors are not normally studied in an industrial design experiment. Exploring the interactions among the noise and signal factors is a waste of resources. However, explore the interaction between control and noise factors for achieving robustness.

Step 7: Orthogonal array
The choice of an appropriate Orthogonal Array (OA) and the assignment of design and process parameters and their interactions is the next step. OAs are a set of tables of numbers created by Taguchi that allow experimenters to study the effect of a large number of control and noise factors on the quality characteristic in a minimum number of trials. If noise factors are considered for the experiment, then two OAs are required. Taguchi proposed the use of OAs for planning the optimization experiments. The choice of OA depends on the numbers of factors to be studied for optimization, number of interactions to be examined, number of levels required for each factor, objective of the experiment, and the budget and resources. To assure that the chosen OA design provides sufficient degrees of freedom for the experiment, the number of degrees of freedom for the OA should be greater than or equal to the degrees of freedom required for studying the main and interaction effects.

Having chosen the appropriate OA design for the experiment, the next step is to assign factors and locate interactions. For some experiments, a standard OA can be used, or in some cases, modifications need to be done on the selected OA. Interaction tables and confounding structures must be constructed while assigning the factors and the interactions of interest to the OA.

Step 8: Conducting phase
Conducting the experiment and recording the results is the next step. To ensure the validity of the experiment, consider the following points prior to conducting the experiment.

• Location: Select an appropriate location that is unaffected by external sources of noise. The environment should be as close as possible to the user's environment.
  
• Resource availability: Make sure that the necessary equipment, operation and materials are available before starting.
  
• Cost-benefit analysis: Verify that the experiment is necessary and justify that the benefits to be gained from the experiment will exceed the cost of the experiment.
  
• Data sheets: Use uncoded data sheets for running the experiment and coded data sheets for analyzing the data. The data sheet should list the levels of each factor, date and time of the test and who has conducted the experiment. It should have space to record responses or output values.
  
• Randomize the trials: Randomization is critical to ensure that bias is evaded during data gathering. Whether or not to randomize the experimental trials depends on two main considerations: the cost, and whether time-dependent factors will alter the results.
  
• Replicate the experiment: Replication is a process of running the experimental trials in a random order.

Step 9: Analysis phase
After the experiment, analyze and interpret the results. If the experiment was planned and designed properly and conducted in accordance with the data sheet, then statistical analysis will provide sound and valid conclusions. In design and process optimization experiments, the following are the possible objectives:

• Determine the design and process parameters that affect the product or process' performance.
  
• Determine the design and process parameters that influence performance variability.
  
• Determine the design parameter levels that yield the optimum performance.
  
• Determine whether further improvement is possible.

In Taguchi methods of experimental design, a performance statistic called Signal-to-Noise ratio (SNR) is used that yields the pre-dictive performance of a product and process in the presence of noise factors or other variables. The factors that yield the highest SNR should be selected because it implies better product and process performance. Analysis methods include the analysis of variance for identifying the key design and process parameters and the key interactions, analysis of SNR for achieving process and design robustness and the prediction of performance at the optimum condition. A confidence interval around the predicted mean performance can then be constructed. The equations and calculations involved in the SNR can be obtained from Taguchi's system of experimental design. The selection of an appropriate SNR de-pends on the type of quality characteristic that has been measured during the experiment. For mul-tiple quality characteristics, use Multiple Signal-to-Noise ratio derived from Taguchi's quality loss function.

Step 10: Implementation
To validate the conclusions from the experiment, a confirmatory experiment should be performed. If the results from the confirmation experiment fall outside the confidence interval determined in Step 9, possible causes must be identified. Some of the possible causes may be:

• Wrong choice of OA for the experiment.
  
• Incorrect choice of quality characteristic.
  
• Some important parameters or interactions have not been included in the experiment.
  
• Inadequate control of noise factors, which cause variation.

If the results from the confir-mation experiment fall inside the confidence interval determined in Step 9, then improvement action on the product or process is recommended. The new design or process parameters settings should be implemented with the involvement of top management. After the solution has been implemented, construct control charts on the quality characteristic or key parameters.

Experimental design techniques based on Taguchi can offer simultaneous improvements in product quality and cost. The experimental design methodology advocated by Taguchi emphasizes pushing quality back to the design stage, in an effort to design and develop products and processes that are robust against all sources of variations.

Dr. JiJu Antony and Graemne Knowles are senior teaching fellows in the Warwick Manufacturing Group at the University of Warwick (Warwick, UK). They can be reached at [email protected] and [email protected]. Tolga Taner is a research student in the Institute of Biomedical Engineering at Bogazici University (Istanbul, Turkey). He can be contacted at [email protected]

10 STEPS TO DEVELOP ROBUST PRODUCTS AND PROCESSES
Planning Phase
Step 1: Problem recognition, formulation and organization of the team

Step 2: Selection of quality characteristic and measurement system

Step 3: Selection of design or process parameters that may influence quality control

Step 4: Classification of design or process parameters into control, noise and signal factors

Step 5: Determination of the number of levels for design or process parameters

Step 6: Determination of the interactions to be studied

Step 7: Choice of appropriate orthogonal arrays and assignment of design or process parameters and their interactions

Conducting Phase
Step 8: Conducting the experiment and recording the results

Analysis Phase
Step 9: Analyzing the experimental data and interpreting the results

Implementation Phase
Step 10: Conduct a follow-up experiment to verify results and implement solutions