Introduction To Robust Design - Robustness Strategy

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	Related Tools & Articles A Comprehensive Robust Design Approach for Decision Trade-Offs in Complex Systems Design Taguchi Methods: Some Technical, Cultural, and Pedagogical Perspectives More About Robust Design / Taguchi Method
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	Discussion Forum "Taguchi theory says there are two types of variables which will define a system: 1. Parameters in which level affects process variation. 2. Parameters in which process variation is unaffected by level. The idea behind robust design is to set Type 1 parameters at the level which minimizes total process variation. Type 2 parameters are used to control and/or adjust the process. Can we assume from this that Taguchi would define a stable process as 'robust'? that is, levels are chosen which will maintain the process 'on target at minimum variance' as per Wheeler's definition. Does this imply an truly stable process would self-correct?" Stable Processes - Taguchi / Robust Design

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By Madhav S. Phadke

Page 1 > Introduction To Robust Design

2. Robustness Strategy
Variation reduction is universally recognized as a key to reliability and productivity improvement. There are many approaches to reducing the variability, each one having its place in the product development cycle.

By addressing variation reduction at a particular stage in a product's life cycle, one can prevent failures in the downstream stages. The Six Sigma approach has made tremendous gains in cost reduction by finding problems that occur in manufacturing or white-collar operations and fixing the immediate causes. The robustness strategy is to prevent problems through optimizing product designs and manufacturing process designs.

The manufacturer of a differential op-amplifier used in coin telephones faced the problem of excessive offset voltage due to manufacturing variability. High offset voltage caused poor voice quality, especially for phones further away from the central office. So, how to minimize field problems and associated cost? There are many approaches:

1. Compensate the customers for their losses.
2. Screen out circuits having large offset voltage at the end of the production line.
3. Institute tighter tolerances through process control on the manufacturing line.
4. Change the nominal values of critical circuit parameters such that the circuit's function becomes insensitive to the cause, namely, manufacturing variation.

The approach 4 is the robustness strategy. As one moves from approach 1 to 4, one progressively moves upstream in the product delivery cycle and also becomes more efficient in cost control. Hence it is preferable to address the problem as upstream as possible. The robustness strategy provides the crucial methodology for systematically arriving at solutions that make designs less sensitive to various causes of variation. It can be used for optimizing product design as well as for manufacturing process design.

The Robustness Strategy uses five primary tools:

1. P-Diagram is used to classify the variables associated with the product into noise, control, signal (input), and response (output) factors.
2. Ideal Function is used to mathematically specify the ideal form of the signal-response relationship as embodied by the design concept for making the higher-level system work perfectly.
3. Quadratic Loss Function (also known as Quality Loss Function) is used to quantify the loss incurred by the user due to deviation from target performance.
4. Signal-to-Noise Ratio is used for predicting the field quality through laboratory experiments.
5. Orthogonal Arrays are used for gathering dependable information about control factors (design parameters) with a small number of experiments.

2.1 P-Diagram
P-Diagram is a must for every development project. It is a way of succinctly defining the development scope. First we identify the signal (input) and response (output) associated with the design concept. For example, in designing the cooling system for a room the thermostat setting is the signal and the resulting room temperature is the response.

Next consider the parameters/factors that are beyond the control of the designer. Those factors are called noise factors. Outside temperature, opening/closing of windows, and number of occupants are examples of noise factors. Parameters that can be specified by the designer are called control factors. The number of registers, their locations, size of the air conditioning unit, insulation are examples of control factors.

Ideally, the resulting room temperature should be equal to the set point temperature. Thus the ideal function here is a straight line of slope one in the signal-response graph. This relationship must hold for all operating conditions. However, the noise factors cause the relationship to deviate from the ideal.

The job of the designer is to select appropriate control factors and their settings so that the deviation from the ideal is minimum at a low cost. Such a design is called a minimum sensitivity design or a robust design. It can be achieved by exploiting nonlinearity of the products/systems. The Robust Design method prescribes a systematic procedure for minimizing design sensitivity and it is called Parameter Design.

An overwhelming majority of product failures and the resulting field costs and design iterations come from ignoring noise factors during the early design stages. The noise factors crop up one by one as surprises in the subsequent product delivery stages causing costly failures and band-aids. These problems are avoided in the Robust Design method by subjecting the design ideas to noise factors through parameter design.

The next step is to specify allowed deviation of the parameters from the nominal values. It involves balancing the added cost of tighter tolerances against the benefits to the customer. Similar decisions must be made regarding the selection of different grades of the subsystems and components from available alternatives. The quadratic loss function is very useful for quantifying the impact of these decisions on customers or higher-level systems. The process of balancing the cost is called Tolerance Design.

The result of using parameter design followed by tolerance design is successful products at low cost.

2.2 Quality Measurement
In quality improvement and design optimization the metric plays a crucial role. Unfortunately, a single metric does not serve all stages of product delivery.

It is common to use the fraction of products outside the specified limits as the measure of quality. Though it is a good measure of the loss due to scrap, it miserably fails as a predictor of customer satisfaction. The quality loss function serves that purpose very well.

Let us define the following variables:
m: target value for a critical product characteristic
+/- D₀: allowed deviation from the target
A₀: loss due to a defective product

Then the quality loss, L, suffered by an average customer due to a product with y as value of the characteristic is given by the following equation:

If the output of the factory has distribution of the critical characteristic with mean m and variance s², then the average quality loss per unit of the product is given by:

2.3 Signal To Noise (S/N) Ratios
The product/process/system design phase involves deciding the best values/levels for the control factors. The signal to noise (S/N) ratio is an ideal metric for that purpose.

The equation for average quality loss, Q, says that the customer's average quality loss depends on the deviation of the mean from the target and also on the variance. An important class of design optimization problem requires minimization of the variance while keeping the mean on target.

Between the mean and standard deviation, it is typically easy to adjust the mean on target, but reducing the variance is difficult. Therefore, the designer should minimize the variance first and then adjust the mean on target.Among the available control factors most of them should be used to reduce variance. Only one or two control factors are adequate for adjusting the mean on target.

The design optimization problem can be solved in two steps:

1. Maximize the S/N ratio, h, defined as
   h = 10 log₁₀ ( h^2~ / s² )
   This is the step of variance reduction.
2. Adjust the mean on target using a control factor that has no effect on h. Such a factor is called a scaling factor. This is the step of adjusting the mean on target.

One typically looks for one scaling factor to adjust the mean on target during design and another for adjusting the mean to compensate for process variation during manufacturing.

2.4 Static Versus Dynamic S/N Ratios
In some engineering problems, the signal factor is absent or it takes a fixed value. These problems are called Static problems and the corresponding S/N ratios are called static S/N ratios. The S/N ratio described in the preceding section is a static S/N ratio.

In other problems, the signal and response must follow a function called the ideal function. In the cooling system example described earlier, the response (room temperature) and signal (set point) must follow a linear relationship. Such problems are called dynamic problems and the corresponding S/N ratios are called dynamic S/N ratios.

The dynamic S/N ratio will be illustrated in a later section using a turbine design example.

Dynamic S/N ratios are very useful for technology development, which is the process of generating flexible solutions that can be used in many products.

Next Page > Steps in Robust Parameter Design
Page 4 > Robust Design Case Studies

Page 1 > Introduction To Robust Design

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