ROBUST DESIGN PROCESS

In Section 5.3 we related reliability degradation to quality loss and concluded that reliability can be improved through robust design. In this section we describe the process of robust design.

5.4.1 Three Stages of Robust Design

Robust design is a statistical engineering methodology for minimizing the per-formance variation of a product or process by choosing the optimal conditions of the product or process to make the performance insensitive to noise factors.

According to Taguchi (1987), a robust design consists of three stages: system design, parameter design, and tolerance design.

System design involves selection of technology and components for use, design of system architecture, development of a prototype that meets customer requirements, and determination of manufacturing process. System design has sig-nificant impacts on cost, yield, reliability, maintainability, and many other perfor-mances of a product. It also plays a critical role in reducing product sensitivity to noise factors. If a system design is defective, the subsequent parameter design and tolerance design aimed at robustness improvement are fruitless. In recent years, some system design methodologies have emerged and shown effective, such as

the axiomatic design and TRIZ (an innovative problem-solving method). Dieter (2000), Suh (2001), Rantanen and Domb (2002), and K. Yang and El-Haik (2003) describe the system design in detail. Nevertheless, there are few systematic approaches in the literature, largely because system design is skill intensive.

Parameter design aims at minimizing the sensitivity of the performance of a product or process to noise factors by setting its design parameters at the optimal levels. In this step, designed experiments are usually conducted to investigate the relationships between the design parameters and performance characteristics of the product or process. Using such relationships, one can determine the optimal setting of the design parameters. In this book, parameter design is the synonym of robust design in a narrow sense. In a broad sense, the former is a subset of the latter.

Tolerance design is to choose the tolerance of important components to reduce the performance sensitivity to noise factors under cost constraints. Tolerance design may be conducted after the parameter design is completed. If the parame-ter design cannot achieve sufficient robustness, tolerance design is necessary. In this step, the important components whose variability has the largest effects on the product sensitivity are identified through experimentation. Then the tolerance of these components is tightened by using higher-grade components based on the trade-off between the increased cost and the reduction in performance variabil-ity. Jeang (1995), P. Ross (1996), Creveling (1997), C. C. Wu and Tang (1998), C. Lee (2000), and Vlahinos (2002) describe the theory and application of the tolerance design.

5.4.2 Steps of Robust Design

As stated earlier, robust design implies the parameter design in this book. The steps of a robust design are structured to save time and cost and to improve the robust reliability in an efficient manner. The steps are as follows:

1. Define the boundary. Robust design is usually performed on the sub-systems or components of a complex product. This step is to determine the subsystem or component within the product for robust design and to identify the impact of neighboring subsystems and components on the subsystem or component under study in terms of functional interactions and noise disturbance. In the remainder of this chapter, the subsystem or component under study is referred to as a system unless stated otherwise.

Section 5.5 delineates the system boundary definition.

2. Develop a P-diagram (a parameter diagram). It shows pictorially the (a) system for robust design, (b) design parameters (control factors), (c) noise factors, (d) inputs (signals), (e) outputs (functions, responses), and (f) failure modes. A P-diagram contains all information necessary for subsequent robust design. In Section 5.6 we discuss the P-diagram in detail.

3. Determine the key quality characteristic that characterizes the functions of the system to the greatest extent. The characteristic is to be monitored

ROBUST DESIGN PROCESS 131

and measured in experimentation. For a binary-state system, life is usually the key quality characteristic and is used as the experimental response.

For a degradation system, the critical performance characteristic is the key quality characteristic. In Chapter 8 we discuss selection of the critical performance characteristic.

4. Identify the key noise factors and determine their levels. In general, numer-ous noise factors apply to the system under study. It is impossible or impractical to include all noise factors in a robust design; only the key factors can be studied. The key noise factors are those that have the largest adverse impact on the functions of the system. The range of noise levels should be as broad as possible to represent real-world use conditions. The number of noise levels is constrained by the test time, cost, and available capacity of test equipment.

5. Determine the main control factors and their levels. The main control factors are those to which the functions of the system are most sensitive.

The range of control factor levels should be as wide as possible while maintaining the intended functions. The number of levels is restricted by the availability of time, budget, and test resource. In this step it is important to identify potential interactions between control factors. An interaction between two factors exists if the effect of a factor on the system function depends on whether the other factor is present.

6. Design the experiment. In this step, the orthogonal arrays are employed to design the experiment. An inner array is selected to accommodate the control factors and their potential interactions. An outer array is used to lay out the noise factors. In Section 5.8 we describe the design of experiment in detail. In this step we should also decide an appropriate number of replicates at each experimental condition to obtain sufficient statistical accuracy with available resources. The order in which the exper-iments are conducted is randomized to avoid biased effects. The test equipment, measurement tools, and measurement frequency on the key quality characteristic are selected in this step. If necessary, a study of gauge repeatability and reproducibility, commonly known as gauge R&R, should be performed. Montgomery (2001a), for example, presents gauge R&R methods.

7. Conduct the experiment. This step is to generate and collect measurement data on the key quality characteristic of test units at each experimental condition. In experimentation it is essential to comply with the opera-tional standards of the test facility and reduce human errors. In some applications, a computer simulation may replace physical testing to save time and cost. The simulation does not need experimental replicates, because every run of the simulation gives the same results. The most critical factor for a successful computer simulation is to create a model that represents the system adequately.

8. Analyze the experimental data. In this step we (a) identify the con-trol factors that have statistically significant effects on the experimental

response, (b) determine the optimal setting of the significant control fac-tors, and (c) predict the response under the optimal setting. Graphical response analysis or analysis of variance (ANOVA) is usually performed in this step.

9. Run a confirmation test. The optimality of the control factor levels is confirmed by running a test on the samples at the optimal setting.

10. Recommend actions. The optimal setting should be implemented in design and production. To sustain the improvement, follow-up actions such as executing a statistical process control are recommended. Montgomery (2001a) and Stamatis (2004), for example, describe quality control appro-aches, including statistical process control.

5.5 BOUNDARY DEFINITION AND INTERACTION ANALYSIS