In Chapter 9, Response Surface Methods, techniques used to optimize the response were discussed. Once an optimum value of the response has been achieved, the next goal of the experimenter should be to make the optimum response value insensitive to the noise factors so that a consistent performance is obtained at all times. For example, if the yield from a chemical process has been optimized at 95%, then this value of yield should be obtained regardless of the variation in factors such as the quality of reactants or fluctuations in humidity or other weather conditions. These factors, that are called noise factors, are beyond the control of the operator. Therefore, the product or process should be such that it is not affected by minor fluctuations in these factors. [Note] The process of making a system insensitive to noise factors is referred to as Robust Design. Robust design was pioneered by the Japanese industrialist Dr. Genichi Taguchi in the early 1980s. This chapter briefly discusses his approach.
This section is divided into the following subsections:
Taguchi's philosophy is based on the fact that any decrease in the quality of a system leads to customer dissatisfaction. This occurs even if the departure in quality lies within the specified limits of the system and is considered acceptable to the customer. For example, consider the case of a laptop that develops a defect on its screen within the warranty period. Although the customer is able to get a warranty-replacement for the screen this might lead to a little dissatisfaction on the part of the customer. If the same laptop then develops a problem with its DVD drive, the customer might declare the laptop "useless," even if the problem occurs during the warranty period and the customer is able to get a free replacement. Therefore, to maintain a good reputation, the laptop manufacturer needs to produce laptops that offer the same quality to all customers consistently. This can only be done when the required quality is built into the laptops. Note how this approach differs from traditional quality control where it is considered sufficient to manufacture products within certain specifications and carry out pre-shipment quality-control inspections (sampling inspections) to filter out products that fall out of specification.
Taguchi's philosophy requires that systems be designed in such a way that they are produced, not just within the specified limits, but right on target specifications or best values. Such a proactive approach is much more fruitful and efficient than the reactive approach of sampling inspections. The philosophy of Taguchi is summarized by his quality loss function (see Figure 10.1). The function states that any deviation from the target value leads to a quadratic loss in quality or customer satisfaction. Mathematically, the function may be expressed as:
where represents the performance parameter of the system, represents the target or the nominal value of , represents the quality loss and is a constant.
Taguchi's approach to achieve a high quality system consists of three stages, namely, system design, parameter design and tolerance design. System design refers to the stage when ideas for a new system are used to decide upon the combinations of factors to obtain a functional and economical design. Parameter design refers to the stage when factor settings are selected that make the system less sensitive to variations in the uncontrollable factors affecting the system. Therefore, if this stage is carried out successfully, the resulting system will have little variation and the resulting tolerances will be tight. Tolerance design refers to the final stage when tolerances are tightened around the best value. This stage increases cost and is only needed if the required quality is not achieved during parameter design. Thus, using parameter design, it is possible to achieve the desired quality without much increase in the cost. This stage is discussed in detail next.
Taguchi divided the factors affecting any system into two categories - control factors and noise factors. Control factors are factors affecting a system that are easily set by the experimenter. For example, if in a chemical process the reaction time is found to be a factor affecting the yield, then this factor is a control factor since it can be easily manipulated and set by the experimenter. The experimenter will choose the setting of the reaction time that maximizes the yield. Noise factors are factors affecting a system that are difficult or impossible to control. For example, ambient temperature may also have an effect on the yield of a chemical process, but ambient temperature could be a noise factor if it is beyond the control of the experimenter. Thus, change in ambient temperature will lead to variations in the yield but such variations are undesirable.
Taguchi studied the interaction between the control and noise factors using two experiment designs - the inner array and the outer array. The inner array is essentially any experimental design that is used to study the effect of the control factors on the response. Taguchi then used an outer array for the noise factors so that each run of the inner array was repeated for every treatment of the outer array. The resulting experiment design, that uses both inner and outer arrays, is referred to as a cross array.
To illustrate Taguchi's use of the inner and outer arrays consider the case of a chemical process where the experimenter wants the product to be neither acidic nor basic (i.e. the pH of the product needs to be as close to 7 as possible). It is thought that the pH of the product depends on the concentration of the three reactants, , and , used to obtain the product. There are three control factors here, namely the concentration of each of the three reactants. It has also been found that the pH of the product depends on the ambient temperature which varies naturally and cannot be controlled. Thus, there is one noise factor in this case - the ambient temperature. The experimenter chooses Taguchi's robust parameter design approach to investigate the settings of the control factors to make the product insensitive to changes in ambient temperature. It is decided to carry out a 2 experiment to study the effect of the three control factors on the pH of the product. Therefore, the 2 design is the inner array here. It is also decided to carry out the experiment at four levels of the ambient temperature by using a special enclosure where the surrounding temperature of the chemical process can be controlled. Therefore, the outer array consists of a single factor experiment with the factor at four levels. Note that, in order to carry out the robust parameter design approach, the noise factor should be such that it can be controlled in an experimental setting. The resulting setup of the robust parameter design experiment is shown in Table 10.1. The experiment requires 2 runs in all as each run of the inner array is repeated for every treatment of the outer array. Table 10.1 also shows the pH values obtained for the experiment. In DOE++, this design is set up by specifying the properties for the inner and outer arrays as shown in Figures 10.3 to 10.5. The resulting design is shown in Figure 10.6.