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The purposes of this chapter are: (1) to describe six sigma strategy and (2) to propose opportunities for additional research and evolution of six sigma. Part I of this book describes several methods that can structure activities within a project. Part II focuses on design of experiment (DOE) methods that can be used inside six sigma projects. DOE methods are complicated to the extent that decision-making about them might seem roughly comparable to decision-making about an entire project. [ABSTRACT FROM AUTHOR]

Design for six sigma (DFSS) methods can be viewed as part of six sigma methods or an alternative method as described in Chapter 1. These methods generally involve teams that have control over the design nominal dimensions and specifications. Having this ˵design control″ often means that the teams have relatively great power to improve the system quality. It has been said that 80+% of product quality is determined by the product design specifications meaning that manufacture and delivery can play only a relatively small role. Design teams, therefore, have great responsibility to ensure that new products or processes are put in place smoothly and foster high quality levels. This chapter describes DFSS methods that are generally intended to offer deliberate and principled procedures that structure the processes of design. The examples here focus on DFSS in manufacturing contexts, but DFSS methods have added value in other sectors, including in government. [ABSTRACT FROM AUTHOR]

The selection of confirmed key system input (KIV) settings is the main outcome of a six sigma project. The term ˵optimization problem″ refers to the selection of settings to derive to formally maximize or minimize a quantitative objective. Chapter 6 described how formal optimization methods are sometimes applied in the assumption phase of projects to develop recommended settings to be evaluated in the control or verify phases. Even if the decision-making approach used in practice is informal, it still can be useful (particularly for theorists) to imagine a quantitative optimization problem underlying the associated project. This imagined optimization problem could conceivably offer the opportunity to quantitatively evaluate whether the project results were the best possible or the project could be viewed as a lost opportunity to push the system to its true potential. The phrase ˵project decision problem″ refers to the optimization problem underlying a given six sigma project. [ABSTRACT FROM AUTHOR]

As is the case for other six sigma-related methods, practitioners of six sigma have demonstrated that it is possible to derive value from design of experiments (DOE) and regression with little or no knowledge of statistical theory. However, understanding the implications of probability theory can be intellectionally satisfying and enhance the chances of successful implementations. Also, in some situations, theory can be practically necessary. For example, in cases involving mixture or categorical variables (Chapter 15), it is necessary to go beyond the standard methods and an understanding of theory is needed for planning experiments and analyzing results. This chapter focuses attention on three of the most valuable roles that theory can play in enhancing DOE and regression applications. For a review of basic probability theory, refer to Chapter 10. [ABSTRACT FROM AUTHOR]

In this chapter, two additional case studies illustrate design of experiments (DOE) and regression being applied in real world manufacturing. The first study involved the application of screening methods for identifying the cause of a major quality problem and resolving that problem. The second derives from Allen et al. (2000) and relates to the application of a type of response surface method. In this second study, the design of an automotive part was tuned to greatly improve its mechanical performance characteristics. Note that Chapter 13 contains a student project description illustrating standard response surface methods and what might realistically be achieved in the course of a university project. Also, Chapter 14 reviews an application of sequential response surface methods to improve the robustness and profitability of a manufacturing process. [ABSTRACT FROM AUTHOR]

Regression is a family of curve-fitting methods for (1) predicting average response performance for new combinations of factors and (2) understanding which factor changes cause changes in average outputs. In this chapter, the uses of regression for prediction and performing hypothesis tests are described. Regression methods are perhaps the most widely used statistics or operations research techniques. Also, even though some people think of regression as merely the ˵curve fitting method″ in Excel, the methods are surprisingly subtle with much potential for misuse (and benefit). [ABSTRACT FROM AUTHOR]

Linear regression models are not the only curve-fitting methods in wide use. Also, these methods are not useful for analyzing data for categorical responses. In this chapter, so-called ˵kriging″ models, ˵artificial neural nets″ (ANNs), and logistic regression methods are briefly described. ANNs and logistic regression methods are relevant for categorical responses. Each of the modeling methods described here offers advantages in specific contexts. However, all of these alternatives have a practical disadvantage in that formal optimization must be used in their fitting process. Section 2 discusses generic curve fitting and the role of optimization. Section 3 briefly describes kriging models, which are considered particularly relevant for analyzing deterministic computer experiments and in the context of global optimization methods. In Section 3, one type of neural net is presented. Section 4 defines logistic regression models including so-called ˵discrete choice″ models. In Section 5, examples illustrate logit and probit discrete choice models. [ABSTRACT FROM AUTHOR]

In Chapter 4, it is claimed that perhaps the majority of quality problems are caused by variation in quality characteristics. The evidence is that typically only a small fraction of units fail to conform to specifications. If characteristic values were consistent, then either 100% of units would conform or 0%. Robust design methods seek to reduce the effects of input variation on a system΄s outputs to improve quality. Therefore, they are relevant when one is interested in designing a system that gives consistent outputs despite the variation of uncontrollable factors. [ABSTRACT FROM AUTHOR]

The methods presented in this chapter are primarily relevant when it is desired to determine simultaneously which of many possible changes in system inputs cause average outputs to change. ˵Factor screening″ is the process of starting with a long list of possibly influential factors and ending with a usually smaller list of factors believed to affect the average response. More specifically, the methods described in this section permit the simultaneous screening of several (m) factors using a number of runs, n, comparable to but greater than the number of factors (n ~ m and n > m). [ABSTRACT FROM AUTHOR]

Response surface methods (RSM) are primarily relevant when the decision-maker desires (1) to create a relatively accurate prediction of engineered system inputoutput relationships and (2) to ˵tune″ or optimize thoroughly of the system being designed. Since these methods require more runs for a given number of factors than screening using fractional factorials, they are generally reserved for cases in which the importance of all factors is assumed, perhaps because of previous experimentation. [ABSTRACT FROM AUTHOR]

Design of experiments (DOE) methods are among the most complicated and useful of statistical quality control techniques. DOE methods can be an important part of a thorough system optimization, yielding definitive system design or redesign recommendations. These methods all involve the activities of experimental planning, conducting experiments, and fitting models to the outputs. An essential ingredient in applying DOE methods is the use of procedure called ˵randomization″ which is defined at the end of this chapter. To preview, randomization involves making many experimental planning decisions using a random or unpatterned approach. [ABSTRACT FROM AUTHOR]

Some people view statistical material as a way to push students to sharpen their minds, but as having little vocational or practical value. Furthermore, practitioners of six sigma have demonstrated that it is possible to derive value from statistical methods while having little or no knowledge of statistical theory. However, understanding the implications of probability theory (assumptions to predictions) and inference theory (data to informed assumptions) can be intellectually satisfying and enhance the chances of successful implementations in at least some cases. This chapter focuses attention on two of the most practically valuable roles that theory can play in enhancing six sigma projects. First, there are many parameters to be selected in applying acceptance sampling. In general, larger sample sizes and lower acceptable limits reduce the chances of accepting bad lots. However, it can be helpful to quantify these risks, particularly considering the need to balance the risks vs costs of inspection. [ABSTRACT FROM AUTHOR]

This chapter contains two descriptions of real projects in which a student played a major role in saving millions of dollars: the printed circuit board study and the wire harness voids study. The objectives of this chapter include: (1) providing direct evidence that the methods are widely used and associated with monetary savings and (2) challenging the reader to identify situations in which specific methods could help. In both case studies, savings were achieved through the application of many methods described in previous chapters. Even while both case studies achieved considerable savings, the intent is not to suggest that the methods used were the only appropriate ones. Method selection is still largely an art. Conceivably, through more judicious selection of methods and additional engineering insights, greater savings could have been achieved. It is also likely that luck played a role in the successes. The chapter also describes an exercise that readers can perform to develop practical experience with the methods and concepts. The intent is to familiarize participants with a disciplined approach to documenting, evaluating, and improving product and manufacturing approaches. [ABSTRACT FROM AUTHOR]

In the previous chapters several methods are described for achieving various objectives. Each of these methods can be viewed as representative of many other similar methods developed by researchers. Many of these methods are published in such respected journals as the Journal of Quality Technology, Technometrics, and The Bell System Technical Journal. In general, the other methods offer additional features and advantages. [ABSTRACT FROM AUTHOR]

If the project involves an improvement to existing systems, the term ˵control″ is used to refer to the final six sigma project phase in which tentative recommendations are confirmed and institutionalized. This follows because inspection controls are being put in place to confirm that the changes do initially increase quality and that they continue to do so. If the associated project involves new product or service design, this phase also involves confirmation. Since there is less emphasis on evaluating a process on an on-going basis, the term ˵verify″ refers evaluation on a one-time, off-line basis. [ABSTRACT FROM AUTHOR]

In Chapter 3, the development and documentation of project goals was discussed. Chapter 4 described the process of evaluating relevant systems, including measurement systems, before any system changes are recommended by the project team. The analyze phase involves establishing cause-and-effect relationships between system inputs and outputs. Analyze phase methods are based on a variety of data sources and generate many types of visual information for decision-makers. Methods that can be relevant for these analyses include the design of experiments (DOE) methods covered in Part II of this book and previewed here. Also, QFD cause and effects matrices, process mapping, value-stream mapping, spaghetti diagrams, and lean methods are addressed. Note that DOE methods include steps for both analysis and development of improvement recommendations. Lean manufacturing techniques areas provide potentially powerful methods and concepts for making systems more efficient. As usual, all methods may conceivably be applied usefully in any project phase or occasion. [ABSTRACT FROM AUTHOR]

In Chapter 5, methods were described with goals that included clarifying the inputoutput relationships of systems. The purpose of this chapter is to describe methods for using the information from previous phases to tune the inputs and develop tentative recommendations. The phrase ˵improvement phase″ refers to the situation in which an existing system is being improved. The phrase ˵design phase″ refers to the case in which a new product is being designed. [ABSTRACT FROM AUTHOR]

In Chapter 2, it was suggested that projects are useful for developing recommendations to change system key input variable (KIV) settings. The measure phase in six sigma for improvement projects quantitatively evaluates the current or default system KIVs, using thorough measurements of key output variables (KOVs) before changes are made. This information aids in evaluating effects of project-related changes and assuring that the project team is not harming the system. In general, quantitative evaluation of performance and improvement is critical for the acceptance of project recommendations. The more data, the less disagreement. [ABSTRACT FROM AUTHOR]

The phrase ˵statistical quality control″ (SQC) refers to the application of statistical methods to monitor and evaluate systems and to determine whether changing key input variable (KIV) settings is appropriate. Specifically, SQC is associated with Shewhart΄s statistical process charting (SPC) methods. These SPC methods include several charting procedures for visually evaluating the consistency of key process outputs (KOVs) and identifying unusual circumstances that might merit attention. [ABSTRACT FROM AUTHOR]

This chapter focuses on the definition of a project, including the designation of who is responsible for what progress by when. By definition, those applying six sigma methods must answer some or all of these questions in the first phase of their system improvement or new system design projects. Also, according to what may be regarded as a defining principle of six sigma, projects must be costjustified or they should not be completed. Often in practice, the needed cost justification must be established by the end of the ˵define″ phase. [ABSTRACT FROM AUTHOR]

In this chapter, six sigma is defined as a method for problem solving. It is perhaps true that the main benefits of six sigma are: (1) the method slows people down when they solve problems, preventing them from prematurely jumping to poor recommendations that lose money; and (2) six sigma forces people to evaluate quantitatively and carefully their proposed recommendations. These evaluations can aid by encouraging adoption of project results and in the assignment of credit to participants. The main goal of this book is to encourage readers to increase their use of six sigma and its associated ˵sub-methods.″ Many of these sub-methods fall under the headings ˵statistical quality control″ (SQC) and ˵design of experiments″ (DOE), which, in turn, are associated with systems engineering and statistics. [ABSTRACT FROM AUTHOR]

˵Tolerance design″ refers to the selection of specifications for individual components using formal optimization. Specifications might relate to the acceptable length of a shaft, for example, or the acceptable resistance of a specific resistor in a printed circuit board. Choices about the specifications are important in part because conforming component parts can cause the entire engineered system to fail to conform to specifications. Also, sometimes the specification limits may be needlessly ˵tight″ requiring expensive manufacturing equipment that does not benefit the customer. [ABSTRACT FROM AUTHOR]