Essentials of Design Robustness in Design for Six Sigma (DFSS

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Essentials of Design Robustness in Design for Six Sigma (DFSS

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Essentials of Design Robustness in Design for Six Sigma (DFSS) Methodology
Matthew Hu, John M. Pieprzak and John Glowa
Ford Motor Company

Reprinted From: Reliability and Robust Design in Automotive Engineering (SP-1844)
2004 SAE World Congress Detroit, Michigan March 8-11, 2004
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Essentials of Design Robustness in Design for Six Sigma (DFSS) Methodology
Matthew Hu, John M. Pieprzak and John Glowa
Ford Motor Company
Copyright © 2004 SAE International

Design for Six Sigma (DFSS) is a systematic process and a disciplined problem prevention approach to achieve business excellence. Robust design is the heart of DFSS. To enable the success of robust parameter design, one should start with good design concept. Axiomatic Design, a fundamental set of principles that determine good design practice, can help to facilitate a project team to accelerate the generation of good design concept. Axiomatic Design holds that uncoupled designs are to be preferred over coupled design. Although uncoupled designs are not always possible, application of axiomatic design principles in DFSS presents an approach to help DFSS team focus on functional requirements to achieve design intents and maximize product reliability. As a result of the application of axiomatic design followed by parameter design, the DFSS team achieved design robustness and reliability. A hydraulic lash adjuster case study will be presented.
Keyword: Design for Six Sigma, robustness, innovation and axiomatic design, parameter design.
1. Introduction to Design for Six Sigma (DFSS)
In order to be successful in today's business, any company needs to strategically plan all development projects with the right level and the right kind of development to achieve maximum efficiency. It has been estimated that 85 percent of the problems with new products not working as they should, taking too long to bring to market, or costing too much is the result of a poor design process (Ullman, 1997). A good

design process is supported by a set of efficient methodologies. It has been widely accepted that the early phases of the engineering design process are the most critical to the technical and economical success of a new product. Therefore, the use of an efficient methodology for this crucial stage is most important. DFSS consists of a set of needs-gathering, engineering and statistical methods to be used during product development. Engineering determines the physics and technology to be used to carry out the product's functions. DFSS ensures that those functions meet the customer's need and that the chosen technology will perform those functions in a robust manner throughout the product's life.

To achieve a cultural shift focused on continuous improvement, we must go beyond Six Sigma by leveraging extensive experience in a full suite of performance improvement tools. We need to develop the skills and resources to help us to select and use the most effective tool to address the issues we are facing. Whether those are within the traditional Six Sigma framework or other process improvement methodologies, the details need to be developed to assist us in making the right choice to get the right value.

Often during the implementation of a Six Sigma

program a robustness limit is encountered. This

limit is due to inherent design issues. To reach

a break through result requires a review of some

or all of the processes, components or systems

and a redress of the deficiencies. This process

of redesign is called Design for Six Sigma


Improving the robustness of a

hydraulic lash adjuster, shown in Figure 1, to the

noise factor of oil aeration will be used to





The hydraulic lifter provides a hydraulic lash compensation device to automatically eliminate

Excessive Lash Adjuster Movement
Lash Adjuster

Missed closing Ramp (Valve close too early) Due To Sponge Lash Adjuster

Air mixed
with oil

Failure Mode: Excessive Closing Velocity

Figure 1: Lash adjuster and valve accuation mechanism
all spaces (lash) between the valve train components of an operating engine. The hydraulic lifter has replaced the mechanical lifter in many automotive engines. A typical lash adjuster overall function diagram is show in Figure 2.

Lash Adjuster System Overall Function

Force, pressure
Oil, air
Oil quantity/oil property

Lash Adjuster System
Energy Material Information

Force, pressure
Oil, air
Ball plunger travel distance; oil quantity/oil property

Figure 2

Hydraulic valve lifter operation is based on the incompressibility oil trapped in the high-pressure chamber and the controlled leakage of oil from that chamber. Although the hydraulic lash adjuster offers several specific advantages, it also has some disadvantages. One of the disadvantages is less overall valve train stiffness. If air is captured in the oil (aeration), the bulk modulus of elasticity of the oil is reduced. This further reduces the stiffness of the valve train. The hydraulic lash adjuster is one of the key concerns to cause the valve failures when it cannot maintain sufficient stiffness to perform its intended function. The improvement of hydraulic lash adjuster robustness against aeration in the lubrication

system is essential as engine aeration levels increase. Previous atempts to solve valve failures due to this failure mode achieved limited results through continuous quality improvement efforts. These efforts used traditional hardware design of experiments, CAE modeling study and correlation studies. However, such repeated efforts become efforts of cause detection only. No matter how tightly the components were controlled, the performance of the lash adjuster in terms of plunger movements was not acceptable in the presence of high aeration, shown in Figure 3. The ideal performance should be no difference when the hydraulic lash adjuster system is exposed to high levels of oil aeration. To obtain this ideal performance, a breakthrough approach is required.

Position (in)

2.00E-02 1.50E-02
1.00E-02 5.00E-03 0.00E+00
0 -5.00E-03
-1.00E-02 -1.50E-02 -2.00E-02

Ball Movement 6500 RPM
Base 0% Aeration - 5min Base 15% Aeration - 2min









Time (sec)

Figure 3
It is therefore a challenge for the team to have a breakthrough approach to improve the robustness of lash adjuster design against aeration.
Instead of constantly debugging products and processes that already exist, a re-examination of the function and design parameters is required. The process best suited to this task is DFSS.
DFSS starts from scratch to design the product or process to be virtually error free. This effectively replaces the usual trial-and-error or built-test-fix style and results in product designs that consistently meet customer requirements. There are several different types of roadmaps or models with different focus on generic technology development or product commercialization such as I2DOV (Invention, Innovation, Develop, Optimize and Verify); CDOV (Concept, Design, Optimize and Verify); IDDOV (Identify, Define, Develop, Optimize and Verify); DMADV (Define, Measure, Analyze, Design and Verify) and etc.


Table 1 shows the comparison of different DFSS roadmaps.

Table 1: Comparison of Different DFSS Roadmaps

DFSS Value Creation & Prevention Timing: Start early

Phase 1 1. Invention Innovation
2. Concept
3. Identify Define


Phase 2

Phase 3

Develop Optimize



Develop Optimize

4. Define



5. Define Measure

Analyze Design

6 Sigma (DMAIC) Defect &
Cost Reduction

6 Sigma is applied to continuous improvement of existing processes as well as to the design of new process.

Phase4 Verify Verify Verify Verify Verify

I2DOV- Focus on technology development.
CDOV- Focus on product commercialization based on the optimized technology. It is best used with model 1 together. IDDOV- a combined model in terms of technology development and product commercialization. DCOV - a combined model in terms of technology development and product commercialization. DMADV – a model similar to DMAIC with different focus. Measure in DMAIC is to determine current performance and analyze the root causes of the defects and costs. The measure in DMADV is to determine Customer needs and analyze, design the process options to meet the customer needs. Measure Analyze Improve Control

From the Table1, the name of the roadmap or model in DFSS is not important but the contents and tasks needed to be carried out at each phase as defined are. A typical Ford Motor Company's Design for Six Sigma has four phases –Define, Characterize, Optimize and Verify (DCOV) and can be summarized as follows:
Define – Identify market needs. Define customer requirements and project goal. Identify Critical to Satisfaction (CTS’s) and Related Functional Targets.
Characterize - Understand System and Select Concepts. Flow Down to CTS’s to lower level (y’s) Relate CTS’s (y’s) to Critical to Quality (CTQ) design parameters (x’s).
Optimize - Design for Robust Performance Minimize product process sensitivity to manufacturing & usage conditions.

Verify - Assess integrated system, subsystem, Performance, Reliability & Manufacturing. Verification that design performance and ability can meet customer's requirements.
This process, however, does not identify how to develop a design to meet the functional requirements. As a systematic tool, Axiomatic Design, a function focused scientific approach for the synthesis and analysis of product design, developed at MIT by Nam Suh [1], is one of the DFSS tools that can help to ensure that the design specifications, manufacturing capabilities and systems integration are fully aligned with the voice of customers. Axiomatic Design provides a rational structure basis for evaluation of proposed solution alternatives and the subsequent selection of the best alternative. When the limitation of a given design optimization is evidenced, the concept design improvement may have to be considered.


2. Introduction to Axiomatic Design
Axiomatic Design is a principle-based design method focused on the concept of domains that seeks to reduce the complexity of the design process. It accomplishes this by providing a framework of principles that guide the designer or engineer. The primary goal of axiomatic design is to establish a systematic foundation for design activity by two fundamental axioms and a set of implementation methods [1]. The two axioms are:
Axiom 1: The Independence Axiom: Maintain the independence of functional requirements.
Axiom 2: The Information Axiom: Minimize the information content in design.
In the axiomatic approach, the design world consists of four distinct domains: a customer domain with customer attributes (CA:s), a functional domain with functional requirements (FR:s), a physical domain with design parameters (DP:s) and a process domain with process variables (PV:s). The design process involves mapping between these four domains and can be fitted in the four phases of DFSS as shown in Figure 4. A specific design is modeled as a mapping process between a set of functional requirements (FRs) in the functional

domain and a set of design parameters (DPs) in the physical domain. This mapping process is represented by the design equation:




Aij= ∂FRi (2) ∂DPj

Suh defines an uncouple design as a design

whose A matrix can be arranged as a diagonal

matrix by an appropriate ordering of the FRs and

DPs. He defines a decoupled design as a

design whose A matrix can be arranged as a triangular matrix by an appropriate ordering of FRs and DPs. He defines a coupled design as a design whose a matrix cannot be arranged as a triangular or diagonal matrix by an appropriate ordering of the FRs and DPs. The categories of design based on the structure of the design matrix are shown is Figure 5.
The first axiom advocates that for a good design, the DPs should be chosen so that only one DP satisfies each FR. Thus the number of FRs and DPs is equal. The best design has a strict one-to-one relationship between FRs and DPs. This is known as uncoupled design. If DP influences the FR, this element is non-zero. Otherwise it is zero. The independence axiom is satisfied for uncoupled design matrix [A] having all non-zero elements on its diagonal, indicating that the FRs are completely independent. However, complete uncoupling may not be easy to accomplish in a complex world, where interactions of factors are common. Designs where FRs are satisfied by more than one DP are acceptable, as long as the design matrix [A] is a triangular, that is, the non-zero elements occur in a triangular pattern either above or below the diagonal. This is called decoupled design. A decoupled design also satisfies the independence axiom, provided that the DPs are specified in sequence such that each FR is ultimately controlled by on unique DP. Any other formation of the design matrix that cannot be transformed into triangular one represents a coupled design, indicating the dependence of the FRs. Therefore, the design is unacceptable, according to Axiomatic Design.
The Information Axiom provides a means of evaluating the quality of designs, thus facilitating a selection among available design alternatives. This is accomplished by comparing the information content of the several designs in terms of their respective probabilities of successfully satisfying the FRs.
A primary tenet of axiomatic design theory is the first axiom, stating that independence of


functional requirements should be maintained throughout the design process. As the high level requirements are decomposed into greater detail, and information added to the design with the goal of creating a realizable system, the designer creates subsystems that satisfy the first axiom. While higher-level decisions imply an intent that should be maintained as detail is added, this is often not done.
3. Limitations on General Optimization Phase in DFSS and DMAIC
Six Sigma is one of the most innovative and successful methodologies to have been introduced in recent years at an industrial level. The goal of this approach is to increase the efficiency of the company system and to generally reduce the costs involved in the production process. Six Sigma is, therefore, generally used for optimizing processes. After an initial Define phase, Six Sigma can be subdivided into: Measure, Analyze, and Improve & Control. Product optimization can be developed in greater detail by using Design For Six Sigma (DFSS) techniques during the Improve phase. The efforts will be much more effective if DFSS is used in the earlier design stage. These techniques adopt a statistical approach in order to assess which design solutions are best and the system response associated with the solution chosen. However, with an existing design, the success of optimization can only be reached to certain level. The desired success cannot be achieved without changing the concept (structure) of the product or process design. The lash adjuster robustness improvement project is such an example that, with the given design, no matter how the optimization was investigated the goal of a robust design could not be realized. The bottom line is that every attempt reaches the same conclusion about the same significant factors but fail to provide proper improvement direction.
When a company attempts to execute poor design concepts and wrong design decisions made during the design stage, the competitiveness of the company is compromised. Unfortunately, this situation currently exists in many of today's Six Sigma or Design for Six Sigma projects. Decisions made during the design stage of product and process development profoundly affect product quality and productivity [Suh95].

The traditional approaches to design optimization or robust parameter design are limited to optimization of design parameter values and neglect opportunities at concept design. Especially, traditional statistical based problem solving focused on symptoms rather than design intent optimization. Very few efforts are focused on the design functional structure (concept).
There are many grounds for claiming greater power and opportunity for improving robustness at the concept design stage. Figure 6 supports this point using broad empirical evidence from numerous studies.
As seen in Figure 6, by the completion of concept design, approximately 75% of the final quality is determined. Decisions made during concept design have an overwhelming impact on many quality determinants such as number of parts, fabrication methods, allowable manufacturing variations, and yield. Delaying improvements beyond the concept design phase limits the potential for increasing quality.
Figure 6 also shows the greatest deign flexibility coinciding with the greatest number of quality determining decisions. The concept phase is a period of great latitude, design freedom, and many design options. Upon entering the detail design phase, the engineer’s ability to change the design is severely limited by a commitment to specific design features and a greater investment of time and resources. The combination of great design flexibility and great impact on total quality makes concept design the point of greatest opportunity for improvement. Robust parameter design approach to increasing robustness by making improvements in the detail design stage amounts to improving subsequent prototype iterations. Such changes, of course, are much better than no efforts in

optimization before the production launch but cannot remedy bad first designs. Robust design must be applied at the concept phase to facilitate good first design. Taguchi does recognize and promote the need of robust design efforts in early design stage such as system design.
Since the attainable level of robustness is very much reliant on the chosen conceptual solution for the technical system. Robust design focusing on parameter optimization can reduce performance variation but only to a limited extent. Figure 7 illustrates how
parameter optimization and better concept identification can affect the robustness. Two different conceptual solutions utilizing different solution principles may feature completely different robustness properties. It is very likely that this initial robustness, or conceptual robustness, provides the necessary foundation that makes future optimization by means of designed experiments more rewarding. One concept solution may, for example, be very sensitive to changes in temperature, whereas the other solution shows no signs of such weaknesses. If the future product has to operate in an environment that features temperature variation, the second concept will probably serve better.
From the previous discussion, it is obvious that engineering designers need a tool for robust design in the conceptual design phase. The creative process has been described as an ideation process that is highly subjective and dependent upon the specific knowledge of the designer and their ability to integrate this knowledge. Suh proposes a design approach based on the idea that the design process should not remain in the field of experience and artistic skill but should be guided by a formal axiomatic design methodology. Axiomatic

design can be used to enhance creativity. It demands the clear formulation of the design objectives through the establishment of functional requirements (FRs) and constraints. It provides the criteria for good and bad design decisions, which help in eliminating bad ideas as early as possible, enabling designers to concentrate on promising ideas. The analytic process is deterministic, based upon basic principles, and serves to evaluate the concepts of the creative process. Suh provides two axioms used in the analytic process for the purpose of distinguishing good designs from bad. Without these axioms, Suh considers design decisions to be made at best on an “ad hoc” or “empirical” basis such as algorithmic design. For example, design for assembly (DFA) and design for manufacturability (DFM) techniques are algorithmic methods.
4. Transfer Function and CTQ (Critical-toQuality) Selection
The transfer function plays key a role in engineering and is part of Design for Six Sigma strategy. The transfer function is a subsystemto-system input-output relationship. Transfer functions are set up as equations expressed in Y=f(X). Y relates to output measure. X relates all input variables. Transfer functions are either developed from analytical engineering models or estimated empirically through directed experiments. Transfer functions can be formulated at each level of the system flowdown structure.
As an example, when we discuss about the customer driven six sigma projects, the Kano Model of quality for customer satisfaction is a good high level transfer function. Y, as a system output, can be identified as customer satisfaction (CS). X, as a system inputs, can be expressed in terms of performance quality, basic quality and excitement quality. The format of Y=f(X) may be written as following:
YCS=f(Performance Quality, Basic Quality, Excitement Quality) (3)
Where, performance quality represents the "spoken", or verbalized, wants from customers. Basic quality represents the requirements that customers will not usually talk about or even think to request (just be there). Excitement quality is "unspoken" and is unexpected by customers. Based on the transfer function, one


can identify a specific area as a CTQ for the quality improvement efforts. A simplified lash adjuster Kano Model may be shown in Figure 8.
Based on the Kano Model, the basic quality of robust against high aeration in lash adjuster is a CTQ and absolute essential for the key function of lash adjuster design. The high level basic transfer function (BF) may be expressed as following: YBF=f(Reliable, No Noise/Ticking) (4) DFSS commences from flow-down design specifications, parameters, and variables based on the Voice of Customer (VOC). As a systemic tool, axiomatic design can guide project teams through the process. In axiomatic design, synthesized solutions that satisfy the highestlevel FRs are created through a decomposition process that requires zigzagging between the functional domain and the physical domain as shown in figure 9.

It decomposes a top-level FR into leaf level FRs, which are not decomposable any further. Designer creates leaf level DPs in his braor extracts those from his knowledge base to satisfy the corresponding FRs. Once leaf level DPs are found, they must be integrated to create the whole design artifact, which is then checked to determine if they work well and satisfy FRs based on two design axioms.

One effective way of promoting innovation and

problem solving is to require designers define

the functional requirements first without to any

regard to how such products can be made.

When FRs are unambiguously stated, designers

can evaluate their proposed design. Once FRs

are defined, they should develop basic ideas for

products based on basic principles, making sure

that the chosen DPs satisfy the FRs and the

independence Axiom. A quality product satisfies

all the FRs. Without carefully stated FRs at all

levels of decomposition, the quality of products,

a minimum requirement, can be very difficult to

measure. Even benchmarking cannot be done

without clearly stated FRs. Benchmarking

existing product against competitors can only

deal with DPs rather than FRs, unless FRs is

stated. While Six Sigma focuses on improving

existing designs, DFSS concentrates its efforts

on creating new and better ones.


identification of a CTQ is a key step to have

higher success rate for the Six Sigma project.

Fundamental to the success of a Six Sigma

Project is to estimate the CTQ improvement

margins and the extent of the resultant cost

saving. By calculating the Information Content

of the principal FRs present in the system it is

possible to ascertain from the AD

schematization which is the most critical

characteristic of the process or product (CTQ).

The Information Content measures the

probability for every FR to be satisfied, so it can

be used to evaluate to what extent the main FRs

are able to meet the specifications. This

characteristic can also be expressed in terms of

the process sigma number, thereby making it

possible to compare the two measurements. In

this way the most critical FRs, which will become

the CTQ characteristics of a Six Sigma Project,

can be identified. In the case study of lash

adjuster, a more specific and measurable

transfer function can be expressed as following:

YStiffness=f (Valve Closing Velocity, Plunger Movement) (5)


5. Applying Axiomatic Design Framework To Develop Creative Design Solutions
After utilizing all available tools in Six Sigma and Design for Six Sigma, it was determined that the limitation of optimized results and the improvement efforts may not be effective unless the concept design is challenged. Lash adjuster quality concern related problems generated in the functional and physical domain were discovered during the detail review. From an axiomatic design perspective, this analysis corresponds to Axiom 1. The idea is to review and redefine the function requirements based on the design intents and the quality history and to uncouple the concept as much as possible, to avoid unnecessary interactions. The lash adjuster design functional requirements (FR) may be stated as follows:
FR1=Maintain zero valve train clearance FR2=Support Rocker Arm as A pivot FR3=Supply oil for lubrication FR4=De-aerate
The FR-DP hierarchies are produced by the zigzagging decomposition process. FRs are defined as "what we want to achieve" in functional domain and DPs are defined as "how we want to achieve it" in physical domain. The decomposition process conceptually divides a big, complex problem into solvable small pieces and finds design solution for the divided small problems. It produces language descriptions of decomposed FRs and DPs. A DP is a description of a proposed solution to satisfy the corresponding FR, and play a role as a key design variable as a part of the whole design solution. The term description is used to explicitly represent the meaning of FRs and DPs. The existing lash adjuster design parameters are mapped as followings:
DP1=Hydraulic check valve system DP2=Mechanical system DP3=Oil lubrication system
A mapped functional domain to design parameter domain of the lash adjuster design is shown in Figure 10.

Based on the facts of FR-DP mapping, it is obvious that the number of design parameter is less than the number of functional requirements. The design structure is coupled due to the missing number of design parameter. This process identified a feature not considered by the original design. Identifying the required function enable the development of a new design parameter to satisfy the de-aerate functional requirement, shown in Figure 11.
With the neutral designed DP – air purging method, creative thinking was motivated and encouraged to come up with several new designs. Two of the new designs were filed for patent applications. Since the alternative concept designs are available and being considered, the Pugh Concept Selection process provides an objective way of thoroughly evaluating these design concepts alternatives. In addition, it often helps to synthesize the "best of all worlds," that is, come up with a new design that is better than the initial alternatives. The Pugh technique compares alternative design