Robust Design ME 470 Systems Design Fall 2010

Why Bother? Customers will pay for increased quality! Customers will be loyal for increased quality!

Taguchi Case Study In 1980s, Ford outsourced the construction of a subassembly to several of its own plants and to a Japanese manufacturer. Both US and Japan plants produced parts that conformed to specification (zero defects) Warranty claims on US built products was far greater!!! The difference? Variation Japanese product was far more consistent!

Results from Less Variation Better performance Lower costs due to less scrap, less rework and less inventory! Lower warranty costs

Taguichi Loss Function Loss Target Traditional ApproachTaguichi Definition

Why We Need to Reduce Variation Cost Low Variation; Minimum Cost LSL USL Nom Cost High Variation; High Cost LSL USL Nom

Cost Nom Off target; minimum variability USL LSL Off target; barely acceptable variability Cost Nom LSL USL Why We Need to Shift Means

Definition of Robust Design Robustness is defined as a condition in which the product or process will be minimally affected by sources of variation. A product can be robust against: – variation in raw materials – variation in manufacturing conditions – variation in manufacturing personnel – variation in the end use environment – variation in end-users – wear-out or deterioration

If your predicted design capability looks like this, you do not have a functional performance need to apply Robust Parameter Design methods. Cost, however, may still be an issue if the input (materials or process) requirements are tight!

If your predicted capability looks like this, you have a need to both reduce the variation and shift the mean of this characteristic - a prime candidate for the application of Robust Parameter Design methods.

Variables or parameters which – affect system performance – are uncontrollable or not economical to control Examples include – climate – part tolerances – corrosion Noise Factors

Classes of Noise Factors Noise factors can be classified into: – Customer usage noise Maintenance practice Geographic, climactic, cultural, and other issues Duty cycle – Manufacturing noise Processes Equipment Materials and part tolerances – Aging or life cycle noise Component wear Corrosion or chemical degradation Calibration drift

Operating TemperaturePressure Variation Fluid Viscosity Operator Variation

Countermeasures for Noise Ignore them! – Will probably cause problems later on Turn a Noise factor into a Control factor – Maintain constant temperature in the plant – Restrict operating temperature range with addition of cooling system ISSUE : Almost always adds cost & complexity! Compensate for effects through feedback – Adds design or process complexity Discover and exploit opportunities to shift sensitivity – Interactions – Nonlinear relationships

How to describe the Engineering System? Z1Z2...ZnZ1Z2...Zn Y1Y2...YnY1Y2...Yn X1X2...XnX1X2...Xn Control Factors Noise Factors Inputs Outputs System The Parameter Diagram

Traditional Approach to Variation Reduction Reduce Variation in X’s What are the advantages and disadvantages of this approach? =f( ) Y X1X1 X2X2 XnXn YX1X1 X2X2 XnXn LSL USL

Classifying Factors that Cause Variation in Y Variation in Y can be described using the mathematical model: where X n are Control Factors Z n are Noise Factors

Factors That Have No Effects A factor that has little or no effect on either the mean or the variance can be termed an Economic Factor Economic factors should be set at a level at which costs are minimized, reliability is improved, or logistics are improved A Main Effects Plot

Another Source of Variance Effects: Nonlinearities Expected Distribution of Y Two Possible Control Conditions of A Factor A has an effect on both mean and variance Low sensitivity region High sensitivity region

Summary of Variance Effects Mean Shift Noise A - A + Variance Shift Noise A - A + Mean and Variance Shift A + A - Noise Non-linearity

Robust Design Approach, 2 Steps Step 1 Reduce the variability by exploiting the active control*noise factor interactions and using a variance adjustment factor Step 2 Shift the mean to the target using a mean adjustment factor Factorial and RSM experimental designs are used to identify the relationships required to perform these activities Variance Shift Noise A - A + Mean Shift Noise B - B +

Design Resolution Full factorial vs. fractional factorial In our DOE experiment, we used a full factorial. This can become costly as the number of variables or levels increases. As a result, statisticians use fractional factorials. As you might suspect, you do not get as much information from a fractional factorial. For the screening run in lab this week, we used a half- fractional factorial. (Say that fast 5 times!)

Fractional Factorials A Fractional Factorial Design is a factorial design in which all possible treatment combinations of the factors are NOT run. The runs are just a FRACTION of the full factorial matrix. The resulting design matrix will not be able to estimate some of the effects, often the interaction effects. Minitab and your statistics textbook will tell you the form necessary for fractional factorials.

Design Resolution Resolution V (Best) – Main effects are confounded with 4-way interactions – 2-way interactions are confounded with 3-way interactions Resolution IV – Main effects are confounded with 3-way interactions – 2-way interactions are confounded with other 2-way interactions Resolution III (many Taguchi arrays) – Main effects are confounded with 2-way interactions – 2-way interactions may be confounded with other 2-ways

Factors: 4 Base Design: 4, 8 Resolution: IV Runs: 16 Replicates: 2 Fraction: 1/2 Blocks: 1 Center pts (total): 0 Design Generators: D = ABC Alias Structure I + ABCD A + BCD B + ACD C + ABD D + ABC AB + CD AC + BD AD + BC Minitab Explanation for Screening Run in Lab Means main effects can not be distinguished from 3-ways. Means certain 2-way interactions can not be distinguished. A = Ball Type B = Rubber Bands C = Angle D = Cup Position

Hubcap Example of Propagation of Errors The example is taken from a paper presented at the Conference on Uncertainty in Engineering Design held in Gaithersburg, Maryland May10-11, 1988.

WHEELCOVER REMOVAL

WHEELCOVER RETENTION

COMPETING GOALS

OPERATIONAL GOAL

Retention Force, (N)