Robust Design ME 470 Systems Design Fall 2011

Access objects in the bag quickly and easily. The person must be able to retrieve items of interest in an unawkward fashion. A user should be able to access common items while standing up with minimal effort. Be able to locate items easily in the bag. Customer needs an easier way to pay for purchases. More storage options for better organization. New location for checkbook. Person needs a way to see into the backpack easily so that they can find checkbook easier. Customer needs bag with compartments they can reach while wearing the bag. A wallet with a debit card and built in ID. Hands free way of holding bag so both hands can be used in looking for stuff. Velcro pockets on the outside to hold wallet, checkbook and such. Reflection on Customer Need Statements

Suggested Solutions See how the leather on the bottom of the bag is all scratched; it’s ugly. When I’m standing in line at the cashier trying to find my checkbook while balancing my bag on my knee, I feel like a stork. This bag is my life; if I lose it I’m in big trouble. There’s nothing worse than a banana that’s been squished by the edge of a textbook. I never use both straps on my knapsack; I just sling it over one shoulder. The bag maintains its original appearance with use. Bag allows easy access to items Bag is easy to find. The bag protects fragile items from damage. The bag can rest securely in multiple modes (either or both shoulders.) The bag can be carried comfortably in multiple modes (one shoulder strap, two shoulder straps, or hand hold.)

What are the benefits of increasing the quality of a product? Customers will pay for increased quality! Customers will be loyal for increased quality!

In 1980s, Ford discovered that the warranty claims on US built products were far greater than Japanese built product. All products met the design specifications. There was less variation in the Japanese products

There are measurable results from less variation. Better performance Lower costs due to less scrap, less rework and less inventory! Lower warranty costs

Taguichi developed a loss function to describe the effects of variation. 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 Against variation in manufacturing conditions Against variation in manufacturing personnel Against variation in the end use environment `Against variation in end-users Against 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.

Examples include climate, part tolerances, corrosion, or wear over the life of a component. Noise Factors are variables or parameters that affect system performance and are difficult and or expensive to control.

Noise factors can be classified in many ways – customer noise, manufacturing noise, and life cycle noise can be useful classifications. 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

There are several countermeasures for dealing with 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

The Parameter Diagram is another way to describe an Engineering System. Z1Z2...ZnZ1Z2...Zn Y1Y2...YnY1Y2...Yn X1X2...XnX1X2...Xn Control Factors Noise Factors Inputs Outputs System The Parameter Diagram

The traditional approach to variation reduction is to reduce variation in X’s What are the advantages and disadvantages of this approach? =f( ) Y X1X1 X2X2 XnXn YX1X1 X2X2 XnXn LSL USL

Robust Design identifies 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 Frisbee thrower 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 last week, we started with 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.

-1, -1, -1 +1, -1, -1 +1, -1, +1 +1, +1, +1 -1, +1, +1 -1, -1, +1 +1, +1, -1 -1, +1, -1

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)