August 18, 2015

Six Sigma: Improve Phase : 2 DOE Process variables & Analysis

DOE Analysis Steps How do you select and scale the process variables?  Example Agricultural Experiment Example high performance ceramics experiment What are the uses of DOE? What are the uses of DOE?

DOE Analysis Steps

The following are the basic steps in a DOE analysis.

1. Look at the data. Examine it for outliers, typos and obviousproblems. Construct as many graphs as you can to get the big picture. Response distributions (histograms, box plots, etc.) Typical DOE plots (which assume standard models for effects and errors) Main effects mean plotsinteraction plots

2. Create the theoretical model (the experiment should have beendesigned with this model in mind!).

3. Create a model from the data. Simplify the model, if possible, using stepwise regression methods and/or parameter p-value significance information.

4. Test the model assumptions using residual graphs. If none of the model assumptions were violated, examine the ANOVA. Simplify the model further, if appropriate. If reduction is appropriate, then return to step 3 with a new model. If model assumptions were violated, try to find a cause. Are necessary terms missing from the model? Will a transformation of the response help? If a transformation is used, return to step 3 with a new model.

5. Use the results to answer the questions in your experimental objectives –finding important factors, finding optimum settings, etc.

How do you select and scale the process variables?

Guidelines to assist the engineering judgment process of selecting process variables for a DOE

Process variables include both inputs and outputs-i.e., factors and responses. The selection of these variables is best done as a team effort. The team should

•Include all important factors (based on engineering judgment).

•Be bold, but not foolish, in choosing the low and high factor levels.

•Check the factor settings for impractical or impossible combinations -i.e., very low pressure and very high gas flows.

•Include all relevant responses.

•Avoid using only responses that combine two or more measurements of the process.

For example, if interested in selectivity (the ratio of two etch rates), measure both rates, not just the ratio.

Be careful when choosing the allowable range for each factor

We have to choose the range of the settings for input factors, and it is wise to give this some thought beforehand rather than just try extreme values. In some cases, extreme values will give runs that are not feasible; in other cases, extreme ranges might move one out of a smooth area of the response surface intosome jagged region, or close to an asymptote.

Two-level designs have just a”high” and a “low” setting for each factor

The most popular experimental designs are two-level designs. Why only two levels? There are a number of good reasons why two is the most common choice amongst engineers: one reason is that it is ideal for screening designs, simple and economical; it also gives most of the information required to goto a multilevel response surface experiment if one is needed


Example Agricultural Experiment

Design of experiments was first developed as a research design tool to improve farm yields in the early 1930s. The output, or response variable, y, in such an experiment was usually the yield of a certain farm crop. Controllable factors, x=(x1, x2,.., xn) were usually the ‘farm variables’, such as the amount of various fertilizers applied, watering pattern, selection of seeds and soon. Uncontrollable factors, z=(z1, z2,.., zp) could be soil types, weather patterns and so on. In early agricultural experiment, the experimenter would want to find the cause-and-effect relationship between the yield and controllable factors. That is, the experimenter would like to know how different typesof fertilizers, their application quantities, the watering pattern, and types ofseeds, would influence the yield of the crop.

Example high performance ceramics experiment

Purpose: To determine the effect of machining factors on ceramicstrength Response variable = mean (over 15 repetitions) of the ceramic strength Number of observations = 32 Response Variable Y = Mean (over 15 reps) of Ceramic Strength Factor 1 = Table Speed (2 levels: slow (.025 m/s) and fast (.125 m/s)) Factor 2 = Down Feed Rate (2 levels: slow (.05 mm) and fast (.125 mm)) Factor 3 = Wheel Grit (2 levels: 140/170 and 80/100) Factor 4 = Direction (2 levels: longitudinal and transverse) Factor 5 = Batch (2 levels: 1 and 2)

What are the uses of DOE?

Below are seven examples illustrating situations in which experimental design can be used effectively: Choosing Between Alternatives Selecting the Key Factors Affecting a Response Response Surface Modeling to:Hit a Target Reduce Variability Maximize or Minimize a Response Make a Process Robust (i.e., the process gets the “right” results even though there are uncontrollable “noise” factors)Seek Multiple Goals Regression Modeling


Important practical considerations in planning and running experiments are

Check performance of gauges/measurement devices first.

Keep the experiment as simple as possible.

Check that all planned runs are feasible.

Watch out for process drifts and shifts during the run.

Avoid unplanned changes (e.g., swap operators at halfway point).Allow some time (and back-up material) for unexpected events.

Obtain buy-in from all parties involved.

Maintain effective ownership of each step in the experimental plan.

Preserve all the raw data–do not keep only summary averages!

Record everything that happens.

Reset equipment to its original state after the experiment.