Design of Experiments in a Transactional Environment

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1 Design of Experiments in a Transactional Environment Rick Haynes Master Black Belt Most Lean Six Sigma practitioners have been trained and exposed to Design of Experiments (DOE). It is one of the most powerful tools that can be used to understand the Y=F(x) relationships, although seldom used. Why? DOE Advantages; 1. Allows estimation of process input effects on the output with a relative small amount of data. 2. Allows estimation of process input interaction effects on the output. 3. Provides a predictive model for the process output. 4. Provides a significance estimate for all process inputs. 5. The design of the test provides uncorrelated inputs (sorry about the statistics). This is why DOE is more powerful than using historical process data. DOE Disadvantages 1. Requires the process inputs to be changed in a strict pattern, some combinations of which may not be in normal use. 2. May generate non-compliant product in with some combinations of inputs. 3. All inputs being considered must be changed during the experiment. These issues are in play for any style of DOE be it factorial, fractional factorial, Taguchi, RSM,. A typical Lean Six Sigma (LSS) roadmap lists DOE as a tool used in the improve phase, implying that it is used after the significant parameters found and the actual improvement is being developed. I am not sure why it is in this phase, other than that all of the initial creators of the DMAIC model put it in the improve phase. An improve phase DOE is used to examine the process effect of all the significant inputs at the same time. You are able to identify correlated effects and possibly to identify any inputs that are causal in nature. A second DOE may be executed that uses the causal inputs to develop a predictive process model, the true Y=f(x) equation. Using the predictive model, the process input control systems and specifications can be set, based on their influence on the output. You may be thinking, Sounds great in a high-volume manufacturing environment or It won t work here. The first statement is correct; the second statement may not be true. There are two ways that DOE can be advantageous in the non-manufacturing, or transactional environment: historical DOE and DOE for data collection. 1

2 Historical DOE. Historical DOE is an uncommon way to gain most of the DOE advantages along with avoiding the requirement to force changes to the process. This is available when two conditions exist; A very large amount of historical data exists; e.g., thousands of points Data exists for every process input under consideration for each data point. Yes, this is about using the DOE tool with existing data. Data preparations 1. Compile all of the data into a single file. I will assume that it is in an Excel worksheet, but the steps can be used with many other software packages. 2. Data format: one column for every input variable being considered, and one for the output value. (Figure 1) Other columns can be included with no problem. observation A B Cycle Time Figure 1 3. Sort the entire data set on the first input column. a. Create a new column, named similarly to this input variable column, but add _coded to the end of the original column name. b. Divide the data set into four equal count groups based on the newly-created input column. This can be specified by using the 2 nd, 3 rd and 4 th quartile values as the dividing point between each fourth of the data.. c. Fill in the new xxx_coded column with values. Minimum to 2 nd quartile => -1 2 nd to 4 th quartile => 0 4 th quartile to Maximum => +1 d. Delete the rows that have a value of 0 in the new column. This should be the middle half of the data set. 4. Repeat step 3 for each column of input data. (Figure 2) 2

3 Note: This process reduces the number of data points by 50% with each input variable. Ex. With 5 input variables, the data will be reduced by ½ * ½ * ½ * ½ * ½ = 1/64. This is why you need lots of data. Group Minimum Q1 Median Q3 Maximum A B For Input A code as follows; -1 = to = to = to observation A A_coded B B_coded Cycle Time Figure 2 3

4 Experimental Design Selection StdOrder A B Generate a simple full factorial model with no replications or centerpoints. 2. For combination of inputs (row in the factorial design), determine how many data points exist with this combination in the data set. a. Create a new column on the far left, labeled Condition. Cycle Time b. Sort by each of the coded columns. Choose to sort ascending or descending based on the combination chosen Ex: If looking for +A +B +C D +E, then sort A, B, and C descending, sort D and E Ascending. c. Identify all the rows matching the chosen pattern in the Condition column. The value could be the standard order # from the DOE design or a code showing the levels. Note: If a combination does not exist, just continue with the next combination. d. Repeat 2a-2c until you have worked through all factorial combinations. (Figure 3) Sort for -A-B observation A A_coded B B_coded Cycle Time Figure 3 3. Find the DOE combination that has the least number of members; i.e., rows of data. a. If one or more combinations do not exist, a full factorial model cannot be used. 1. Generate a fractional factorial and determine if the missing combination(s) is (are) in this fraction. 2. If the missing combination(s) is (are) in the fractional factorial, then generate another fraction, until you find one that does not include the missing combination(s). Note: This may require the use of a ½ to 1/8 th fractionation along 4

5 with the use of the non-standard fraction. This is a trial and error effort. 3. When you have a factorial or fraction that includes only combinations that have data, you can move on. Note: If a fraction cannot be found, you may not be able to use this method. Extracting the proper combinations (12 of 50) with the minimum count of 2. Cycle StdOrder observation A A_coded B B_coded Time Figure 4 b. Using the design selected in Step 3a, the combination with the smallest count defines the number of rows to use in the experiment. c. Randomly select the number of rows found in 3b from each combination in the chosen design. Copy all the copied rows into a separate spreadsheet. 4. Prepare data for DOE analysis a. Compute an average of the output data for each combination b. Copy those averages into the generated fractional or full factorial, one value per combination (Figure 5) 5. Analyze the DOE using standard methods. StdOrder observation A A_coded B B_coded Cycle Time CT Avg Figure 5 5

6 Historical DOE Summary That is a historical DOE. What did we do? Well, we created high and low conditions for every input variable, extracted every combination, selected a design that used combinations that existed in these data, averaged each condition, and analyzed the data. When does it fail to work? When two inputs are correlated either by theory or by the method by which the system is controlled, all the data will not have any cases where the two inputs exist as +- or -+. In this case, you may have to drop one from the analysis. The process controls, automatic or manual, hold the input variable value relatively constant so that the + and conditions are very close to the same value. In this case, you may have to drop the input from the analysis. In this case, the magnitude difference between the + and conditions is not high enough to resolve a difference in the output. DOE for Data Collections This is a use of Design of Experiments in the analyze phase. In this phase, practitioners routinely have possible process inputs (Xs) that do not have existing data related to the process output; i.e., project Y value. If the practitioner needs to collect data in order to judge the significance of the input, there are two paths to take. The common method is to create a data collection plan for a fixed period of time that includes all the inputs of interest. A second method, not often attempted, is the DOE method. The DOE data collection method involves the creation of a full or fractional factorial design using the input variables of interest. Each input variable is inspected to determine what value you will assign to the + and to the conditions. Now create a data collection plan that only collects data when those combinations of the inputs exist. You will find that this method may reduce the data collection effort and cost by 50%, 75%, or more, and you will still be able to assess the significance of each input variable. Summary You have now seen two new ways to use the Design of Experiment tool to improve the likelihood of solving your problem quickly. Give them a try. DOE methods can be found in chapters Implementing Six Sigma 2 nd ed. Breyfogle,