Six Sigma was initially deployed in manufacturing. Experimental designs were revolutionary for understanding how to optimize machines depend on several variables. These methods are still important when experiments should be done. But the Six Sigma program has migrated to different industries over the past thirty years, including those focused on services. The application of formal experimental designs outside manufacturing is limited, but at times it can be useful. The process of planning experiments is useful in any application because it presents a logical sequence for data collection and analysis. In this section, the intent is to briefly describe these methods.
Why use experimental design instead of regression analysis to build a model? Regression analysis relies on historical data to build a model. These data may be inconsistent and inaccurate. Running a carefully controlled experiment ensures data collection will be consistent and its data accurate. Historical data often are not collected at the full ranges of the independent variables. As a result, regression models can only interpolate within the limited data range. If an independent variable’s range is only partially sampled, some information will be missing. Planned experiments provide a full range over which a variable is studied. The solution space will be larger. Also, data collected haphazardly may contain correlated errors if there is an underlying periodicity. This will cause some variables to appear important when they are not or vice versa. Experiments randomize data collection, factoring out the effect of time. Finally, some independent variables may be correlated to each other, causing spurious modeling relationships. There are statistical tests to identify multilinearity, but experimental design avoids this situation because the independent variables are not correlated to each other. Independence also maximizes the solution space and enables the evaluation of combinations of independent variables through their interacting effect on Y.
The improve phase of the DMAIC methodology uses the information gained from the analysis phase. This includes information describing those KPIVs that impact the KPOV. These independent KPIVs are important for changing the level of the KPOV, dependent variable, or Y. Once a list of KPIVs has been determined, the DMAIC team experiments by changing their levels in an organized way and evaluating their combined impact on the KPOV. This evaluation is done using experimental designs that measure the impact of each KPIV by itself and in combination on
the KPOV. Full factorial designs study independent variables at two or more levels and assume a linear relationship between the Xs and the Y. Fractional designs are efficient ways to use full factorials by running fewer experiments and trading off unnecessary information on variable combinations or interactions. There are several versions of this concept where relationships between the Xs and Y may not be linear or the variables may be discrete rather than continuous. Other models are used to explain how changes in Xs impact the Y. A few examples are shown in Table 9.18.
Table 9.19 shows the five steps to create an experimental design: planning, selecting a design, conducting an experiment, analysis, and building the model. Planning an experiment is the most important step. It is important that a team agree on the types of information an experiment will need to provide to run an experiment and determine the KPIVs, including an initial evaluation of how they may interact with each other to affect the KPOV. Other considerations include the distribution of the KPOV (i.e., continuous versus discrete), risk mitigation if the experiments do not
FMEA = failure modes and effects analysis; SIPOC = supplier-input-process-output-customer chart.
go as planned, and resource requirements. A continuously distributed KPOV requires significantly fewer experiments to detect its change relative to changes of the KPIV levels. Another important consideration in planning an experimental design is the selection of the KPIVs that are included in the experiment and the range over which they will be evaluated. Important questions include, “Is a KPIV continuous or discrete?” or “Over which range should we evaluate the KPIVs?” Once KPIVs and the KPOV have been selected for experimentation, the design can be selected.
The second step is to carefully plan and conduct the experiment. This includes ensuring all team members know their role during the experiment, how the data will be collected, and the tools and methods to be used, and developing a risk mitigation plan. The analysis of experimental data will be straightforward if experiments are well executed according to the plan. After the experiment and the model is determined, the DMAIC team confirms the model through confirmatory experiments.