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Improve Phase

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

TABLE 9.18

Experimental Designs

Experimental Design

Description

Full factorial designs

An experimental design in which the independent variables are studied at two or more levels. Normally used when the independent variables are discrete.

2k designs

An experimental design in which the independent variables are studied at two levels relative to their linear relationship with the dependent variable. Normally used when the independent variables are continuous.

Fractional factorial designs

A 2k experimental design in which not all factor combinations are evaluated. In fact, higher-order interactions are traded away to reduce the size of the experiment.

Screening designs

Special types of 2k experimental designs in which the fractionation is at a very high level. A special class of screening designs called Plackett-Burman designs allow intermediate numbers of experiments versus the 2k situation to further reduce the number of required experiments.

Response surface designs

Experimental design that allows quadratic modeling between several continuous independent variables and a continuous dependent variable.

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

TABLE 9.19

Planning Experiments

Step

Actions

1. Planning

  • • What functions must the product or process perform?
  • • Set the experimental design objective(s).
  • • Define the time frame of the study.
  • • Select responses (i.e., outputs or Ys).
  • • Select factors (i.e., independent variables or Xs) whose levels will be varied in the experiment; sources of Xs are the cause and effect matrix, FMEA, SIPOC, etc.).
  • • Determine resource requirements.

2. Select design

  • • Select the best design type.
  • • Consider relationships between independent variables (i.e., interactions).
  • • Establish the degree of confounding (i.e., alias structure).
  • • Randomize runs and factors.
  • • Allocate factors to the array.
  • • Document non-linearity of effects

3. Conduct experiment

  • • Make sure everyone knows about the experimental plan.
  • • Know how to measurement of inputs and outputs.
  • • Record experimental conditions.

4. Analyze data

  • • Develop the relationship between the dependent and independent variables (i.e., Y =f{x)).
  • • Analyze each variable independent of others (i.e., main effects).
  • • Analyze variables acting together on the output (i.e., interactions).
  • • Understand the optimum levels to set each of the Xs to put Y on target (i.e., best factor settings).
  • • As the Xs vary within specification, how does Y vary (i.e., prediction interval)?

5. Build model: Y =f(x)

Confirm the regression models terms (i.e., Ys and Xs).

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.

 
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