Welcome to 6 Sigma Black Belt, Course 6, Module 3, Experimentation. This module will be dedicated to experimentation. We will begin by showcasing some one-factor designs, like all one-factor or multi-factor experiments. The examples we discussed are best suited for technology. The calculations are significantly rigorous. We will instead focus more on the uses of the design and the interpretation. Completely randomized designs are essentially one-way ANOVA designs. Under these conditions, we compare a number of factor treatments where all other conditions are kept fixed, at least as best as possible. An example might be the amount of park corrosion based on location. Four distinct tests plates are used, each type of test plate is identical. The test plates are placed in five regions. This design would be randomized in the table shown. After conducting the experiment, the data could be analyzed using an ANOVA. A randomized complete block design is a completely randomized design, but the experiment is divided into blocks or groups of the same type. There will be one measurement for each treatment. We typically block based on uncontrollable factors, or factors that are very costly to control. For example, temperature, humidity, and time. We also must assume there is no interaction effect. Be aware that experimentation seldom goes as we plan. It is common to have a randomized block design with incomplete data. This does not mean that we cannot still learn something useful from our analysis. Let's extend the example we previously discussed. We decide to add a concentrated passivation treatment to each test plate. Test plates are placed in each region in blocks. We will assume that Alpha is 0.05. Here is our statistical analysis. We see that there is a significant difference in the treatment, as evidenced by the low p-value, but not in the regions. If we plot the passivation concentrations by region, we can see that 40 percent offers the most protection. Also note that the lines all appear to be reasonably parallel, so we assume that there is no interaction. A Latin square design is a one-factor design. It attempts to measure the effects of a single key input factor on an output factor. Latin squares has the added benefit of blocking the effects of multiple nuisance factors. These nuisance factors are best characterized as non homogeneous and are averaged. Sometimes these nuisance factors are found to be highly significant. A third variable is imposed in these designs to balance the experiment. As the name implies, these designs must have an equal number of rows, columns, and treatments. We also desire no interactions between the row and column vectors. Such interactions can reduce the sensitivity of the experiment. Recognize that a Latin square design is a fractional factorial design if the dimension parameter of the Latin square is 2_k, k is the number of factors. The three factors will be row, column, and treatment, and can also be studied using the same number of runs and a 2_3k minus k fractional factorial design. Take caution in this approach. Since Latin squares are generated at random, only one square will be orthogonal, all others will be non-orthogonal. Recall that orthogonality ensures that we can independently assess each factor. Choosing a Latin square at random could create many issues and the robustness of our analysis. Let's consider this example. Suppose we manufacture carbide four-blade tips, we have six machines that produce the tips. Six operators are selected for the experiment. Specifically, we're interested in the difference in the manufacturing methods. The hardness of the carbide tip will be the output. The target is a Rockwell hardness of 65 HRC. The factors are the operator, the machine, and the method. The operator is the row factor, the machine is the column factor. The values in each cell represent the difference from the hardness measurements and the standard for each method. We will assume Alpha is 0.05. The results of the Latin square are shown here. We see that there's a significant difference in the method and in the operator. Clearly, blocking the operator made sense here. Perhaps, there is one or more operators that could benefit from further training. We should at least investigate the situation further.
