The statistical theory underlying DOE generally begins with the concept of process models. The output responses are assumed continuous. Experimental data are used to derive an empirical approximation model linking the outputs and inputs. A repetitive approach to gaining knowledge is encouraged, typically involving these consecutive steps:.
Use DOE when more than one input factor is suspected of influencing an output. For example, it may be desirable to understand the effect of temperature and pressure on the strength of a glue bond.
Setting up a DOE starts with process map. ASQ has created a design of experiments template Excel available for free download and use. Begin your DOE with three steps:. Conduct and analyze up to three factors and their interactions by downloading the design of experiments template Excel.
More complex studies can be performed with DOE. The above 2-factor example is used for illustrative purposes. Cart Total: Checkout. Learn About Quality. Designed experiments are often done in four phases: planning, screening also called process characterization , optimization, and verification.
Our intent is to provide only a brief introduction to the design of experiments. There are many resources that provide a thorough treatment of these methods. What is a designed experiment? Analyses can be conducted to determine whether an average value is significantly different from a specified value or from another average. Similar comparisons can be made on the variation in the response quantified using the standard deviation.
When multiple means are to be compared, more advanced analysis techniques can be used. Since these tests use the entire data set in the analysis, occasionally the results can be confusing. Convenient ways to visualize the results of comparative experiments are box-and-whisker plots. The box-and-whisker plot typically includes for each sample a box, a line or symbol near the middle of the box, the whiskers that extend outside the box, and symbols plotted beyond the whiskers.
Unfortunately, there is not an accepted consensus as to what each of these components means. In the example figure, the bottom and top of the box represent approximately the first and third quartile of the data set, the bar in the middle of the box is the median of the data set, the whiskers are the median plus or minus 1. Other statistical measures of the distribution can also be used.
Because of this variation in what the elements of the plot mean, it is always necessary that they be explained in the description of the plot. The purpose of screening experiments, in statistical terminology, is to determine whether any main effects or interactions are different from zero. A main effect is the difference in the average response at different levels of a factor. This is the same as asking whether or not the average response changed when the level of the factor changed.
A main effect can be determined for each factor. Two-factor interactions measure whether or not the magnitude of the change in the response when one factor was changed depends on the level of another factor. Common designs for screening experiments are the factorial designs , the fractional factorial designs , and the Placket-Burman designs. Of these designs, the factorial designs require the greatest number of experiments and provide the most information; the Placket-Burman designs the fewest experiments and provide the least amount of information.
The fractional factorials fall in between. For most cases, factorial, fractional factorial, and Placket-Burman designs can be found in experimental design textbooks or using software packages. If N factors are being studied, a complete factorial requires 2 N experiments at a minimum since that does not include repetition of any of the experiments. The advantage of the complete factorials over the other screening designs is the ability to estimate interaction effects.
A complete factorial can estimate not only main effects and two-factor interactions, it can estimate up to N -factor interactions. Other factorial designs use three levels of the factors or combinations of two and three levels. Fractional factorials designs use a specified subset of the complete factorial designs. Doing a subset of the complete factorial design does mean that some information that a complete factorial would provide is lost. However, when there are a large number of factors, some of which might not be statistically significant, these designs provide a method of estimating all the main effects and lower lever interactions using relatively few experiments.
The Placket-Burman designs are close relatives of the fractional factorial designs but are even more restrictive than the fractional factorial designs.
They are capable under some circumstances of looking at more factors in fewer experiments than the fractional factorial designs. Analysis of factorial, fractional factorial, and Placket-Burman designs to estimate main effects can be done using a variety of software packages or using a spreadsheet program. Analysis of variance ANOVA can be used to rigorously assess the presence and significance of main effects and interactions.
In the analysis of variance, the variation in the response values is separated into two components. One component is associated with changing the levels of the independent factors and one is associated with the natural experimental variability.
By statistically comparing the change in the response due to the change in the factor level with the natural variability measured either through explicit or implicit experimental replication, conclusions can be drawn about the presence or not of main effects and interactions. In addition to box-and-whisker plots, interaction plots are also useful for screening experiments.
To construct interaction plots, the factors are selected pairwise and one factor is plotted along the horizontal-axis and the average response at the high and low levels of the second factor are plotted. Responses at the same level of the second factor are then connected with straight lines.
0コメント