Summary
In designing engineering experiments, there are several guidelines to be considered in the process of achieving the final results. These practical guidelines are needed since they dictate the scope of the experiment. The most important stage is the recognition of the problem statement. This involves coming up with a question that will act as a trigger to guiding the direction of the experiment. It involves defining a problem to help in a better understanding about a phenomenon.
The determination of the problem statement presents platform for the next stage of choosing factors and levels. This stage involves coming up with the independent variables that will be put in investigation during the experiment. The factors can either be qualitative or quantitative; quantitative are usually selected by determining the ranges whereby the factors determined are to be run. There is need for using few levels against the various factors that are to be used in the experiment. There is existence of many factors but only few are significant. Consequently, this prompts for the need of fractional factorial design.
The other important step is recognizing aliasing. This is where the contrast established for the estimation of the main effect A is found to be similar to the contrast utilized in estimation of BC interaction. The aliases are found the table of plus and minus signs in the columns. For aliased effects, Montgomery gives the following notation:
The construction of a one-half fraction takes the following form as shown in the design generate below:
Steps for designing sign table to be used for 2K-P
The first stage is the preparation of a sign table to contain entire factorial design that has k-p factors. After preparing the table, the first column is marked as I. The k-p columns that follow are marked by k-p factors. For the (2k-p-k-p-1) columns that are found on the right, the p columns are chosen and marked with p factors that were not picked in the first step.
For confounding aspect: This requires that computation of combined influence of at least two effects be done. In an equation like this:
We say that D and ABC effects are confounded. There is no problem even if qABC are negligible. When presented with only a single confounding, there is a chance of listing all the available confoundings. There are rules involved and they are as follows: I is recognized as unity and any term that is determined to have a power of 2 is deleted:
I= ABCD
Taking A to multiply both sides
A = A2BCD = BCD
When we multiply all sides by B,C,D and AB we get the following equation
The design resolution has the following elements: the number of terms is equal to the order arising from an effect: that is:
ABCD order = 4, order associated with I = 0
Confounding order is equal to the total sum of two terms’ order, for instance, AB=CDE that gives us order of 5. Additionally, resolution associated to a design should be equal to the minimum of confounding orders. The notations of these are given by:
RIII = Resolution-III = 2k-pIII
Placket-Burman design and type I and II errors
There is use of partial aliasing structure, for the design of Placket-Burman in determining the most important interactions. It gives rise to a model that gives out the main impact of the listed factors in combination with two-factor interactions. In which case, the design is best used to effectively determine all the associated important effects coupled by the two-significant two-factor interactions. However, it is important to note the comparison between the weight of the type I and type II error. For instance, a significant effect maybe identified that was not found initially in the simulation model that was utilized in data generation. The screened type I errors does not always have much impacts as compared to type II errors. This is because type I error will only lead to a non-significant factor that is identified as useful and thereby maintained for use in following analysis and experimentation. Consequently, this factor comes out as not so much important. When a type II error arises, it implies that there was no discovery of a useful factor. This means that there will be need for dropping the variable from the studies that will come after. The continued use of this factor will hugely impact the performance of the process in a negative way.
For the resolution IV design, there is no need for a full fold-over and partial fold-over is much preferred. The process of constructing a partial fold-over involves:
The first step is the construction of a single-factor fold-over. The construction is usually done in a normal way from the original design and it involves altering the signs found on a factor which is associated with a subject interaction, two-factor. The second stage is to choose only half of runs achieved by the fold-over; this is achieved by picking the runs whereby the involved factors are found at their high or low points. The best desirable results is achieved by coming up with the level that is believed to give the required response.
Research and quality implication
In the process of coming up with a response or dependent variable, the researcher is required toe ensure that the chosen response is closely related to the problem statement. Failure to do this will lead to fake results that do not meet the objectives previously determined for the experiment. Further, much thought is required in determine the process to be used in measuring the response and the capability of the used gage to establish the measurements. This kind of experiment will also force the engineer to determine the best strategy for maintaining the gaging system and how it will be calibrated during the experiment.
Another quality implication is on the choice made on experimental design. The engineer is required to be aware of the difference existing between the true response that was posed for detection besides the risk that is to be tolerated. Failure to do this will lead to choosing of inappropriate sample size. There is also need for determining an effective order to be used in collection of data and the technique that will be employed for randomization. This comes with the necessity for working in line with the objective of the experiment. In summary, the engineer is implicated to determine the factors that are likely cause of the determined difference followed by estimation of the size of response change.
Most of all, management implication is also a factor for the experiment. In the process of carrying out this experiment, the engineer is required to effectively monitor the experimental progress to that everything is proceeding as expected in the design. There is need to give much attention to the randomization, accuracy measurement and maintenance of uniform experimental environments.
