Design of Experiment

Experimental design is the process through which valid conclusions are made in an effective, efficient and economical way, through conducting, planning, interpreting and analyzing experiments. When using experimental design as tool of solving problems, engineers should have great statistics knowledge. The challenge that most engineers face is applying the knowledge they have into practice or practical work. The engineers also lack manufacturing skills in applying experimental design. The first step in the design of experiments is identifying the experiment’s goals by using particular questions.

The second step is selecting the treatments to be used in getting the answers to those questions. In this case, statistical concepts are used. The third step is choosing the units of the experiments and the level of replication. The fourth step is to control variability in groups of units by using blocking systems or covariate information about the units. The fifth step is setting treatments for specific units, which are chosen from the rest of the units through randomization. Lastly, the sixth step is the collection of information relating to the goals of the research. In this case, either sampling or the whole unit of experiments can be used.

There are two forms of variables, qualitative and quantitative variables. Quantitative variables use a correct measurement scale. Qualitative variables on the other hand are fixed and random. That is the levels are identified and chosen using a random sample. In determining the number of replicates to be used, the treatments should be compared. In this, the mean values of the treatments are compared. This gives the replicates’ number, by analyzing the formula by which a treatment mean has been approximated. In evaluating the design of experiment, a factorial experiment or design is considered. A factorial experiment is a type of experiment in which all the factors in that experiment are varied simultaneously in their particular levels.

This kind of experiment can either be full or take a fraction. When the interaction and main effects are being evaluated separately, a factorial experiment that is full is used. This kind of experiment is represented by 2^k. The number of trials that are required of a factorial experiment are 4, 8, 16 and the numbers following this sequence. This numbers determined using the following formula: number of trials for the experiment= 2^k. K represents the number of factors of control at 2-level. This type of experiment however, may be impossible to do practically, due to the limits of cost and time. In this case, a factorial experiment in a fractional level is performed. The main effects can be evaluated using a fraction of the factorial experiment. The formula of the fractional experiment is 2^(k-1).

After determining the response values from the factorial experiment, the results are analyzed and interpreted. In this, the computation of interaction and main effects is done. This involves coding the 2^k levels in the design. The levels are indicated as either low, which is donated by – sign or high, donated by + sign. Following this rule, the levels are coded by setting them to -1, at low level and +1 at high level. Assumptions made in a factorial design are that the samples are taken from populations of normal distribution, they are chosen at random and the parameters used are fixed.