Random balance

Random balance design Categorical/qualitative and quantitative Screening of factors... 

The rank histogram shows that the sum of ranks does not change evenly, so that we can accept the solution to include the following four factors into the basic design of experiment X3, X1 X2, and X5. A more cautious approach to drawing conclusions suggests a more detailed check of all six factors in an active experiment for screening factors such as, the method of random balance. 

Active Screening Experiment-Method of Random Balance... 

A design matrix by the method of random balance may be constructed in two ways ... 

Table 2.18 FUFE Table 2.19 Matrix of random balance ...

By random choice from matrix FUFE or Table 2.18, we take for the first group of 2., 1., 3. and 4., row respectively. For the second group of factors we take in the same way 3., 4., 2. and 1. row from the FUFE matrix. In this way, the design matrix for the random balance method is constructed. In this example, the response is represented by the product purity y. 

The following could be said, after all things disclosed, about the active method of screening factors or the method of random balance ... 

Table 2.25 Advantages and disadvantages of random balance method...

For practical application several prepared design matrixes by the method of random balance [18]—[20] are recommended. 

It should be noted that when doing an experiment by the method of random balance, it is not necessary to have a random order of doing design points, since the randomization principle has been introduced in constructing the matrix. 

Adhesion on HLORIN -type fibers, has been studied as a function of five process factors. The names of factors, with their variation levels, are shown in Table 2.32. Matrix 23 of full factorial experiment has been used in constructing random balance matrix. The design matrix by the method of random balance with experimental results is shown in Table 2.33. Note that each design point was repeated 20 to 50 times due to high non reproducibility of the system. 

Hence, the adhesion of fibers is significantly affected by factors X5 X2 and X3. The expected effect of Xi factor proved to be marginal. This may be explained only by the fact that its value in the center of the performed experiment is either maximal or its variation interval has been badly chosen. Further experiments have proved the first assumption. The summarized result of the method of random balance is shown in Table 2.36. 

Factors were not screened out in Example 2.8 by the method of prior ranking, so that a matrix of random balance was constructed for all eight factors, Table 2.37. The experiment was done by one replication of the design point in order to establish the... 

Due to the advantages and disadvantages of the method of random balance, which have been mentioned in this section, a demonstration of efficiency of the method will be given in this example on an artificially constructed problem and where we know, in advance, the effects that should be screened. It will also be shown that, generally speaking, the method of random balance with more than two levels of factor variation has no advantage. A demand for more than two levels is justified only in cases with qualitative factors. 

Assume that twelve factors, Xx to X12, should be screened. The random balance matrix will consist of two independent semi-replicas of a 26 full factorial experiment, with rows or design points that are randomly distributed. The 32 design points thus synthesized will start with the values taken from a normal population with the mean 100 and the standard deviation 60=2.0. The effects of factors have been introduced in the way that the following values were added to the best values of selected factors in the upper level (+) value -15 added to factor X7 value -12 added to factor X4 value +10 added to factor X10 and Xn value +8 added to factor X value +6 added to factor X5 and Xg value +4 added to factor X2 value -4 added to factor X9... 

Table 2.40 shows a complete design matrix by the method of random balance original data taken from normal population y0 y synthesized response to which values of effects were added and the phases of factor screening with corrected response y1 y11 ym and ylv and their standard deviations. 

Former experience of the author of this book, in applying the method of random balance, indicates that there have been no situations where this method has not... 

The method of prior ranking factors has been unsuccessfully applied on the data in Problem 2.4 about factors that affect the petroleum oils refining procedure by phenol. A design matrix was constructed for this reason and for all sixteen factors, for an experimental screening by the method of random balance. The design matrix with outcomes of the experiment is shown in Table 2.42. Process the results by the method of random balance. 

In an optimization process of isomerization of sulfanilamide, a design of experiments has been in the first phase defined by a method of random balance with the idea of doing a screening active experiment. The design of experiments with its results is shown in Table 2.43. Screen factors by significance of their effects on the measured value. 

Information on factor-variation intervals may be drawn from an active experiment by the random balance method. Thus, linear effects of factors XjX2 in Example 2.10 considerably exceed the affects of other factors. This simultaneously may mean that the selected factor-variation intervals X, (- +) X2(- +) are too high. If this is so, then they should be cut in half in the basic experiment. 

Factor space may be obtained from the matrix of random balance and analysis of variance. Information on number of replications of design points-trials in the basic experiment is obtained from analysis of variance, and some proofs about linear or nonlinear relationships between variables of the research subject from correlation analysis. 

Taking all this into consideration, unsaturated designs (f>0) or special designs, which include the influence of interaction effects on linear-effect estimates, are used in practice. An oversaturated design (f<0) was used in Example 2.12 as a random balance method design, but a totally different problem was being solved in that case. 

In Example 2.12, the method of random balance, factors have been selected by the effects of their significance on dynamic viscosity of uncured composite rocket propellant. The screened-out factors are X3 mixing speed X5 time after addition of AP and Xg vacuum in vertical planetary mixer. Since insufficient vacuum in a mixer causes bubbles to appear in the cured propellant, the value of this factor is fixed at the most convenient one. For the other two factors a design of basic experiment has been done according to a FUFE matrix, as shown in Table 2.103, and aimed at obtaining the mathematical model of viscosity change. 

To optimize the process of isomerization of sulphanylamide from Problem 2.6, a screening experiment has been done by the random balance method. Factors X1 X2 and X3 have been selected for this experiment. Optimization of the process is done by the given three factors at fixed values of other factors. To obtain the second-order model, a central composite rotatable design has been set up. Factor-variation levels are shown in Table 2.148. The design of the experiment and the outcomes of design points are in Table 2.149. 

Due to the recommendation that when studying factors one should include all the possible factors that may affect a process, we use two methods in the process of screening them the method of prior ranking of factors and the method of random balance. We may now suggest an optimization research scheme of a multifactor process ... 

Preliminary ranking of factors —> Method of random balance —>... 

Supersaturated designs have their roots in random balance experimentation, which was briefly popular in industry in the 1950s, until the discussion of the papers... 

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