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by W. J. Youden, National Bureau of Standards
Black Box Tests Experimenters Experimental attack is evaluated counterpart of production system
J_iAST AUGUST, at the Gordon Conference on Statistics in Chemistry and Chemical Engineering, a black box substitute for a chemical process was much in evidence during the afternoons. Frank W. Wehrfritz of Esso Standard Oil Co. had the box and played the part of plant operator. Various members of the conference invested their afternoons running simulated experiments. Part of the final morning was made available for a public "contest" between two experimenters. Permission has been given to make use of this conference event in this column. The black box is described in a paper, "Strategy in Research," by D. S. McArthur and J. J. Heigl of the Esso Research and Engineering Co. Your columnist got some firsthand experience with the black box when McArthur presented this paper at the Eleventh Midwest Quality Control Conference in Minneapolis, October 11 and 12, 1956.
using an a n a l o g computer as a
The Black Box
There are really two black boxes that are electrically connected. The experimenter's box has five dials that vary electrical resistance and thus determine an output voltage which appears on a dial on the second box not visible to the experimenter. Also in this second box is a dial, so that the operator can set in a random error comparable to that encountered in practice. The illustration shows a team of experimenters about to enter the settings for an experimental run. The five dials correspond to plant operating factors such as temperature, time, concentration, and pressure. The output dial represents the yield of the process. The game is simple. Determine that combination of dial settings which will give a maximum reading on the output dial. The experimenter commits himself to a particular combination of
dial settings. The plant operator introduces a random error and then reads off the net result to the experimenter. Armed only with this result, the experimenter hazards another combination of dial settings and is informed of the result. As data accumulate, the experimenter hopes to discover the appropriate directions to move the operating factors controlling the process. The functional relationship between dial settings and output yield was made up to have characteristics encountered in chemical systems. The experimenter is told the errorfree yield (23%) with all five dials set at their mid-points (50). Presumably this is the current operating set of conditions. The dials are not associated with named operating factors. Neither is the experimenter told the standard deviation of the yield. Some workers protest at the total absence of chemical information. The game is not designed to VOL. 48, N O . 12
For further information, circle number 56 A on Readers' Service Card, page 123 A
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test the chemical knowledge of the experimenter, but rather to give an opportunity to try out various strate gies of attack. The experimenter is also told that the maximum possible yield is some thing less than 50%. After a few disappointing results are in hand, the experimenter realizes that this maxi mum might in fact be only a little more than the current yield. If this is true, it is useless to continue ex pensive experimentation on the proc ess. A set of mythical economics goes with the game. The pressure to disclose the state of the process with a minimum number of runs is a governing consideration. But there is also the danger of quitting the investigation too soon. A lucky in vestigator may up the yield 5 % after, say, six runs. He may stop because his work shows a substantial profit. Should the actual maximum yield of the process be 1 5 % higher, management will not be happy to discover this at a later date. Several Types of Strategy Tried
About 60 research teams have tried these simulated problems. The most popular method of attack was that of varying one dial at a time, leaving the other four dials at con stant settings. The Box-Wilson technique has been tried in two cases. One mathematician tried random settings of the dials. The statistical design most often used was a one quarter subset of the 32 possible combinations if just two settings are tried on each dial. One possible set of runs for this type of fractional factorial design is indicated below. The letters U and L designate whether an upper or lower dial setting is chosen. Run No. 1 2 3 A
