A blocked two-level factorial experiment was designed to measure the radiolysis of water. Effects of controlled variables are biased by changes in radiation with time and by equipment changes between fuel cycles; the experiment is therefore doubly confound ed. Experimenting is subject to unplanned curtailments with respect to the first bias, and might be expanded with respect to the second. So that the more important parame ters can be estimated free of biases ordinarily resulting from the indefinite size of the experiment, the rationale is given for arranging the blocks of the experiment in a "doubly telescoping" (orthogonally blocked) sequence.
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DESIGN OF EXPERIMENTS AS "DOUBLY TELESCOPING" SEQUENCES OF BLOCKS WITH APPLICATION TO A NUCLEAR REACTOR EXPERIMENTby A r t h u r G. Holms and Steven M. Sidik Lewis Research Center SUMMARY An experiment was designed for observing the time-related pressure rise due to radiolytic decomposition of water in sealed capsules in a nuclear reactor. The effects of eight controlled variables are to be observed and expressed as the parameter esti mates of a model equation. The levels of some of the variables will be changed from time to time during a single fuel burning cycle; however, there is a change in the radia tion component levels with the amount of fuel burned, s o that some of the parameter esti mates a r e biased by (confounded with) the effects of the amount of fuel burned (which therefore constitute one source of block effects).The levels of the controlled variables must be changed from one cycle to the next. Because of the possibility of equipment o r instrument changes between one group of cy cles and another, the design of the experiment must allow for this second source of block effects; that is, it must allow for double confounding.Because of several types of operating problems, cycles are often stopped short of the intended operating time, and thus the size of the experiment is indefinite with respect to the first source of block effects. If the experimenting has been limited by cycle cur tailments s o that additional data is desired, or if the experimenter wishes to increase the scope of the estimated parameters, then additional cycles should be run at new conditions, and this could represent an expansion with respect to the second source of block effects. Thus a strategy of experimenting is needed wherein curtailments with respect to one type of block effects and expansions with respect to another can be accepted without the more important parameter estimates being biased by the time effects (as they would be in a conventionally balanced design). The appropriate strategy will be called "double tele scoping, " and the necessary statistical considerations together with an appropriate de sign are described.
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