Order statistics and test duration

There are two principal issues in statistical planning. One is the accuracy/reliability of statistical inference and the other is the length of test time needed to complete the designed experiment. With regard to the latter, various test schemes have been proposed and applied in statistical literature. These schemes, among others, include type-I censoring, the usual type-II censoring, and progressively type-II censoring. To implement any of these experiments it is necessary that the capacity of the test facility is large enough so that all the items can be tested simultaneously. If, however, instead of having one facility with large capacity there are several facilities with relatively smaller capacities, a differently designed experiment would be necessary. This paper studies and compares elapsed test times and total elapsed test times corresponding to different statistical plans. The results obtained here are useful for performing an experiment that has shorter test time in a certain sense.