Complete Ranking of Reliability-Related Distributions

In reliability and life testing problems, an experimenter often wishes to rank several populations of items (e.g., devices which serve the same function) in order of `goodness'. In many cases it is trivial to decide how to rank the populations, but difficult to decide how many devices of each type to test, and also difficult to evaluate the probability that the ranking is correct. This paper considers these difficult aspects when the `goodness' of a population is simply related to its scale parameter (as is the case for many distributions used in reliability and life testing studies). The techniques provide a guaranteed probability of correct ranking (over usual scale parameter spaces), and in many cases this probability can be evaluated by a Monte Carlo sampling experiment. This furnishes a rational way to choose sample size in reliability and life testing when comparison of competing devices is the basic experimental goal.