Transient-free average working-set size and transient-free missing-page rate for a finite sample of a reference string are defined. Use of these statistics is appropriate if the contents of the working set at the start of the recorded string are unknown. If a certain stationarity condition holds, these statistics provide unbiased estimates of expected working-set sizes, missing-page probabilities, and interreference distance probabilities. Two other pairs of estimators are shown to be biased. Expressions for the transient-free statistics are obtained in terms of interval statistics. Several methods of computation are discussed, the usefulness of each depending on length of the sample, number of distinct references, and the amount of main storage available to the computer performing the calculations. In particular, methods are described for handling long strings containing many distinct page names. © 1977, ACM. All rights reserved.