remove uncertainty regarding critical performance issues, and to support a decision that the system is of requisite quality for its mission, environment or market, is a problem amenable to solution by statistical science. The question is not whether to test, but when to test, what to test and how much to test.

Testing can be justified at many different stages in the life cycle of a software intensive system. There is, for example, testing at various stages in development, testing of reusable components, testing associated with product enhancements or repairs, testing of a product ported from one hardware system to another, and "customer testing" (i.e., field experience). Service in the field is the very best "testing" information, because it is real use, often extensive, and free except for the cost of data collection. The usage model can be the framework, the common denominator, for combining test and usage experience across different software engineering methods and life cycle phases so that maximum use can be made of all available testing and field-use information.

A statistical principle of fundamental importance is that a population to be studied must first be characterized, and that characterization must include the infrequent and exceptional as well as the common and typical. It must be possible to represent all questions of interest and all decisions to be made in terms of this characterization. All experimental design methods require such a characterization and representation, in one form or another, at a suitable level of abstraction. When applied to software testing, the population is the set of all possible scenarios of use with each accurately represented as to frequency of occurrence.

One such method of characterization and representation is the operational usage model. The states-of-use of the system and the allowable transitions among those states are identified, and the probability of making each allowable transition is determined. These models are then represented in the form of one or more highly structured Markov chains (a type of statistical model, see e.g. Kemeny and Snell, 1960), and the result is called a usage model (Whittaker and Poore, 1993; Whittaker and Thomason, 1994).

From a statistical point of view, all of the topics in this paper follow sound problem solving principles and are direct applications of well-established theory and methodology. From a software testing point of view, the applications of statistical science discussed below are not in



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