The statistical variability of tool life in production machining must be accounted for in any rational design of large-volume or automated manufacturing systems. The probabilistic approach needed for such a design is presently limited by lack of data on tool-life distributions and by lack of knowledge of the underlying causes giving rise to tool-life scatter. Given these circumstances, on the basis of relevant physical arguments one may construct probabilistic models that produce distribution functions germane to the problem of tool-life scatter. This paper is concerned with such a study. This first part presents the results obtained on the assumption that the useful life of a tool is terminated by a single, catastrophic injury. Cases where resistance to tool failure is time-independent and time-dependent are examined. The case of tool failure caused by multiple injuries will be presented in Part 2.