*Chapter 7 Statistical Intervals for a Poisson Distribution*

## Objectives and Overview

This chapter describes statistical intervals for the number of events over some interval of time or region of space, assuming independent events and a constant event-occurrence rate. Such situations can often be modeled by the Poisson distribution. For example, the Poisson distribution might provide an adequate description of the number of flaws on the surface of a product. This would require (among other technical conditions) that the product units are all of the same size and that flaws occur at random and independently of each other at a constant rate *λ*. Similarly, the number of unscheduled shutdowns of a computer system over some specified period of time might be described by a Poisson distribution. This would require that unscheduled shutdowns occur independently of one another and that the event-occurrence rate be constant over time and from one system to another. This assumption would not be correct if, for example, environmental factors that cause failure (e.g., lightning) simultaneously affect more than one system or if the failure rate changes with time (this might be the case if some system components are subject to wearout). In this chapter, our discussion will frequently be in terms of *x*, the number of events (e.g., unscheduled shutdowns of a computer system) in a given time interval of length *n*. We could similarly have discussed variables that describe events over constant length, ...

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