A critical analysis is presented of the application of statistics to flight vehicle vibration problems. Analytical engineering procedures are proposed for determining statistical properties of a single vibration record, and for establishing the over-all vibration environment from a collection of vibration records. Jet aircraft and several categories of missiles are broken down into definite operating phases as regards their vibration environment. Simple statistical techniques are developed for reducing the amount of data to be gathered for later processing. Statistical tests are developed for testing fundamental assumptions of randomness, stationary, and normality. Mathematical and physical distinctions are explained between different information obtained by measuring numerous important statistical parameters, such as an instantaneous amplitude probability density function, or a mean square acceleration power spectral density function, or an autocorrelation function.