This course is designed to provide a comprehensive introduction to the basic processing of stationary and non-stationary random measurement data for purposes of Laboratory Vibration Test Specification (LVTS) development. The first half discusses the fundamentals of spectrum analysis and illustrate Fourier based non-parametric spectrum estimation. This includes consideration of random data with embedded sine-tones. The last half considers a general framework and illustration of the development of a LVTS. The objective of the course is to provide procedures for processing field measured random vibration data and using the processed information for LVTS development. The LVTS then may be used to qualify materiel for in-service use.