This paper presents a step-by-step tutorial of the methods and the tools that were used for the reliability analysis of fault-tolerant systems. The approach used in this paper is the Markov (or semi-Markov) state-space method. The paper is intended for design engineers with a basic understanding of computer architecture and fault tolerance, but little knowledge of reliability modeling. The representation of architectural features in mathematical models is emphasized. This paper does not present details of the mathematical solution of complex reliability models. Instead, it describes the use of several recently developed computer programs SURE, ASSIST, STEM, and PAWS that automate the generation and the solution of these models. Butler, Ricky W. and Johnson, Sally C. Langley Research Center COMPUTER SYSTEMS DESIGN; COMPUTER SYSTEMS PERFORMANCE; FAULT TOLERANCE; MARKOV PROCESSES; MATHEMATICAL MODELS; RELIABILITY ANALYSIS; RELIABILITY ENGINEERING; APPLICATIONS PROGRAMS (COMPUTERS); ARCHITECTURE (COMPUTERS); FAILURE ANALYSIS; SYSTEM FAILURES...