This paper describes the use of residual analysis in production rate decline curve fittings and performance predictions. Residual analysis, in statistical term, is an easy and quick check of any assumptions being violated under certain hypothesis test, meaning an attempt to discern regression drambacks or pitfalls if any. In production rate decline analysis, residual analysis technique is used to demonstrate (1) the validity of decline equations or models for given rate-time data, and (2) the reliability of the estimated parameters, such as qi, n, Di, and then that of future performance predictions. The emphasis of the study is on the detecting analysis of Arps' decline equations, with other forms of empirical expressions included. For the hyperbolic equation which is slightly more difficult to solve, eight typical numerical solutions are analyzed. These solutions do not often reach good agreement with each other for field data. Graphical residual analysis shows which solution fits the decline trend best, and which thereafter gives reliable performance and reserve predictions. A microcomputer-aided commercial software is developed and has found applications in China's oilfields.