Rayleigh Defect Prediction: Model the Defect Discovery Curve
What is the Rayleigh Defect Model?
Rayleigh defect prediction uses the Rayleigh distribution to describe how the defect discovery rate changes over the lifecycle of software or a product: the rate rises, peaks and then falls as a single-peak curve. The curve parameters determine when the discovery peak occurs and how many defects exist in total, so fitting the parameters from early test data lets you extrapolate the total defects expected over the whole lifecycle and assess test progress and release risk. Defect data should come from a consistent aggregation of testing and field feedback.
Parameter Estimation and Curve Fitting
The Rayleigh density is f(t) = (t/m squared) times exp(-t squared/(2m squared)) with parameter m, and the cumulative distribution F(t) = 1 - exp(-t squared/(2m squared)) gives the fraction of defects discovered by time t. The tool fits the observed cumulative defect data by maximum likelihood or least squares, outputs the parameter m, goodness of fit and residuals, and plots the observed versus fitted curves. A large fit deviation suggests the data may not follow the Rayleigh shape; check the data definition or consider another model.
Key Output Indicators
The tool outputs the estimated total defects (extrapolated upper bound), peak discovery time (near m, where the discovery rate is highest), convergence time (when the discovery rate drops very low or the cumulative share reaches about 95%), the proportion discovered by the current stage and remaining defect estimates. These indicators tell you whether testing is sufficient, whether release criteria are met and how much more test time is needed, providing quantitative evidence for release reviews.
Step-by-Step Usage
Log in, enter the new defects found in each test stage (weekly or monthly) or the cumulative defect count, set the stage length unit, and the tool fits the Rayleigh model and outputs parameters, a fit plot, a cumulative defect prediction table and peak and convergence times. The model assumes a stable discovery process without major requirement changes, and fitting is unstable with too little data, so wait until the curve covers its descending part before extrapolating and treat results as decision support.