Assumes the life distribution of a test unit for any stress follows a Rayleigh distribution with scale parameterθ , and that Ln(θ ) is a linear function of the stress level. Maximum likelihood estimators of the parameters under a cumulative exposure model are obtained. The approximate variance estimates obtained from the asymptotic normal distribution of the maximum likelihood estimators are used to construct confidence intervals for the model parameters. A simulation study was conducted to study the performance of the estimators. Simulation results showed that in terms of bias, mean squared error, attainment of the nominal confidence level, symmetry of lower and upper error rates and the expected interval width, the estimators are very accurate and have a high level of precision.