Constant-Partially Accelerated Life Tests for Compound Rayleigh Distribution with Progressive First-Failure Censoring

The constant-partially accelerated life tests (PALTs) model under progressive first-failure censoring based on compound Rayleigh distribution is considered in this paper. For this model, the maximum likelihood estimates (MLEs) of its parameters, as well as the corresponding observed Fisher information matrix, are derived. The likelihood equations do not lead to closed form expressions for the MLE, and they need to be solved by using an iterative procedure, such as the Newton-Raphson method. We then evaluate the bias, and mean square error of these estimates; and provide asymptotic, and bootstrap confidence intervals for the parameters. The results in the cases of first-failure censoring, progressive Type II censoring, Type II censoring and complete sample are a special cases. One set of real data has been analyzed for illustrative purposes. Different methods have been compared using Monte Carlo simulations