Statistical testing for the performance of lifetime index of transformed Rayleigh products under progressively type II right censored samples

In practice, process capability indices (PCIs) are widely used in the field of quality control. The lifetime performance index (CL) is used to measure process potential and performance, where L is the lower specification limit. In this paper, we apply data transformation technology to construct a maximum likelihood estimator (MLE) of CL under the two-parameter Raileigh distribution based on the progressively type II right censored sample. The MLE of CL is then utilized to develop a hypothesis testing procedure. Finally, we give the Monte Carlo power simulation to assess the behavior of the lifetime perform index.