In practice, process capability indices (PCIs) are widely used in the field of quality control. The lifetime performance index ( C L ) 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 C L under the two-parameter Rayleigh distribution based on the progressively type II right censored sample. The MLE of C L 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.
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