Inference of the lifetime performance index with power Rayleigh distribution based on progressive first‐failure–censored data

One of the modern statistical methods is assessing quality performance of product. The performance of a process in the manufacturing and services industry is assessed to examine the level of product quality. The product performance is measured using the lifetime performance index , where is a lower specification limit. In this paper, the maximum likelihood estimation (MLE) of for the power Rayleigh distribution is derived based on progressive first‐failure–censored sample on the condition of known is calculated. The hypothesis testing procedure is applied for assessing whether the lifetime of products meets the required level. Finally, real‐life data of the number of revolutions before failure of a ball bearing in endurance life time test are used to illustrate the proposed procedure.